The most common observation in comments I’ve received so far is that my essay is hard to understand, but I’m afraid that this is the common lot of all serious attempts to explain the nature of time. For me, the concept of time is not easy to grasp, unless we reduce it to a progression of numbers. Like the ticking of a clock, the constant, incessant, march of time is nothing more than a...

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The most common observation in comments I’ve received so far is that my essay is hard to understand, but I’m afraid that this is the common lot of all serious attempts to explain the nature of time. For me, the concept of time is not easy to grasp, unless we reduce it to a progression of numbers. Like the ticking of a clock, the constant, incessant, march of time is nothing more than a succession of natural numbers, 0, 0+1, 1+1, 2+1, …n+1, and so on, ad infinitum.

However, in assuming that time is just the inverse of space, we imply that space too progresses, and that this progression of space is just like the progression of time; that is, it’s a succession of natural numbers, 0, 0+1, 1+1, 2+1, …n+1, and so on, ad infinitum. In this way, these two simple progressions, or succession of natural numbers, become two, reciprocal, aspects of one space/time progression, fulfilling Minkowski’s prediction that they must eventually be seen as one entity.

Nevertheless, that the dimensions of the two, inverse, aspects of this space/time progression must be inverse as well, seems to follow from the tetraktys, as explained in the essay. This leads to the question of units. How do we define the physical units of space and time? Do we use meters and seconds? Well, yes, but we know from physical equations, which predict physical phenomena very accurately, that the fundamental, or natural, divisions of these units cannot be simply powers of ten, as neat as that would be.

Physical equations are based on motion of mass, or conservation of mass/energy. Equations of the standard model’s elementary particle interactions, for instance, depend on the constants of energy and motion, while equations of general relativity’s gravity depend upon the constants of mass and motion. So, these three constants of mass, energy and motion are viewed as “universal” physical constants, which, as Max Planck first showed, can be combined to obtain a fundamental length, called the Planck length.

But this length is very, very small, and, consequently, the energy at this length, or the energy that would be required to probe this length, is far beyond anything man can imagine being able to generate, and even if he could, it appears that the act would only generate a black hole. Yet, as John Baez wrote in 2005:

“To be picturesque, we can say that if we have a black hole about the size of the Planck length, and we try to locate it to an accuracy equal to its radius, the Heisenberg uncertainty principle makes the momentum of the black hole so poorly known that there may be enough energy around to create another black hole of that size! I warn the reader to take this with a massive grain of salt, since there is no good theory of this sort of thing yet - much less any experimental evidence. But people have sharpened this sort of thought experiment and seen that things get awfully funny at the Planck length. By analogy with particle physics, one might expect processes involving virtual black holes to be very important at this length scale. Hawking and others have written interesting papers on reactions induced by virtual black holes... but I would not take these predictions too seriously yet.”

It is this “awfully funny” theoretical situation at the Planck length that causes physicists to believe that space becomes emergent, and if space does, then, since time is connected to space as spacetime, this implies that time must be emergent as well. But how do you do physics without time? Carlo Rovelli and others, such as John Barbour, try to answer this question based on the Wheeler-DeWitt equation.

However, the approach that is the subject of my essay avoids the problem altogether by redefining the fundamental lengths of space and time, not based on mass, energy and motion, but rather based on motion and frequency. Of course, physics itself is based on motion and frequency, in the form of harmonic motion, but this motion is always the 1D motion of mass, which is the only motion recognized by physicists. With Planck’s and Einstein’s discoveries, it became possible to use these same principles of harmonic motion with energy and frequency, but it was necessary to quantize the energy in terms of angular momentum and the enigmatic concept of quantum spin, replacing the dimensions of the momentum of moving mass, with the dimensions of Planck’s constant and frequency in the physical equations.

Once this was accomplished, in quantum mechanics, the door was opened that eventually led to the celebrated standard model of elementary particle interactions. Yet, again, this model requires the dimensions of mass, energy, and motion to work its wonders, and these have to be put into the model as parameters, causing Hawking to call it “ugly and ad hoc,” in this respect, from the perspective of those seeking a fundamental theory of physics.

Fortunately, by redefining the nature of space and time, as we have done in my essay, as two, reciprocal, aspects of one entity, motion, we have eliminated the problem of a parameterized theory like the standard model, but we face the challenge of discovering how nothing but motion leads to the observed mass/energy and interactions of particles that are now not elementary, but emergent.

So, with this new approach, the question of how do we do physics without space and time becomes a question of how do we do physics with ONLY space and time. From what we’ve learned so far, the latter question appears much easier to answer, with all due respect to Carlo and John.

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Thanks Jen and Larry,

I appreciate the kudos. Obviously the title of the earlier version of the essay is a play on the words of the title to Lee Smolin’s book, where he refers to “The End of a Science.” This he attributes to many in the string theory community, who are want to follow the lead of Steven Weinberg in embracing the “anthropic principle.” Since string theory research...

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Thanks Jen and Larry,

I appreciate the kudos. Obviously the title of the earlier version of the essay is a play on the words of the title to Lee Smolin’s book, where he refers to “The End of a Science.” This he attributes to many in the string theory community, who are want to follow the lead of Steven Weinberg in embracing the “anthropic principle.” Since string theory research has ended up with a “landscape” of a practically limitless set of possible string theories, depending upon how the Calabi-Yau manifold is used to compactify their extra dimensions, the chances of finding a theoretical string theory universe that predicts the observed universe have diminished significantly.

Hence, one may abandon the effort to find a theoretical universe altogether, and just subscribe to the idea that, like microbes in a Petri dish, we are only able to observe the universe because it happens to have the right conditions for our growth, but the existence of those conditions are just a matter of chance, they are not due to any set of identifiable initial conditions the orderly consequences of which inevitably lead to what we observe as the physical structure of the universe.

However, the message of my essay is not so harsh as that. It’s not the end of a science, but the end of a system of physical theory that we are facing, and, even then, it’s not really the end of that system, it’s only the end of misapplying it that we are referring to.

What is meant by “a system of theory,’ as opposed to just ‘a theory,” can best be understood starting from David Hestenes’ description of Newton’s program of research (see: http://tinyurl.com/3st2g7). Newton, as Hestenes explains, “…is rightly regarded as the founder of the science called mechanics,” and “rightly deserves the title…[not only] because he integrated the insights of his predecessors into a comprehensive theory, [but because he also] inaugurated a program to refine and extend that theory…[T]herefore, [Newton’s mechanics] is more than a scientific theory, it is a well defined program of research into the structure of the physical world.“

As Hestenes goes on to explain very lucidly, the goal of Newton’s program is to describe and explain all properties of physical objects, in terms of “a few kinds of interactions among a few kinds of particles,” but the “great power of [the program] is achieved by formulating [those] generalities…in specific mathematical terms.” The key mathematical terms he refers to, of course, are the position of a particle over time: He writes: “To express the continuous existence of the [moving] particle in some interval of time, the function x(t) must be a continuous function of the variable t in that interval. When specified for all times in an interval, the function x(t) describes a motion of the particle.”

Thus, Newton’s program of research was a “system of theory” based on this very important definition of motion. As Hestenes goes on to explain, “The central hypothesis of [the system] is that variations in the motion of a particle are completely determined by its interactions with other particles.” These interactions are the f=ma interactions, from Newton’s second law of motion, which leads to the characterization of Newton’s system of theory as one that rests on the law that asserts that “a definite differential equation [determines] the motion of a particle, only when the force f is expressed as a specific function of x(t) and its derivatives.” This is still the system of theory, even after the limits of the meaning of the terms position and momentum were realized, with the advent of quantum mechanics. Even though force is now understood more in terms of particle exchange, this doesn’t alter the fact that the “dictum” of Newton’s system of theory, has always been understood to be, “focus on the forces,” as Hestenes puts it.

Now, Carlo Rovelli argues in his essay that it is possible to formulate physics in a different manner, that doesn’t necessarily have to rely on the function x(t), which I see as tantamount to defending a new system of theory. His is a new system, which formulates particle interactions on a basis that changes the central role of time, t, in Newton’s system, by placing it on the same level as x.

However, the Reciprocal System of Physical Theory (RST), is a new system of theory that alters the definition of motion itself, in that it also places t on the same level as x, but in a different manner: It eliminates x altogether, in the sense that the position x of a particle is not necessary to define motion, as it is in Newton’s system, but it defines motion from the observed scalar progression of space and time itself. Thus, the new system separates the familiar vectorial motion of objects from location to location, from an inherent scalar motion that constitutes the particle itself.

In the application of the new system, described in my essay, the 1D function, x(t), of particle motion, is replaced by a 3D function, v(t), of pseudoscalar motion, and it then becomes possible to return force to its original definition, as a property of motion, since the motions giving rise to the forces of particle interaction can now be identified in the new system, and there is no need to resort to an ill-advised concept of autonomous forces, as required under the old system, where the underlying motions of the forces, defined by the inadequate definition, x(t), cannot be identified.

Certainly, there is much, much, more that has to be said on such a fundamental subject, but I hope this helps.

Doug

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Hi Andreas,

If your conclusion is that the merits of the essay are reduced by my attempt to encourage members of ISUS with a report of the success it has enjoyed to this point, I think you are quite mistaken in this respect.

If you are insinuating that the votes it’s received are because of that encouragement, you are really mislead. Not only were most of the public votes that...

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Hi Andreas,

If your conclusion is that the merits of the essay are reduced by my attempt to encourage members of ISUS with a report of the success it has enjoyed to this point, I think you are quite mistaken in this respect.

If you are insinuating that the votes it’s received are because of that encouragement, you are really mislead. Not only were most of the public votes that have been cast for it, already cast in its favor at that point, but also not many ISUS members would be inclined to support it in any event. Let me explain why.

The purpose and objective of ISUS, which has been around for more than forty years, is to promote the works of Larson. However, for the last few years, I have been developing an RST-based theory that departs from Larson’s own application of the system, maintaining that it’s his system of physical theory that is his greatest contribution, not necessarily his subsequent development of theory using it.

As previously explained in the posts above, it’s Larson’s recognition of the relation of space and time as two, reciprocal, aspects of motion, and the nature of the symmetry of space and time, that constitutes a new system of theory, because it is not based on the same 1D function, x(t), as is Newton’s system of theory.

The spatial position, x, of an object, which does not change in Newton’s system, is constantly changing in Larson’s system. This constant change is not with reference to the set of locations satisfying the postulates of geometry, which we normally think of when we think of space, but rather it is a change of the space of the 3D progression, which is the space aspect of the object’s inherent motion, the scalar motion that constitutes the object and gives it its properties of mass, charge, spin, etc, in the system.

The reference for this motion, its physical datum, is the unit motion, c. In Larson’s theoretical development, this motion consists first of a discrete linear vibration, then rotations of the vibration, and in the case of the atomic elements, two such rotational systems are combined. This leads, in a remarkable way, to the periodic table of elements, based on a 4n^2 relationship of discrete scalar motion combinations (see: http://www.lrcphysics.com/wheel).

However, Larson was never able to calculate the atomic spectra, other than hydrogen, from these combinations of discrete scalar motion, even though he was able to calculate the inter-atomic distances in molecular substances, using closed form equations. Consequently, filling this so-called “lacuna” in Larson’s theoretical development has been the challenge facing ISUS members ever since.

My efforts to meet this challenge have resulted in the concepts described in my essay, which, as you can readily discern by reading it, depart substantially from Larson’s approach. The most surprising development to come from it are the regular combinations of discrete units of scalar motion that form the entities of the standard model, as demonstrated by the toy model of the first generation, and the subsequent formation of the elements of the periodic table, illustrated in the essay.

However, let me assure you that many members of ISUS are skeptical of these results, and are far from convinced that this is the way to go. Therefore, you will undoubtedly perceive that my attempt to encourage them with an update of the essay’s progress in the contest was just that, and not an attempt to stuff the ballot box. Had this not been the situation, the essay would have had many more than 15 public votes by now.

Cheers,

Doug

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The interesting conversation is going on in Carlo’s forum. The point of his essay is “that dynamics can be expressed as correlations between variables, and does not NEED a time to be specified,” while it’s the flow of time (Hamilton’s “order in progression”) that is emergent. Evidently, some commentators have construed this to mean that he intends to replace dynamics with the...

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The interesting conversation is going on in Carlo’s forum. The point of his essay is “that dynamics can be expressed as correlations between variables, and does not NEED a time to be specified,” while it’s the flow of time (Hamilton’s “order in progression”) that is emergent. Evidently, some commentators have construed this to mean that he intends to replace dynamics with the thermal time hypothesis.

But Carlo explains: “The thermal time is only the one needed to make sense of our sense of flowing time, it is not a time needed to compute how a simple physical system behaves. The last can be expressed in terms of correlations between a variable and a clock hand, without having to say which one is the time variable. Therefore the question about the flow of time defined by bodies at different temperature is a question about thermodynamics out of equilibrium. Unfortunately, like much of today's physics, I have not much to say on this. In any case, I am aware that the thermal time hypothesis is highly speculative. I would like the readers to keep it separate from the main idea defended in the essay, which is that mechanics can be formulated without having to say which variable is the time variable.”

In his response to this statement, John Merryman writes: “My point is that time and temperature are both descriptions of motion. Temperature is the level of activity against a given scale. Time is the rate of change relative to a given reference frame, or point. If you change the level of activity, you affect the rate of change. The candle burns faster if it is hotter. As a person in space ages slower than a person in a stronger and more active gravity field. So there is the element of time in temperature and the element of temperature in time.”

This is interesting from several points of view. First, the “motion” of temperature is scalar, just as John states. Like the prices of the stock market, temperature “moves” “up” or “down” relative to a given point. Its relative increase, or decrease, can be described as motion, but the motion is scalar; that is, it has no direction in space. Likewise, time is measured as a scalar change, but just as the motion of an object from location to location cannot be described without a change of time, so too the scalar change of temperature cannot be measured without a change of time.

In other words, there can be no motion, vectorial or scalar, without a change in time. Thus, to assert that “time and temperature are both descriptions of motion,” as John does is not accurate. Motion, by definition, requires two, reciprocal, changes of scalar quantity. Time is one of these changing scalars, while the other may be distance, prices, or temperature.

In the case of Rovelli’s timeless point of view, the motion of a clock is still a change of two, reciprocal, positions; that is, the hands move in one direction, while the face moves in the opposite direction, but, as he writes, ”General relativity describes the relative evolution [i.e. relative change] of observable quantities, not the evolution of quantities as functions of a preferred one. To put it pictorially: with general relativity we have understood that the Newtonian “big clock” ticking away the ‘true universal time’ is not there.”

This leads to the conclusion that evolving the wave equation in time, in a quantum theory of gravity, will not make sense; Indeed, it [would be] “quite unnatural in a general relativistic context,” because, in this context, there is no way to determine which variable is the evolving variable, which variable is the preferred choice to be the independent variable that evolves the equation. It is in this sense that he urges us to “forget time” in our quantum gravity theory.

To emphasize his point, Carlo analyzes the moving hands of the clock to show that it’s only an arbitrary choice of reference points, even in non-relativistic frames, that provides us with a measure of the reciprocal changes (like the pendulum and pulse example, which of the two “clocks” is the clock measuring time?)

What’s interesting about this is how it doesn’t contradict Hamilton’s concept of “order in progression,” which he proposed as an intuitive basis for algebra, to put it on an equal footing with geometry, which is grounded in the scientific intuition of space. That is, we can observe the properties of space. We can see that it’s limited to three dimensions, that each dimension has two, opposed directions, and that its magnitudes, in certain cases, are incommensurable.

But this is not so with algebra, a fact that troubled Hamilton immensely (see my preliminary essay for more on this:

http://www.lrcphysics.com/storage/documents/Mystic%20Dream%2
0Prelim.pdf).

But given that one moment of time is either equal to, earlier than, or later than, another moment (the point John is trying to make in his discussion with Carlo, although I haven’t quoted the relevant text of the discussion here,) it’s possible to use this order in progression to put algebra on an equal, scientific, basis with geometry, as Hamilton was able to show for two dimensions, at least.

What Carlo has done is to show that you can’t measure the order in just one of the two progressions; that is, since space and time are reciprocal aspects of the same thing, like two sides of the same coin, we cannot measure one without the other. It takes two, reciprocal, progressions to measure distance, and it takes two, reciprocal, progressions to measure time. Another way to say the same thing is that space cannot be measured without motion, just as time cannot. Space does not exist without time, anymore than time exists without space, because, again, they are two, reciprocal, aspects of one thing, motion.

We can easily prove that space, defined by a set of points, satisfying the postulates of geometry, is only a history of past, or contemplated, motion. The distance between the points can either be the result of an object’s motion that occupies the locations at different times, or it can be the contemplated distance between calculated points. The fact that either of the two reciprocal variables entering into the calculation can be selected as the independent variable is not, however, the important point. The important point is that ONE of them must be selected.

In the space/time progression of my paper, the two, reciprocal, progressions are distinguished by their physical dimensions. Thus, time may be the zero-dimensional aspect, and space the nonzero-dimensional aspect, or vice versa. It makes, no difference, except in one you get a progressing spatial pseudoscalar, and in the other you get a progressing temporal pseudoscalar. With one, the motion creates expanding space coordinates, while with the other, expanding time coordinates. In each case, a time (space) s can be measured along their worldlines, which is not the time t of x(t).

Hence, I agree with Carlo, we can forget which variable we must designate as the “time” variable in quantum gravity, but the variable we choose must be zero-dimensional.

Regards,

Doug

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Hi Brian,

Thanks for your comments and your concern. I know it must sound awfully naïve to claim that force is a property of motion, at this late stage of physical science, when for centuries the prevailing attitude of the physics community has regarded force as an autonomous entity, but please bear with me, while I try to explain.

First, the fact is that, as you correctly point...

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Hi Brian,

Thanks for your comments and your concern. I know it must sound awfully naïve to claim that force is a property of motion, at this late stage of physical science, when for centuries the prevailing attitude of the physics community has regarded force as an autonomous entity, but please bear with me, while I try to explain.

First, the fact is that, as you correctly point out, force is defined as a product of mass and acceleration, but it’s important to recognize that the reason for this is because when a quantity of units of moving mass, momentum (or quantity of motion) is accelerated, the time rate of change in the velocity of that quantity, the acceleration, is an acceleration of each unit of mass on an individual unit basis, and we label the total, i.e. the product of the acceleration and all the mass units collectively, with the word “force.”

The crucial point is that the label “force” is simply used to refer to the time rate of change in the quantity of motion, or in the momentum, of the set of mass units in the equation. Clearly, the label cannot be properly treated as an autonomous entity apart from motion, by definition. Therefore, every fundamental force must be the label of a fundamental motion, even if that motion appears impossible to identify.

Next, you conclude that I’m making a false distinction between identical physical properties. You wrote: “…the pivotal argument is centered around the kinematical equation X(t) = V*t. Your reciprocity argument hinges on this equation being rewritten as X(t) / t = V and t / X(t) = 1 / V. I should point out that all three of these equation are identical but you use X(t) / t and t / X(t) as if they represented distinct physical properties.”

I don’t know how you came to the conclusion that this equation you have written, as the pivotal “reciprocity argument,” does not represent distinct physical properties. The pivotal reciprocity argument is that the true nature of time is found in its reciprocal relation to space, in the equation of motion. Hence, if we write X(t) = V*t = (s/t)*t = s, so that space, s, is a function of time, then rewriting it as X(t)/t = s/t and t/X(t) = t/s = 1/(s/t) clearly does represent distinct physical properties, lest we maintain that the dimensions of velocity, s/t, cannot be distinguished from the dimensions of energy, t/s, something we obviously don’t want to do.

Next, you argue that deriving the natural units of space and time, by combining the constants c and Ry, as I have done, following Larson, is ruled out by empirical evidence. However, the claim is not that smaller intervals of space and time cannot be measured, but it is that these intervals are the intervals that enter into the fundamental physical equations such as E = mc^2 and E = hnu.

I must concede that the proof of this claim is yet to be provided. Certainly, it’s the subject of ongoing investigation. In his work, Larson was able to obtain remarkable results with it, including the interatomic distances of many substances, and the clarification of many basic properties of matter (see Volume II of The Structure of the Physical Universe.)

However, his success was due to something he called the “inter-regional ratio,” which was an empirically derived value that he explained, theoretically, as due to the statistical relationship between combinations of X(t) / t and t / X(t) units of motion, to put it in terms of your equation above.

This ratio, and the fact that space and time are reciprocals, leading to a concept of “equivalent space,” together with the fact that the compounding of X(t) / t and t / X(t) units of motion, which constitute the theoretical atoms, actually result in net time structures, accounts for the apparent discrepancies in atomic and particle radii quite convincingly.

Finally, in applying the distinction between classical and relativistic theories, which clearly separates Newtonian mechanics in the limit of small potential and low velocity, from relativistic mechanics, to RST-based theories, you are mistakenly comparing apples and oranges. This distinction has to do with the physics of the one-dimensional velocities of the vector motions of mass, and is not properly applied to the n-dimensional scalar motion of RST-based theory, which takes a more fundamental position.

The best way to understand the regime of RST-based physics is to consider the dilemma of the charged point particle and its enigma, invoking Poincaré stresses, and the spectre of singularities, which string theory addresses so admirably.

Ok, I hope I have responded adequately to your criticisms, Brian. Please don't hesitate to continue the challenge. I really do appreciate your willingness to honestly engage in the discussion.

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Doug,

I thought I should expand on my view a little;

"First, the “motion” of temperature is scalar, just as John states. Like the prices of the stock market, temperature “moves” “up” or “down” relative to a given point. Its relative increase, or decrease, can be described as motion, but the motion is scalar; that is, it has no direction in space. Likewise, time is...

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Doug,

I thought I should expand on my view a little;

"First, the “motion” of temperature is scalar, just as John states. Like the prices of the stock market, temperature “moves” “up” or “down” relative to a given point. Its relative increase, or decrease, can be described as motion, but the motion is scalar; that is, it has no direction in space. Likewise, time is measured as a scalar change, but just as the motion of an object from location to location cannot be described without a change of time, so too the scalar change of temperature cannot be measured without a change of time.

In other words, there can be no motion, vectorial or scalar, without a change in time. Thus, to assert that “time and temperature are both descriptions of motion,” as John does is not accurate. Motion, by definition, requires two, reciprocal, changes of scalar quantity. Time is one of these changing scalars, while the other may be distance, prices, or temperature.

In the case of Rovelli’s timeless point of view, the motion of a clock is still a change of two, reciprocal, positions; that is, the hands move in one direction, while the face moves in the opposite direction, but, as he writes, ”General relativity describes the relative evolution [i.e. relative change] of observable quantities, not the evolution of quantities as functions of a preferred one. To put it pictorially: with general relativity we have understood that the Newtonian “big clock” ticking away the ‘true universal time’ is not there.” "

Temperature is an average of a quantity of motion, not a specific motion. Time, on the other hand, is the duration of a specified process. The difference is that if the level of activity remains stable, temperature does not change. It can be defined as a specific point. On the other hand, time cannot be confined to a specific point, as that would imply the cessation of this particular motion. Just as the temperature of absolute zero would be the cessation of all motion. Think if you were to specify the exact location of the molecules of water which manifest the temperature; If they had an exact location, than they wouldn't have motion, the water would freeze and the temperature would drop. If you were then to specify the exact location of the sub-atomic particles of this ice, than it would effectively vanish, as there would be no relationship between what are nearly dimensionless points and than you would have a temperature of absolute zero. (In fact, there seems to be no base layer of substance, only emergent effects of more fundamental layers of motion. What are those 'dimensions' curled up inside strings, but the inner surfaces of smaller vortexes?) Any specified motion relative to its context creates the hands and face of its own clock and there is no ‘true universal time.' So while temperature as an average can remain stable, time as a measure of specific motion cannot be defined as a exact point.

The problem with describing time as a dimension is that it implies specific points on a line, but if you describe time as a point, it is meaningless. Part of the problem has to do with describing space as three dimensional. Three dimensions are the coordinate system of the center point. The problem with this coordinate description of space is that the default state is assumed to be that dimensionless center point, thus if there is no energy and structure in space, it would shrink to this absolute zero point. While the point on a line between positive and negative numbers is zero, that doesn't mean zero is a point, but rather it is the absence of any numbers, or points. The real absolute for geometry is the blank sheet of paper, not the point at the center of it. The absolute is the vacuum. This means that energy and geometry define space, rather than create it, because there could well be any number of center points.

Also, space can be defined as volume as well as the distance implied by dimensionality. The same logic used to say time is the fourth dimension of space could be used to say that temperature is an additional parameter of volume, as they both relate properties of energy. Just as it takes a specific amount of time for light to travel a specific distance, therefore they are interchangeable, regulating the volume of a specific amount of energy causes its temperature to change accordingly. An useful example is the CMBR, which is described as decreasing in temperature as the volume of the universe expands.

Nature is a fluctuating vacuum, with distance and volume as description of the vacuum and time and temperature as description of the fluctuation. So space is the basis of motion, while time is a consequence of it.

Regards, John

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Hi John,

Thanks for expanding on your ideas. In my case, however, I’m forced by the postulates of the RST to follow their logical consequences. The first postulate is:

The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

The first challenge is to understand what...

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Hi John,

Thanks for expanding on your ideas. In my case, however, I’m forced by the postulates of the RST to follow their logical consequences. The first postulate is:

The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.

The first challenge is to understand what this postulate means. The first question most people ask upon encountering it is “The motion of what?” The traditional cosmological premise was that space is a pre-existing container of matter. However, as we now know, with the advent of Einstein’s general relativity theory (GR), Lemaître proposed what became known as the Big Bang theory (BB) of cosmology, which he called his “hypothesis of the primeval atom” that posits that the universe is composed of space, time, and matter, but with a beginning, a starting point characterized as the beginning of motion, the outward motion of matter, but not the motion of matter into a pre-existing container of space over time, but rather the motion of matter together with the motion, as expansion, of space and time, as well.

As an application of GR, the BB arises from the spherically symmetric dust solution of Einstein’s field equations. Thus, like the standard model (SM) of particles physics, the BB model of cosmology has free parameters. Of these, two are the cosmic time coordinate t and the comoving radial coordinate r, which Dr. E uses as the basis for his moving dimensions theory (MDT). We can say without contradiction that, in contrast to the time and space of the steady state theory cosmology, which it replaced, the time and space of BB cosmology expands, or increases, and it increases from a theroretical beginning point in the past.

In contrast to BB cosmology, then, cosmology based on the first fundamental RST postulate has nothing to say about a beginning, or an endlng, and upon reflection we can see that this is because it posits only the expansion of space and time, defined as motion, leaving out Lemaître’s “hypothesis of the primeval atom” of matter. Instead, it posits that matter is composed of discrete, or quantum, units of space and time.

But how on earth is it possible to go from the continuum of a uniform expansion of space and time (as a dustless solution to Einstein’s field equations we might say) to the units of a discretium of space and time? This question plaqued Einstein, who wrote to his friend Walter Dällenbach:

“The problem seems to me [to be] how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction, not justified by the essence of the problem, [a construction] which corresponds to nothing “real.” But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way.”

The solution to this problem is described in my essay. We can observe the expansion of time; We can observe the expansion of space, and we can observe that the relation of the two, as the reciprocal aspects of motion, is constant, the constant c. In light of the postulate, then, this leads us inexorably to the observation that, since we have learned that continuous waves and discrete particles are dual aspects of the same phenomena, the concept of vibration is key to the concept of quantization, which then leads us to look for a constant of vibration that might correspond to the constant of uniform motion.

The Rydberg constant may not be the correct one, but it’s a likely one to start with. You might say it’s a candidate for the “pulse” of the universe, with which we can measure the periodicity of the “swinging chandeliers” we see all around us, if you know what I mean.

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Doug,

To a certain extent we arrive at somewhat similar conclusions from vastly different foundations, in that I've come to doubt the central premise of an expanding universe.

I certainly didn't set out to disagree with the cosmological standard model when I first tried to make sense of it, but one particular observation has led me to where I am now. It is that, "Omega=1."

...

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Doug,

To a certain extent we arrive at somewhat similar conclusions from vastly different foundations, in that I've come to doubt the central premise of an expanding universe.

I certainly didn't set out to disagree with the cosmological standard model when I first tried to make sense of it, but one particular observation has led me to where I am now. It is that, "Omega=1."

If, as tests by COBE and WMAP would seem to prove, the rate expansion of space is evenly balanced by gravitational contraction, Lemaitre's Big Bang theory doesn't make sense. If the expansion of intergalactic space is offset by the contraction of gravity, then there is no overall expansion, because these gravitational wells are effectively consuming the expanding space. When this first occurred to me, it seemed some sort of cycle would better explain the situation, where the mass falling inward, expands back out as energy, until it cools and starts to collapse again. This would logically explain why these opposing effects are in overall balance.

It seems quite likely that the cosmic redshift is evidence of Einstein's cosmological constant, which was originally proposed to balance the universe and prevent gravity from causing it to collapse. So I find it interesting that the effect attributed to dark energy has been found to fit the cosmological constant. If space, or the path light travels across it, expands at a constant rate, this would cause redshift to compound, so that the further light travels, the greater the multiplier effect and so the faster the source appears to recede, until it appears to be traveling away from us at the speed of light. Obviously this creates a horizon line over which visible light will not pass, though black body radiation would.

The original understanding of galaxies simply flying away from each other was modified to say that space itself has expanded from an initial point because it would otherwise appear that we are at the center of the universe, given that other, non local galaxies are redshifted so that they all appear to be moving directly away from us. It seems to me the flaw in this logic is that the speed of light should have to increase accordingly, since it is our constant measure of space, but this doesn't make sense. If two galaxies are x lightyears apart and the universe doubles in size, are they 2x lightyears apart? If so, that's not expanding space, but an increasing distance in stable space. If they still appear x lightyears apart, as the speed of light increases along with the expansion, by what measure are we saying the universe is expanding, since no matter how big it gets, everything still appears the same distance apart?

The question of what might cause light to redshift and thus our perception of space to expand is an open question. For one thing, I think that light must effectively travel as waves and it is only when it contacts some sufficiently opposing force that if effectively "condenses" out as a quanta of light, or photon. For one thing, this would explain why light remains so focused when it travels over billions of light years. If it were traveling as discrete particles it would seem the potential for scattering would be much greater and there would be enough instances of diffused light to measure this. It might explain redshift as well. The idea of "tired light" was dismissed for the very reason that light was so clear and if anything had interfered with the photons to slow them, the scattering would be apparent, but if light travels as a wave, the further it expands, the more area it has to cover and this increase in volume would reduce the energy of a wave, but not its focus, as that would quantize out as an individual photon.

I could offer some more points on this, if I go through my brain some more, but either you see my position or not, so I'll expand the context.

You propose something similar to Dr. E's theory of the expanding fourth dimension. As I pointed out to him, if, as he seems to suggest, this expanding wave is light, or represents light, than according to Einstein, light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave.

What if, as seems likely, there is both expansion of light and contraction of gravitational structure. Then add to that my observation of a cycle balancing these two sides out. So what you have is light/energy expanding out as continuous waves from all directions, in all directions, so that the space defined by these waves is effectively expanding. They then either reach a point where they connect with/ground out on something else, much like a lightning bolt quantizes its energy to a single connection point. Or they travel so far that they fall off the spectrum of visible light and end up as a sea of black body radiation, which would have a clear demarcation temperature of 2.7k, because that is the "dew point/phase transition" above which it isn't stable and starts to condense out as interstellar gases. These than start to collapse back down and start the gravitational process all over again. This gravitational collapse eventually reaches the point where it heats back up and ignites, radiating the energy back out as waves. So you have both an expanding continuum and a collapsing discontinuum.

Since, as I argued in my own entry, time is energy going past to future, while the information and structure are the effect of events which go from being in the future to being in the past, than these two sides of the cycle are effectively the two directions of time. As the energy goes from one event to the next, all this discontinuous structure amounts to information which is first in the future, be it our individual lives, or those of stars and galaxies, then ends up in the past. Even Big Bang theory posits the entire universe as a unit which is first in the future, then is present, then is past, as its internal narrative goes from beginning to end.

I realize this is all speculation and given personal experience, is for nought, since astrophysics dismisses any theory not founded on the Big Bang model. This is actually more a problem for them than me though, as I am not a scientist, only someone motivated by curiosity. Even the leading physicists admit physics has been spinning its wheels for a generation. The result has been that in an age when all the sciences have been advancing at warp speed, the next generation of visionaries have tended to go to those sciences which are making the most advances, because there is the ability to question and re-examine anything and everything, while physics has been taken over by the disciplinarians who can most closely hew to the central tenets that have been laid down, with the hope of someday reaching the top of the pile and adding a few more steps. The problem is they lack the vision to realize every step they have taken was originally wild speculation in its day and out of that coalesced a reasonably workable model, but one which any number of cracks might still run through the foundations and only be plastered over in time. Since only those who make it to the top of this ladder are allowed the prerogative of questioning it, it isn't questioned, as those at the top of the ladder are the ones most dependent on it. They speculate about such things as multiple universes to explain this one and "block time" rising out of the fact that narrative is modeled as a dimension, while those of us on the outside offering ideas are the cranks.

Regards, John

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John,

I understand what you are saying, but on the other hand professional physicists are continuously deluged by the half-baked ideas of the public, and they understandably become inured to this kind of thing. Yet, my hope is similar to Lee Smolin’s, which is that one of us non-professionals could help find the mountain in the landscape of possibilities that the professionals would then...

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John,

I understand what you are saying, but on the other hand professional physicists are continuously deluged by the half-baked ideas of the public, and they understandably become inured to this kind of thing. Yet, my hope is similar to Lee Smolin’s, which is that one of us non-professionals could help find the mountain in the landscape of possibilities that the professionals would then be able to scale. Did you happen to catch the Science Friday show with Brian Green and Lee Smolin? If you read my preliminary essay, you will find part of my original narrative on the show in there, but I’ll repeat it here in its entirety, for the first time, just for you:

Begin narrative:

After discussing Smolin et al's criticism of string theory's failure to predict new physical phenomena, and the effective suppression of new ideas due to its thorough domination of academia, they turned to discussing the physics crisis itself.

As Green explained how tests of the consistency of string theory calculations, and comparisons with the established concepts of physics, show that the "theory comes through with flying colors every step of the way and keeps us thinking that things are at least headed in the right direction," Flatow turned to Smolin and asked, "Well, Lee, what would be wrong with that, if things are working like that?"

Smolin's answer was very telling, and it's well known in the community: In spite of these favorable things that one can say about string theory, there are some very important things that "it doesn't come close to doing," asserted Smolin. Then he hit the nail squarely on the head:

“If you really put quantum mechanics together with the description of space, then we know, from general considerations, that the notion of space should disappear. Just like the notion of the trajectory of a particle disappears in quantum mechanics, ...the same thing should happen to space and the geometry of space.”

"So far, string theory doesn't address this very directly," Smolin said, "while other approaches do," referring, of course, to his own continuum-based theory of quantum gravity, called loop quantum gravity (LQG), but before he could explain this further, Flatow took a call from a listener who suggested that "thinking outside the box," is what's required, which momentarily distracted the conversation away from the idea that “the notion of space should disappear,” in the union of quantum mechanics and the description of space (the spacetime of relativity theory).

Smolin replied to the listener’s comment, stating that, while he agrees with her, he definitely feels that it has to be the trained minds of professional physicists that do the "out of the box" thinking, who "go back in the decision tree," looking for new answers to foundational questions, because only they are prepared to readily scale the true mountain of knowledge, once the location of the highest peak in the landscape is discovered. Whereupon Flatow interjected with the obvious conclusion, in the form of a penetrating question:

“Are we at a point now, where you just have to sit and scratch your head and think, "We need some revolution, don't we?" I mean, we need a revolution in physics; maybe, we need a new physics!”

However, Smolin's reply to this conclusion reveals just how difficult it is for the minds of professionals, trained from the start in what Thomas Kuhn termed “normal science,” to think "outside of the box." Instead of agreeing with Flatow’s conclusion that a “new physics” is required, he demurred. "Nothing can happen without experiments," he asserted laconically, deftly inferring a different meaning of the phrase “new physics,” which is a phrase that today is commonly used to refer to new experimental anomalies, not a new foundation for theoretical physics, something that is nearly inconceivable to the professional physicist. Yet, the truth is, the trouble with physics is not due to a lack of available, inexplicable, empirical data, but to the fact that there is no satisfactory explanation of the existing data from many, many experiments, including the anomalous results behind the so-called dark energy and dark matter enigmas, and the famous Yang-Mills mass-gap problem, to name just a few.

Clearly, however, Smolin revealed his hand with his comment: While he’s certainly dismayed with the emphasis on string theory research, which seeks to unify the discrete with the continuous through modification of the current discrete paradigm, with which the string theorists are most familiar, Smolin and company prefer to approach the problem from within the context of the current continuous paradigm, with which they are most familiar.

Smolin’s argument is not that a new foundation for theoretical physics is required, but that a shift in academic research emphasis is required, from the “let’s modify the existing discrete theory” to solve the problem (string theory), to the “let’s modify the existing continuous theory” to solve the problem (loop quantum gravity). The pressing need, from Smolin’s point of view, is to complete the “unfinished revolution,” which Planck and Einstein started, by exploiting Einstein’s concept of the continuum, in order to unite the disparate theories, instead of modifying Einstein’s concept of the quantum, in order to unite them.

Yet, the most logical conclusion that naturally occurs to the non-professional, didn’t escape Flatow: “We need a revolution in physics; maybe, we need a new physics!” he had interjected, implying the need for a completely new foundation for theoretical physics, which doesn’t require the reconciliation of two, incompatible, theoretical concepts of space and time, one static and fixed, the other dynamic and changing, but finds a new concept of space and time that works as nature works; that is, a new concept that works as the dual properties of one component, where the discrete and continuous realities are simply two aspects of the same thing.

Truly, as unpalatable, as unlikely, and as inconceivable, as the prospect is to the many of the minds of today’s practitioners of “normal science,” the possibility that a totally new solution exists that would revolutionize existing discrete and continuous concepts, and that would explain the dual quantum and continuum nature of reality, as two aspects of the same entity, has to be regarded as a legitimate alternative that needs to be seriously considered, though it may seem iconoclastic to today’s scientists.

Evidently, as the NPR interview continued, since Smolin had dismissed the possibility of a "new [theoretical] physics," which he had suggested, Flatow turned to Green to get his comments, and Green seemed more willing to admit that something truly revolutionary in physical concepts is needed in our conception of space and time:

“I full well believe that we will, when we do complete this revolution that Lee is referring to, have a completely different view of the universe. I totally agree with Lee, that everything we know points to space and time not even being fundamental entities...We think that space and time...rely upon more fundamental ideas...What those fundamental entities are...that make up space and time, we don't know yet, ...but, when we get there, I think that we will learn that space and time are not what we thought they are. They are going to morph into something completely unfamiliar, and we'll find that, in certain circumstances, space and time appear in the way we humans interpret those concepts, but fundamentally the universe is not built out of these familiar notions of space and time that we experience.”

Flatow stumbled a little, trying to get his head around an idea of what this might mean in terms of changes to existing concepts, which prompted Green to add:

“It would change the very notion of reality...We all think about reality existing in a region of space and taking place through some duration of time, but we've learned that those basic ideas of the arena of space and the duration of time are not concepts that even apply, in certain realms, and if the notions of space and time evaporate, then our whole conception of reality, the whole container of reality will have evaporated, and we'll have to learn to think about physics and the universe completely differently.”

End of narrative

Of course, I believe that this new notion of reality is that everything consists of nothing but motion, a reciprocal relationship of space and time. However, it took me two months of full-time effort to simply write a ten-page essay in 5000 words on it, because there is so much to say that it’s easy to get off track, when trying to capture it succinctly.

Many of the things you mention are interesting, and I would love to discuss them with you sometime, but the challenge I face right now is to try to convince Green, Smolin and company, to take a serious look at this mountain that I’m writing about. I think it’s worth scaling, but he’s right – you and I are not prepared to do it. We can only try to get their attention. Sometimes I have wished that Steven Weinberg were my uncle. LOL!!

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John,

I agree that it’s easy to get cynical sometimes, but I also realized a long time ago that people do what they have to do and think what they have to think. You can’t blame them for that, since we all do it.

Building an alternative, if it can be done, is the only course that will work. In my case, I found that there was no need to focus on trying to convince other people,...

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John,

I agree that it’s easy to get cynical sometimes, but I also realized a long time ago that people do what they have to do and think what they have to think. You can’t blame them for that, since we all do it.

Building an alternative, if it can be done, is the only course that will work. In my case, I found that there was no need to focus on trying to convince other people, which is something I learned from Larson’s example.

Years ago, before I learned this lesson, I would write Steven Weinberg about once a year. He was kind enough to always reply, although it was usually a simple line or two, dismissing my comment or question, in the “not even wrong” sense. When I realized that he really had no other option and that I probably would have done the same thing, had I been in his position, I felt embarrassed, and I stopped writing him out of compassion. Can you imagine getting constantly flooded with messages appealing to ideas that are not even wrong?

So, the first task of an “uncommitted investigator” is to be sure his thinking can be wrong, and to gain a thorough understanding of how to tell if it can be wrong. I was fortunate, because I was starting with 1, 2, 3, and 4. It’s pretty simple, something that surely could be wrong, but it gets complicated fast, so I wasn’t always so sure.

Eventually, things began to work out. Now, I just take it one step at a time, hoping I can still tell if it’s wrong, or not, but many times, it’s not easy. The thing is, though, most of the time, I’m the one who is now in a position to judge whether or not it is possible that something is wrong. That’s a good position to be in because it gives you confidence. Once in this position, you don’t need the confirmation of experts in the same sense that you do when you are not in it. Does this make any sense?

For example, the idea that force, such as an electric charge, can be autonomous, a “fundamental” entity, is something that you can tell is wrong, without having to get anybody to agree with you. You do this by determining what the meaning of the word is. As I’ve already explained, the word force is only a label defined to express a product: It tells us how much of a quantity of motion is undergoing a time rate of change. It’s like evaluating a currency that is undergoing a time rate of change in its exchange value. We could call it the force of inflation, but we wouldn’t ever think that this force could be autonomous. How could you refer to a force of inflation without the notion of its exchange value?

It’s the same with the electron. It appears to have a charge without any underlying motion, like an inflating currency that has no underlying exchange value. Huh? This just doesn’t make any sense! It’s not even wrong!

Yet, the entire modern physics community will look narrowly upon you, if you try to maintain it, because they long ago invoked an illegitimate alternative to motion produced force, when there seemed to be no other way out. But are you going to be able to convince them, at this point? If you think so, I have a bridge that you may be interested in as well.

The thing is, John, you don’t need to convince them. You only need to know if it can be wrong or not. If it can’t be wrong, then you follow the consequences, if you are able to do so. That’s all there is to it. It keeps you from getting cynical.

I hope this helps.

P.S. This argument against autonomous force has been made moot now by the adoption of the concept of “exchange force,” used in the standard model, but it still serves to illustrate the point, I think.

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Hi Larry,

The answer to your first question is yes. Unfortunately, the error in this graphic is misleading. The word “proton” should be “protium” instead. The electron, composed of three “negative” preons (three “red” S|T units), neutralizes the three net “positive” charges of the proton, composed of one down quark, with one net “negative” charge, and two up quarks,...

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Hi Larry,

The answer to your first question is yes. Unfortunately, the error in this graphic is misleading. The word “proton” should be “protium” instead. The electron, composed of three “negative” preons (three “red” S|T units), neutralizes the three net “positive” charges of the proton, composed of one down quark, with one net “negative” charge, and two up quarks, with four net “positive” charges, which balances the protium atom, with four “negative” and four “positive” charges, as shown

Your second question is more difficult to answer. It has to do with the fundamental duality of the two systems. In the system of vectorial motions, the fundamental duality is that of potential and kinetic energy, where the total energy of the system is conserved. This is best illustrated in the swinging mass of a pendulum. At the top of the swing on either side, there is a point where the mass is stationary, so the kinetic energy must be zero at those two points, but at the bottom of the swing, halfway between these two points, the kinetic energy is at its maximum, and the gravitational potential energy is zero.

Now, what I will have to say about this below is based on Peter Rowlands analysis of the factor of 2 in fundamental physics

(see: http://arxiv.org/PS_cache/physics/pdf/0110/0110069v1.pdf).

We can compare this relationship between the potential and kinetic energy of the system, the symmetry of which incorporates the law of conservation of total energy, to geometry, because the area of a given right triangle is one-half the area of a corresponding rectangle:

A = (base x height)/2,

where two, dual, triangles are formed by bisecting a rectangle along a diagonal, each with area = A. The correspondence to kinetic energy is made by noticing that the diagonal, bisecting the rectangle, taken as the straight-line graph of velocity, v, multiplied by time, t, defining a uniform acceleration, determines the distance traveled, d, as the area underneath the line, or d = vt/2. When this accelerated motion is the acceleration of mass, the corresponding energy equation that applies has the dimensions of energy derived from the kinetic energy equation, E = ½ (mv)v, or momentum (mass time velocity) times velocity, or mass times velocity squared, divided by two (corresponding to ½ of the area of the rectangle, the area of the triangle.)

On the other hand, if the motion were unaccelerated, the area underneath the horizontal line of the rectangle (the top line of the rectangle), represents the distance traveled, or d = vt. When this unaccelerated motion is the velocity of mass, the corresponding energy equation that applies has the dimensions of energy derived from the potential energy equation, E = mv^2, or mass times velocity squared, not divided by two (corresponding to the total area of the rectangle, the area of both triangles combined.)

In general terms, then, there is a fundamental distinction being made here between continuous conditions (constant motion) and continuously changing conditions (accelerating motion,) and the distinction is made by a factor of two, because the continuously changing conditions invoke the Merton mean speed theorem, where the total distance traveled under uniform acceleration must equal the product of the mean speed and the time.

This reflects a very ancient foundational principle that incorporates what has been called the mediato/duplatio, or halving/doubling, basis for counting systems such, as the Mayan long count and other ancient counting systems, and there is much more to say about it than I can say here.

But briefly, recall that the fundamental duality in the new system, the scalar motion system, is the duality of spatial and temporal pseudoscalars, which also comes from a factor of 2, but the factor of 2 here is not related to the simple 1D geometric principle of the diagonal of the rectangle, which applies to the straight-line function of vt, or the space of 1D vector distance, but rather it is related to a much more complex 3D geometric principle of the diameter of the sphere, which applies to the function of v^3t, or the space of 3D pseudoscalar volume.

As Peter Rowlands shows in his paper, “…the factor 2 makes its appearance in molecular thermodynamics, quantum theory and relativity. It is, in a sense, the factor which relates the continuous aspect of physics to the discrete, and, as both these aspects are required in the description of any physical system, the factor acquires a universal relevance.”

Hence, the relevance this factor has in the new system is the focus of our program of research. On this basis, we have been able to construct the toy model of the standard model illustrated in figure 1 of my essay, as well as the periodic table of elements, as shown here: http://www.lrcphysics.com/wheel

Our current goal, however, is the calculation of the atomic spectra. In this connection, it should be noted that the difference between the factor of 2 periods of the QM-based periodic table, and the factor of 2 periods of the RST-based periodic table, is a factor of 2! That is to say, in the QM-based theory, the periods are a 2n^2 cycle, while in the RST-based theory, the periods are a 4n^2 cycle.

The trouble is, in the QM-based theory, though the 1D motion concepts (electronic orbitals, angular momentum, electron spin, etc.), were conceived based on the experimental observations of energy transitions in spectroscopy, there are so many possible transitions, and the calculations get so complicated, that, to this day, the solutions of the wave equation can only be found “in principle,” for most of the elements (see Tomonaga’s “The Story of Spin”).

We have similar problems in the new system, but the main difference between the two systems is in the treatment of mass. In the QM-based system, mass is a given, just like space and time, so the mystery remains, what is its origin? On the other hand, in the RST-based system, we know that the origin of mass has to be scalar motion, but how does this come about? Starting with space and time only, how does mass, energy and radiation emerge?

Well the factor of two introduced by the kinetic energy equation, where the potential energy term is twice the kinetic energy term, is found schematically in the toy model. The red circle of an S|T unit in the model represents the vibrating spatial pseudoscalar, while the blue circle at the opposite end of the black line that joins them, represents the vibrating temporal pseudoscalar, and since these two are inverses of one another, while the one expands, the other must contract, and vice-versa.

It is this inverse relationship, the redistribution of scalar motion, that is a striking analog of the redistribution of kinetic energy in an f = ma system, but since no mass is involved, only changing space and time, something else has to bind the two pseudoscalars together. It turns out that it is possible to show that this bond is a result of the continuous “flow” of space and time, thus completing the analogy of the relationship of potential and kinetic energy in the viral theorem. The scalar progression, t^0, of the spatial pseudoscalar oscillation, and the scalar progression, s^0, of the temporal pseudoscalar oscillation make it possible for them to combine, and, if two instances of them do combine, there is no event to separate them ever after.

I hope this is helpful Larry.

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In his FQXI essay, Phillip Gibbs describes a crucial difference between time and space, in spite of their unification by Minkowski, through the symmetry in the Lorentz transformation. He writes,

”Time can distinguish itself from space in this way because the spacetime metric has a Lorentz signature that assigns a different sign in the time dimension versus the three space directions....

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In his FQXI essay, Phillip Gibbs describes a crucial difference between time and space, in spite of their unification by Minkowski, through the symmetry in the Lorentz transformation. He writes,

”Time can distinguish itself from space in this way because the spacetime metric has a Lorentz signature that assigns a different sign in the time dimension versus the three space directions. Thus in locally flat Minkowski spacetime distances are measured by the invariant quantity



ds^2 = dx^2 + dy^2 + dz^2 – c^2dt^2



Part of the mystery of time is to understand where this signature comes from. Why three plus signs for space and only one minus sign for time? Even with this separation of dimensions there should remain symmetry under time reversal t -> -t, but the arrow of time breaks this symmetry. What is the origin of this arrow? From what bow did it take flight?”

One of the founders of FQXI, Max Tegmark, talks about the same thing here:

http://www.youtube.com/watch?v=2pLCOizNSLI

He says that, if it weren’t for the minus sign in the above equation, it can be proven mathematically that there would be no point in having a brain even, because we wouldn’t be able to predict things in the way we do.

Yet, the equation has a minus sign only because of the mathematics of an expanding sphere. Why should it be so amazing that the radius from the center of a sphere, expanding at light speed, should be equal to a point on its surface, defined by its rectangular coordinates? Isn’t it clear from this that BOTH space and time are expanding? There is only one minus sign for time because it is the zero-dimensional expansion, whereas space expands three-dimensionally.

The true symmetry Gibbs is unwilling to sacrifice is preserved in the independent reality of the union of space and time, just as Minkowski predicted it would be, but then, if this is true, why should we look for symmetry in something that has no independent reality, like time, or space, apart from motion? Neither can have any meaning without the other.

As Tegmark observes, this one-way nature of time is indisputable mathematically, so Rovelli urges us to “forget time” and Gibbs declares, “Temporal causality has to go,” when all that is really necessary is to recognize that the symmetry of space/time is reflected in the binomial expansion of the tetraktys: Three dimensions are the inverse of zero dimensions and these four are joined together, reciprocally, just as surely as space and time are joined together, reciprocally, to the extent that neither has any meaning apart from this union.

Thus, both the symmetry of space/time and temporal causality can be reconciled through the four dimensions of the tetraktys. There is no need to give up either of them. The mystic dream of four becomes an independent reality, when the 3 of space and the 1 of time are recognized as the two, reciprocal, aspects of the same underlying reality, motion.

This is clear when space, or time, is quantized by unit vibration. Writing the equations for the cycles of the respective unit pseudoscalars, and their product, clearly shows this:

f = 1/t = 1/2, and fbar = s/1 = 2/1, so s/t = f * fbar = 1/2 * 2/1 = 2/2 = 1/1 = 1,

where the radius, r = ct, expands, then contracts, in 2 units of time. We can write it as eight units out and eight units back and get the same result:

s/t = f * fbar = 16/2 * 2/16 = 32/32 = 1/1 = 1,

or, in terms of the unit sphere,

s/t = f * fbar = 2π/2 * 2/2π = 4π/4π = 1/1 = 1.

Certainly, succumbing to the demands of symmetry, by looking to the intuitive concept of motion, in which the inverse of this independent reality requires the admission of 3D time 0D space, seems much more reasonable than insisting that we should give up causality and invent extra dimensions.

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For whatever it’s worth, my vote for a single FQXI essay, of all that have been submitted so far (excluding my own of course!), would be Peter Lynd’s essay. This is because he argues, very cogently, that the only independent reality that can exist logically is continuity, or constant change (i.e. motion). Yet, at the same time, his favorite quantum gravity theory would have to be Rovelli et...

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For whatever it’s worth, my vote for a single FQXI essay, of all that have been submitted so far (excluding my own of course!), would be Peter Lynd’s essay. This is because he argues, very cogently, that the only independent reality that can exist logically is continuity, or constant change (i.e. motion). Yet, at the same time, his favorite quantum gravity theory would have to be Rovelli et al’s loop quantum gravity (LQG) theory, which requires the definition of discrete units of space and time!

He writes to Carlo:

“I very much enjoyed your essay. Naturally, I very much agree with its general drive too. I have a question though. As a proponent (and founder) of Loop Quantum Gravity, are you not assuming the existence of time by asserting that time (and space) are quantized, and come as minimum, indivisible atoms in LQG? I think one can see this just in general, but also that by asserting the existence of indivisible, minimum time and space intervals, one is also assuming the existence of instants in time and spatial points (things that would constitute the building blocks of time and space and which certainly do not exist) to bound and determine such intervals. I naturally have no problem with Planck time and distance - intervals beyond which clocks and rulers can no longer have meaning – but this does not mean that continuity ceases beyond this point, not (sic) does Planck time and distance require the existence of instants and spatial points.

Best wishes

Peter

PS: I should note that, considering its emphasis on background independence and its adherence to 4-d, I find LQG the most promising current approach to quantum gravity. It is just the "atoms of time and space" that I have a real problem with. I'm not sure if LQG could be reformulated without this feature and still be ‘LQG’ however.”

This opinion is very pleasing to me, of course, because any RST-based theory MUST be background independent and adhere to 4D. However, Carlo’s response to this was also very interesting. In essence it’s the same trick Einstein employed when dealing with the aether concept: He wants to just change the name of spacetime to gravitational field! Einstein did this when he changed the name of the aether to spacetime, giving it different properties (length contractions and time dilations,) and now Carlo wants to change the name of spacetime to gravitational field, giving it different properties (space points and time instances.) He explains to Peter:

“Einstein great discovery, of course, is that the two things are in fact the same. The two things are: on the one hand, the gravitational field, and on the other the two "entities" that Newton put at the basis of his picture of the world, and called "space" and "time". Now, when you discover that mister A and mister B are the same person, you can equally say that mister A is in reality mister B, or that mister B is in reality mister A. Books like to say that the gravitational field, in reality, is nothing but the spacetime, which happens to curve and so on. I prefer the opposite language: namely that the entities that Newton called "space" and "time" are nothing else than the gravitational field, seen in the particular configuration where we can disregard its dynamical properties, and assume it to be flat.”

While the unphysical concept of the aether was called upon to explain the propagation of radiation, Einstein did away with this requirement by calling upon the properties of Maxwell’s concept of the electromagnetic field and the principles of invariance, enabling him to eliminate Newton’s concept of absolute space and time in the process.

Taking it a step further, he was able to eliminate the concept of the aether altogether, by calling upon the properties of a hypothesized gravitational field and the principles of covariance. Thus, Einstein eliminated the concept of an unphysical aether, by substituting for it a different concept of physical fields, which for physicists, at least, “are as real as the chair they sit on,” to use the words of the genius himself.

Of course, a field is continuous, not discrete, and, in the case of the hypothesized gravitational field, the continuity consists in the smooth change of 4D spacetime, which in the absence of matter, would be flat in Einstein’s theory, so Carlo argues that what Newton conceived of as absolute space and time, and what Maxwell conceived of as continuous aether, are, in reality, only a set of electromagnetic and gravitational fields, before matter is introduced into the theoretical picture; that is, without matter, only spacetime and light are conceivable.

But we know that light is quantized, which means that the electromagnetic field must be quantized, and, if the electromagnetic field is quantized, then the gravitational field must be quantized as well. This means, then, that all observables are simply functions of the various field interactions.

Well, in quantum field theory, the quanta of the electromagnetic field is the photon, while the quanta of the gravitational field is the graviton, so what’s the problem? Why can’t we just turn out the lights and go home?

The reason is, in a word, renormalization. Renormalization is the key that opened up the escape hatch for quantum field theory faced with the absurdity of singularities, but because of the weakness of the gravitational force, renormalization in connection with the graviton, at high energy, doesn’t work. A work-around for this is a concept called “effective field theory,” in which a non-renormalizable theory is regarded as merely a theory in which these high-energy interactions are highly suppressed.

Nevertheless, the scales, at which these effective field theories would be able to do their magic, are woefully out of reach from the human scale, so that approach seems literally out of reach.

Yet, the problem Peter has with LQG is even more fundamental than that. His paper shows how, logically, there can be no discrete interval of duration in which there is no change, which prevents the quantization of the G field a-priori; that is, there can be no “atoms of time and space,” because if there were, it would require that change, or motion, would have to be non-existent, during that interval, no matter how small the interval might be. If this is the case, how can gravity be explained in terms of “atoms of space and time,” even if their names are changed?

Larson never let this bother him. He simply asserted that the required change during the natural interval proceeded, from one boundary to the next, smoothly, crossing boundaries as if they weren’t there. Though no one ever challenged him on this, they should have and Peter would have been able to do so quite handily, in my opinion.

So, if Carlo can’t get away from this well articulated, philosophical, objection to the quantization of spacetime, what about the RST-based theory? How does it deal with this deepest of all physical mysteries: How DOES nature manage to be discrete and continuous, at the same time?

I’ll take a stab at it in the next post.

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In the previous post above, I promised to deal with Peter Lynds’ (indirect) question, as to the mystery of discrete and continuous space and time, but first, I want to address the comments of John and Le Rouge that have been posted in the meantime. Their comments and questions focus on the same thing, actually. Le Rouge questions the origin of the eightfold cube, while John questions the...

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In the previous post above, I promised to deal with Peter Lynds’ (indirect) question, as to the mystery of discrete and continuous space and time, but first, I want to address the comments of John and Le Rouge that have been posted in the meantime. Their comments and questions focus on the same thing, actually. Le Rouge questions the origin of the eightfold cube, while John questions the space/time expansion of the sphere it contains.

John asks:

“If space has no independent reality from motion, then presumably the most stable description of distance we have is c, so how can it be said that space expands at c?”

The answer is that c is a velocity, a space/time ratio, defining the expansion of its space aspect relative to its time aspect. To measure the expansion requires a point of reference to be established relative to one aspect or the other of the space/time expansion. If we choose to measure the time aspect, we must “stop” the space aspect’s expansion and vice-versa. Thus, “stopping” the progression of the space aspect, say by imagining that instead of continuously increasing, the space expansion alternately increases/decreases, yielding a net spatial increase of zero (spinning its wheels so-to-speak), a reference point in the spatial expansion is established that enables us to measure the passage of time, which continues increasing uniformly, 1, 2, 3, …n, as a dimensionless scalar.

On this basis, the spatial pseudoscalar reverses its “direction,”at the boundaries of 0 and 1, meaning it reverses from inward to outward, at 0, and, again, from outward to inward at 1, creating the oscillating unit sphere (max circumference = π).

Notice, now, that the radius of this unit sphere is also the x4 = ict coordinate of Dr. E’s MDT expansion, which, while it is unit distance (d = s/t * t = s) from the origin, just reaching a point, x, y, z, on the surface of the sphere, it is also equal to the unit time interval (the i term is due to the use of the Pythagorean theorem to define the length of the radius, in which the square root of –1 is employed in the equation showing the equivalence of the polar and rectangular coordinates. When this equivalence is compared, by subtracting one from the other, the result is 0.)

Hence, the minus sign is no big mystery. It’s just the result of the procedure used to talk about the radius of the unit expansion. The really big deal is that the radius is equal to both ct and t! To see the significance of this important detail, we have to understand that the pseudoscalar DIAMETER expands by two units, for every 1 unit of time increase.

The eightfold cube forms by virtue of the dimensionality of the pseudoscalar, but the 1D motion of the radius is a 1:1 ratio; that is, in 2 units of time, at c-speed, the radius is d = s/t * 2t = 2s, or d = s/t * nt = ns, for any number, n, of unit time expansion. The 2D area of the pseudoscalar is (2n)^2s/t * nt = 16s, when n = 2, and the 3D volume is (2n)^3s/t * nt = 64, when n = 2.

What this means is that c remains constant in terms of a single direction (a selected radius of the expanding sphere), defined in terms of three dimensions, from the origin, because the space/time ratio remains at 1:1, in this 1D direction, no matter how long the expansions continues.

In your example, taking a lightyear as one unit, two points x lightyears apart, expanding for two lightyears, as measured from one of them (i.e. one is at the origin), would not be 2x, or x, lightyears apart, but they would be 2x + x lightyears apart.

As for your question of what determines c = s/t = 1/1, the answer is that the value of the ratio, the speed, is observed relative to all matter (which is composed of these oscillating pseudoscalars recall), but the space and time units are assumed to be revealed in the Rydberg constant, as explained in my essay. These discrete units are constant. They do not change, only the length, area and volume of the pseudoscalar changes, according to the dimensionality of the tetraktys.

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Doug,

" These discrete units are constant. They do not change, only the length, area and volume of the pseudoscalar changes, according to the dimensionality of the tetraktys."

It still seems to me what you are describing is increasing distance in stable units of space, as opposed to space itself expanding.



To put this in the context of my own thinking, if space is...

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Doug,

" These discrete units are constant. They do not change, only the length, area and volume of the pseudoscalar changes, according to the dimensionality of the tetraktys."

It still seems to me what you are describing is increasing distance in stable units of space, as opposed to space itself expanding.



To put this in the context of my own thinking, if space is ultimately flat, with areas of gravitational contraction balanced by the seeming apparent expansion of the field of space itself, then there is no overall expansion, since this field effect is absorbed into those gravitational sinks. When we measure redshift, it is of light that has crossed large expanses of space and not fallen into intervening gravity sinks, until it falls into our telescopes. Since this space is effectively expanding for the light crossing it, the redshift is compounded so that the further it travels, the faster the source appears to recede. Eventually this recession exceeds the speed of light, creating a horizon line for visible light. This doesn't mean the source is actually moving away, only that the path the specific light travels is growing, much like running up a down escalator doesn't mean the levels of the building are moving apart. Gravity curves space around gravitational sources and this causes the source of that light to appear to move as it travels behind the source, but that doesn't mean the actual source is moving, only the light traveling from it is bent. So is there a way that light could be redshifted by the effects of extreme distance, much like it is bent by gravity?

The idea of "tired light" was dismissed because any effect which would slow the passage of photons would also scatter them and distant star wouldn't be nearly as clear. What if light really doesn't travel as particles of light, but as waves and it's only when it contacts something is it quantized? For one thing, it would provide a far more effective mechanism for transmitting light over the distances required and not having their clarity compromised, while it would also provide a reasonable explanation for how they lose energy, as the volume of space increases exponentially with distance, so the energy of the wave is reduced. When striking our telescopes, the energy of individual photons is the same, since the quanta of light are a function of the absorption, but their number is reduced.

Mass and energy are interchangeable, but what is the mechanism? If light expands as a wave, but is absorbed as particles, or units of energy, it would seem this quantization of light is the first step of energy being converted into matter. Plants do it all the time.

Eventually this structure ignites through chemical reaction or pressure and radiates back out, continuing the cycle.

So the expansion is a function and consequence of the unitary wave nature of light, while gravity is the collapse of this wave into discrete units. That would explain how nature can be both continuous and discontinuous.



This way, we can have expanding space, without having to explain the entire universe expanding from a point. Since it is a property of energy and space, it amounts to a cosmological constant, not the result of a singularity and there is no need for "dark energy."

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John,

Please pardon the delay in my response. I’ve had to contend with a flooded basement, among other distractions. In trying to hurry under duress, I’ve only managed to mangle the stream of thought in this forum, by inadvertently posting the same comment three times!

What I would like to do, to get back on track, is to note that the major threads of thought developing here are...

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John,

Please pardon the delay in my response. I’ve had to contend with a flooded basement, among other distractions. In trying to hurry under duress, I’ve only managed to mangle the stream of thought in this forum, by inadvertently posting the same comment three times!

What I would like to do, to get back on track, is to note that the major threads of thought developing here are actually related. We were discussing the discrete vs. continuous essay of Peter Lynds, related to his comments in Rovelli’s forum on LQG in the context of the discussion of the arrow of time there.

In addition, we were discussing Gibbs’ point on the need to give up causality for the sake of symmetry, in string theory, insisting that it’s not really necessary to do this, and also to resort to string theory’s extra dimensions, when we recognize that the symmetry of motion, not space, not time, meets the requirement for spacetime symmetry without sacrificing causality and adherence to 4D.

To summarize, with our RST-based system, we get background independence in four dimensions, maintaining causality, through the symmetry of discrete magnitudes of space/time and time/space. Yet, there remains the need to explain how motion can be discrete, in the face of Peter’s challenge of LQG, showing the logical contradiction inherent in the concepts of discrete and continuous units of space and time.

In the meantime, you write:

“It still seems to me what you are describing is increasing distance in stable units of space, as opposed to space itself expanding. To put this in the context of my own thinking, if space is ultimately flat, with areas of gravitational contraction balanced by the seeming apparent expansion of the field of space itself, then there is no overall expansion, since this field effect is absorbed into those gravitational sinks.”

The communication problem here, I believe, is that you are thinking in terms of space, not in terms of motion. When we realize that space can have no independent meaning outside its relation with time, we see that it cannot expand, anymore than it can warp, because it has no properties independent of those it has in its union with time. The concept of “flat” space makes no sense, and the only reason that we can think of “flat” spacetime is that the spacetime concept incorporates the expansion of spacetime, as the only independent reality.

While physicists such as Gibbs and Tegmark are intrigued with the single negative coordinate of time in spacetime, Dr. E, is captivated with its identity as an expanding dimension, but I don’t think its possible to understand space or time, unless we recognize that the only meaningful way to approach either is as the two, reciprocal, aspects of motion.

Space is a measure of motion, either past or contemplated. It is not something that can be treated as if it existed between two or more points, as one, two, or three-dimensional magnitudes. But here is the rub, isn’t it? How do we relate points to lines, areas and volumes? Peter’s point is that, while this may be trivial in geometry, it’s clearly not the case in physics, where change is the central concept. Newton recognized this long ago, when he said that:

“…if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics; and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things.”

The key is “those few principles, brought from without.” Today, we can design and build mechanical devices upon those non-geometrical principles of math and physics that can recreate even the roughness of nature with great accuracy, let alone the smooth figures of right lines and circles. But what we discovered along the way, is that, no matter how we try, we cannot escape the delimma that has plagued and vexed the intellectuals of mankind from the beginning of time: What is the meaning of a point?

A point has no dimensions, it has no extent. How then can it be charged? How can it spin? How can it be the basis of changing magnitude? Obviously, nature’s magnitudes are infinitely divisible. How can this be? Sure, we can intellectually start with an empty set, and then we can count this empty set as a member of a non-empty set, but let’s face it, we are only fooling ourselves for the sake of getting a grip on something practical. The ancient Greeks have the last laugh. In the end, we are just as perplexed by the physical point as they were.

So, while I really would like to discuss your ideas, some of which are very consonant with my own, I first have to deal with this most fundamental challenge of all: How does nature reconcile the seemingly irreconcilable dichotomy inherent in the discrete versus continuous concepts, so handily? Unless we are able to solve that problem, in a background-independent, four-dimensional, context, nothing else matters, really.

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Hello John & Doug!

Great conversations here! I'll be re-reading Doug's paper on the treadmill in a few minutes.

John--above you write to Doug, "You propose something similar to Dr. E's theory of the expanding fourth dimension. As I pointed out to him, if, as he seems to suggest, this expanding wave is light, or represents light, than according to Einstein, light is the constant and...

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Hello John & Doug!

Great conversations here! I'll be re-reading Doug's paper on the treadmill in a few minutes.

John--above you write to Doug, "You propose something similar to Dr. E's theory of the expanding fourth dimension. As I pointed out to him, if, as he seems to suggest, this expanding wave is light, or represents light, than according to Einstein, light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave."

Where did Einstein state this? That's awesome, as it's exactly what MDT states in the attached mini-paper! If you can give me the source for "according to Einstein, light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave", that would rock!

John--I think this is what you've been trying to say to me above and in the forum for MDT.

In the attached mini-paper, I show how the gravitaional redshift and the gravitational slowing of clocks both arise from a more fundamental invariant--the fundamental invariant which also happens to define Planck's length and the velocity of light: The fourth dimension is expanding relative to the three spatial dimensions at the rate of c, manifesting itself as a spherically-symmetric wavefront in our 3D, which has a wavlength of Planck's length. This is the "invariant standing wave!"

Please see the attached mini-paper to see how MDT explains the gravitational slowing of clocks, the gravitational slowing of light, and the gravitational redshift; with simple diagrams superimposing an invariant, standing wave over space which can strecth! with these diagrams, MDT explains why clocks run slower in stronger gravitational fields where space is stretched. It shows that time, as measured on a clock, is also stretched, but only because of an underlying invariant which is never stretched—the expansion of the fourth dimension relative to the three spatial dimensions--which manifests itself as a standing sine wave in the figures. For even though time and space are stretched, the expansion of the fourth dimension remains invariant: dx4/dt = ic. And too, it shows that space is continuous, and all quantization arises from the quantized invariant expansion of the fourth dimension relative to the three spatial dimensions, or dx4/dt = ic. The invariant wavelength of the fourth expanding dimension, which is Planck's length, chops measurements of space—of time, energy, and momentum—into units of the Planck length, while providing the fundamental wave nature that gives rise to Heisenberg’s Uncertainty Principle in all realms, as well as Hugens' Principle in all realms.

So it is that the absolute invariance of the expanding fourth dimension, whose wavelength and rate of expansion never changes, when superimposed on continuous space that can be stretched by a mass, results in clocks ticking more slowly in stronger gravitational fields.

Yes--entanglement, entropy, time, nonlocality, Huygens' Principle, relativity--how mysterious are all these! And yet if you ask foundational questions such as *why* entanglement, *why* entropy, *why* time, *why* nonlocality, *why* Huygens' Principle, *why* relativity, the richest, wealthiest establishment in the history of physics, which also happens to be the establishment which has contributed the least (perhaps money cannot buy physics and philosophy?), sends forth anonymous postdocs and grad students to launch the snarky, ad-hominem attacks they perfect under the guidance of their pseudo-physicist political mentors.

But hey--everyone's got to make a living.

Behold MDT--the great unifier and invariant source underlying all these *physical* phenomena--in relativity and quantum mechanics--in statistical mechanics and entropy.

For the first time in the history of relativity, *change* has been *physically* woven into the fundamental fabric of spacetime, with dx4/dt = ic. And that's where change needs to be! For can you name any branch of physics in which change, and time, do not exist? Without change, no measurement can be made.

MDT is unique in that it offers a *physical* model underlying entropy, entanglement, and nonlocality, and too, all of relativity can be immediately derived from its simple postulate and equation, as can the gravitational slowing of clocks and light, as well as teh gravitational redshift.

I expect MDT to bring additional boons for years to come!

Thanks for the conversations, and thanks for the reference, John! Would love to see where Einstein states, "light is the constant and gravity is actually shrinking the three dimensional geometric space, relative to this standing wave.""

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Thanks for the comment, Dr. E. I’ll come to your forum to post a response, as soon as I can make time to do so. In the meantime, I’m trying to get to the discussion of the discrete vs. continuous issue raised by Peter Lynds’ essay.

People have been asking me to clarify the concept of binary oscillation, or rotation by ð, as opposed to quadrantal oscillation, or rotation by ð/2. The...

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Thanks for the comment, Dr. E. I’ll come to your forum to post a response, as soon as I can make time to do so. In the meantime, I’m trying to get to the discussion of the discrete vs. continuous issue raised by Peter Lynds’ essay.

People have been asking me to clarify the concept of binary oscillation, or rotation by ð, as opposed to quadrantal oscillation, or rotation by ð/2. The best way to do this, I think, is to refer to my discussion of it here, and then, if there are any questions concerning it, I’ll be glad to entertain them in this forum.

The entire foundation of quantum mechanics rests upon the principles of rotation, but the mathematics of rotation employed in the theory is based on complex numbers, which are made possible by the ad hoc invention of the imaginary number, “i.” The complexity of the approach is compounded by the role that Lie groups and Lie algebras play in applying the concepts of rotation to gauge groups, but in essence, the idea is this: Rotation enables us to view the continuous spectrum of magnitudes in terms of discrete units, marked out by units of rotation, which is, by definition, a continuous change.

In quantum mechanics, this takes the form of the U(1) group of rotations, or 1D rotations in the real unit circle, the SU(2) group of rotations, or 2D rotations in the complex unit circle, and the SU(3) group of rotations, or 3D rotations in the complex unit circle. By means of the properties of these Lie groups and the interactions of their Lie algebras, modern physicists have been able to construct the standard model of particle physics, as the basis for the electroweak theory (U(1) & SU(2)), and the strong nuclear force theory (SU(3)).

The great advantage in using complex numbers in the SU groups of rotations, over the real numbers in R(n) groups of rotations, is that additional degrees of freedom are attained that enable physicists to incorporate quantum variables in their theories, such as 720 degree spin, for instance, which would be impossible to do otherwise.

Of course, the nature of scalar motion excludes the concept of rotation, altogether, since it requires something to rotate. Larson tried to get around this by using a concept of rotating scalar vibrations, in his RST-based theory, but this has been replaced by the concept of pseudoscalar vibration in this development of an RST-based theory.

It turns out, though, that the expanding/contracting pseudoscalar is isomorphic to binary rotation, or rotation by pi, but, since we are talking about scalar vibration, and not vector rotation, the principle involved is new. Recall that in the pseudoscalar oscillation, the diameter of the sphere contained within the eightfold cube expands from 0 to 2 in one unit of time, and contracts from 2 to 0, in the next unit of time.

At first glance, it doesn’t seem possible to compare such an expansion/contraction to rotation, binary or quadrantal, but when we recognize that, in the dual direction property of dimensions, we have an analog of Newton’s third law of motion, that conclusion must be revisited. The fact is, that for every direction in a dimension, there is an equal and opposite direction.

This means that, just as soon as we choose a reference point in the rotation of a radius in the unit circle, any subsequent degree of displacement from that mark may be matched by an equal, but opposite, displacement, in the other direction; that is, a chord of the circle is defined at every point in the continuous spectrum of points making up the circumference of the unit circle.

As the rotation of the radius continues around the circle, then, a reciprocal radius rotating in the opposite direction, marks the second point, defining the chord’s length, at any given instant, across the circle, which reaches its maximum extent after ð/2 radians of rotation, when the two, reciprocal, radii are diametrically opposed, coincident with the diameter of the circle.

Since two rotations of ð/2 radians are required to reach this point, one in each direction of rotation, this is a total rotation of ð radians. As the rotation continues from this point, the length of the chord, demarked by the two radii, decreases, as they converge at the ð radian point. Arriving at the ð radian point, the two radii are coincident with each other, meaning that they then rest on the same point of the circumference, effectively defining the zero-length diameter of the contraction for one instant of change.

As the two, reciprocal, rotations continue, back to the starting point, the chord length again expands, from zero, to maximum, at the 3ð/2 mark, and contracts as before, to zero again, at the 2ð mark, where the radii are once more coincident, together having rotated a total of 2 * 2ð = 4ð radians in the completed cycle.

Consequently, we not only see the equivalent of binary rotation in the oscillating pseudoscalars, but we also see a simple, physical, equivalence of 720 degree “spin” per cycle of rotation. Not only this, but we also see the definition of a point, with zero extent, in the coinciding radii, defining a discrete interval of change between them.

To my mind, this resolves Peter Lynds’ philosophical issue, by showing that the discrete interval, defined by its boundaries, is, in fact, an interval of continuous, reciprocal, progression, a progression of zero-dimensional, extentless, points, rather than a succession of non-zero, extended, space and time intervals, during which no change can take place.

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Hello Doug,

re:

[Hamilton] was a genius, but is, at the same time, roundly dissed by many lesser lights, on several accounts, especially for his attempt at poetry!

maybe sticking with math... ;-)

i'm not being terribly serious here, just trying to have a little fun with it. as i was with my quip about John's 'crazy idea' about light. i'd been considering the same thing...

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Hello Doug,

re:

[Hamilton] was a genius, but is, at the same time, roundly dissed by many lesser lights, on several accounts, especially for his attempt at poetry!

maybe sticking with math... ;-)

i'm not being terribly serious here, just trying to have a little fun with it. as i was with my quip about John's 'crazy idea' about light. i'd been considering the same thing so i have a frame of reference there. :-)

i notice Hamilton seems to have been most taken with '4', when the most notable feature of the tetraktys at first glance is the triangular configuration of which 4 is merely a subset of fairly equal value to 3, 2 and 1. curious.

looking into 'tetrakys' a little, i came across a devotional prayer of sorts in its praise (not written by Hamilton). there doesn't appear to be any counting in it.

re:

We get a distorted saw tooth wave that looks like it has hysteresis.

first thing that came to mind was Fourier Series, suggesting a compound wave formation - more than one function going on there. i'm not terribly strong on math and can't say i actually understand Fourier Series analysis of sine waves, but came across them looking for a solution to another trig problem (looking for a triangular wave form which i could control the specific angle of while translating it onto a curve - you'd think it would be easy. doing it as a mechanical drawing only took about a half hour, but coming up with a function... i've come close... forgot all about 'red shift' just trying to solve the illustration problem). i'm no expert, but Fourier Series might be useful in untangling threads there. you may well be aware of it already. (Fourier Series Sawtooth. there's other variations as well.)

re: the 1D pseudoscalar looking like molar teeth - sounds like a slight variation on a square wave - suggesting abrupt phase shifts of otherwise relatively constant states. since we don't have an electrical switch of any sort here, it's somewhat suggestive of Planck's discrete units...

sine wave's the easiest - you've got a frequency and an amplitude. but that's not terribly interesting or informative in itself. only in relation to the other two.

i've been looking at what you and Dr.D. are doing with interest. i like Einstein's work. i have the impression he may have quit a little too early, perhaps overcome with 'catastrophic success', as Bruce Springsteen has recently dubbed the condition, with his major contributions. it took him over 36 years to get around to looking at space, finally recognizing that it's got a remarkably long list of physical characteristics for 'nothing'. in Appendix A, added in the 1953 edition of his popular treatment of GR and SR, he talks a little about 'space'. arbitrarily placing a vector location in space and subtracting all extraneous influences, he concludes that what he has left is gravity.

a bit of a glimpse into how he thought about gravity.

what is gravity? something we don't appear to be able to see or find any particular particle for or any sort of 'radiation', but it's primary characteristic is that it imparts acceleration.

what is acceleration?

looks like ∆ to me.

x4=ict.

what is that? words... they can be remarkably troublesome.

looks like ∆ to me.

but then, i don't have any formal science training; all i can do is look at the patterns. looks like directional vectors to 'gravity' (innie and outie), emerging before 'time', instigating acceleration from which space, particles and time emerge (Einstein had said that matter is an extension of space). nicely accounts for observed relatively even distribution of matter in the universe, accounts for background microwave radiation without a big bang - it's just 'coming into existence' everywhere, we've got an 'innie' gravity, from here it looks like it's going backward in time accelerating outward (accounting for our local experience of the specific temporal arrow at a macro level and permitting light to manifest), dark matter's got an outie gravity, outwardly accelerating outward, so it doesn't clump together, can't be signaled from here (we'd say it's in the wrong time zone), light can't manifest, stays 'dark'. seems to nicely pull together a few loose ends.

but i don't have much of a science background. just looking at patterns, sort of like a jigsaw puzzle, how the pieces fit together or not. just having fun. i like puzzles.

our perceptions are fairly much a matter of pattern recognition. that's all we are capable of recognizing. we appear to be at the edge of the patterns here. that we are part of the patterns, what they spring from - what's behind them - seems beyond our physical ability even to contemplate. like asking what was before the 'big bang'.

matt.

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Thanks for the comments Matt. I’m just happy that there’s a way to analyze the motion of the pseudoscalars. It wasn’t apparent for a while how that the sine and cosine of changing angle could be used to describe the expanding/contracting pseudoscalars, but it turns out it works out well, especially since the expanding/contracting diameter of the sine is the reciprocal of the...

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Thanks for the comments Matt. I’m just happy that there’s a way to analyze the motion of the pseudoscalars. It wasn’t apparent for a while how that the sine and cosine of changing angle could be used to describe the expanding/contracting pseudoscalars, but it turns out it works out well, especially since the expanding/contracting diameter of the sine is the reciprocal of the expanding/contracting diameter of the cosine, the one moving horizontally across the circle, the other moving vertically.

Your suggestion for using the Fourier series is right on. Our immediate objective is to calculate the atomic spectra, and, now that we have a spectra (!) to work with, the Fourier analysis will be the first tool we will want to use. It was Heisenberg’s use of the Taylor series, following Kramer, which led him to the non-commutative multiplication that proved the key to quantum mechanics.

In the meantime, many people want to talk about cosmology more than particle physics, so I thought I would now turn the focus of the discussion in that direction. John’s comments are especially inviting. He makes some excellent observations, but to lay the groundwork for the cosmological implications of our RST-based theory, I need to explain the fundamentals of space/time, as the new physical datum, replacing zero in a spacetime framework, with the one of the tetraktys.

That the tetraktys can be related to gravity will no doubt be a surprise to many, but we first have to understand how those ten dots relate to the faith that the early Greeks had in the integers. For them, the dots of the tetraktys represented their cosmology; not only did it reflect a profound truth about the first four numbers of arithmetic, but within its mystery, the principles of harmony, physics, and geometry all came together into a unified whole, enabling them to teach the meaning of life through a knowledge of answers to foundational questions, something ‘que nos falta hoy dia.”

To the Greeks, the monad was the father of all, the dyad was the mother of all, and their union in the triad was completed in the tetrad. Not only were these numbers found in the proportions of fundamental harmony, but they also figured in a fundamental way in the secrets of physics (the motion of heavenly bodies - through mediato/duplatio) and geometry, as well. Until, that is, the incommensurables were uncovered. The incommensurables such as the square root of 2 seemed to destroy the faith these ancients had in the integers. That numbers could exist that were not ratios of integers did as much violence to the beauty and harmony of their cosmology as the singularities of today’s theories do to ours, and for the same reason: the discrete seems incompatible with the continuous, yet one cannot escape the compulsion to believe that because nature somehow reconciles the dichotomy, we should be able to do so too.

Einstein “plagued” himself over this, but had he and the Greeks realized the simple fact that nothing exists but motion, he would have easily overcome the difficulty. There is no incommensurable in the square root of 2, because, as any school child can discover, you can’t square two symmetrical objects; that is, you can’t arrange two symmetrical objects into anything but a line. No matter how hard you try, you can’t arrange them into a square pattern.

In the case of the unit triangle, it’s half of the unit square, but to understand the meaning of how the numbers of its sides relate to the number of its diagonal, it’s necessary to understand the fundamental nature of distance: Distance is simply the space aspect of one-dimensional motion, nothing else. The length of the diagonal, the hypotenuse of the triangle, can’t be drawn without BOTH space and time, or motion. But, as Newton clearly understood, the science of geometry has nothing to say about the origin of right lines and circles. They are input from without, based upon the science of non-geometric principles.

In the context of these principles of non-geometric science, the geometric fact that the square of the hypotenuse is the sum of the squares of the sides is relevant. What matters, in drawing the hypotenuse that geometry studies, is that space increases in a one-to-one ratio with the increase of time. If this ratio changes, the slope of the line changes. In the non-geometric context, the hypotenuse of the right triangle, with unit sides, represents the number 1, not the square root of 2.

This fact is the phenomenon responsible for the principle of relativity, or covariance. There is no independent reference frame based on a fixed location, a zero reference, from which to measure motion. Everything must relate to 1, the unit ratio of changing space and changing time, the 1:1 ratio of the unit sides that PRODUCES the hypotenuse of the right triangle.

When we start with the right triangle of unit motion, or what we will call unit motion, there are two, and only two, possibilities to alter the motion: If the changing space aspect of the unit motion oscillates, this produces a spatial reference point in which only time continues to increase uniformly, effectively collapsing the triangle to a vertical line. If the changing time aspect of the unit motion oscillates instead, this produces a temporal reference point in which only space continues to increase uniformly, effectively collapsing the triangle to a horizontal line.

We can easily plot this on a spacetime chart, plotting time vertically and space horizontally. As long as the 1:1 ratio is maintained, the change of space, as a function of the change in time, or vice versa, is the diagonal slope, what we can call the unit slope, but the slope changes to the vertical, or horizontal, if the change in one aspect, or the other, is effectively nullified by continuous oscillation, like a soldier marching in place, he goes nowhere, even though he continues to move his feet. We can say that he is just “spinning his wheels.”

Clearly, however, if instances of these two possibilities are combined, the result of the combination is unit motion, again, where the vertical change is contributed by the oscillating spatial component, and the horizontal change is contributed by the oscillating temporal component. These combinations will always move at unit speed along the diagonal relative to the temporal vertical line and the spatial horizontal line, which constitute fixed spatial, or temporal, reference frames relative to the diagonal, regardless of their position on the chart.

Small changes in the position of these fixed lines on the chart have little effect on the how the diagonals are plotted, while large changes will definitely affect it and so must be taken into account. One thing is clear, however: There is only one unit diagonal.

Every plot of ratios on the chart has to be equal to, greater than, or less than, this unit ratio. Thus, the values only range from the vertical (1:2 = zero effective spatial change) to the 1:1 ratio, or from the horizontal (2:1 = zero effective temporal change) to the 1:1 ratio. In numbers, we can write this range as a system of ratios: –0 à 1 ß +0, which, of course, is the inverse of the range: -1 à 0 ß +1, giving us a fundamental symmetry in which to work the laws of conservation.

In the former system of ratios, there is a continuous spectrum of magnitudes possible, analogous to the unit circle. In the latter system of ratios, the magnitudes form two, reciprocal, discrete numbers, which may be combined to form any discrete natural number. How these ratios give rise to irrational numbers is another, fascinating, story.

But that’s enough for now. I have to go paint a house, before it gets too cold, more on this later.

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Hello Doug,

Over at http://www.lrcphysics.com/trouble-with-physics/?currentPage=
2, your write, "John Baez is fascinated by the mystery of these numbers too, but, being in the midst of the “Madding Crowd,” he can’t see these eight 3D directions, as we are seeing them now. He sees them as Clifford first saw them,"

Does John Baez also reject Einstein's General Relativity and...

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Hello Doug,

Over at http://www.lrcphysics.com/trouble-with-physics/?currentPage=
2, your write, "John Baez is fascinated by the mystery of these numbers too, but, being in the midst of the “Madding Crowd,” he can’t see these eight 3D directions, as we are seeing them now. He sees them as Clifford first saw them,"

Does John Baez also reject Einstein's General Relativity and the fact that General Relativity is founded upon dimensions that can warp, bend, and move?

I am trying to grasp the meaning of your paper, but the fact that you reject Einsteins' GR makes it difficult to do so.

I understand that we live an an era where the Foundational Papers are being banned and deconstructed, and zero progress in physics has been institutionlized, but even so, rejecting Einstein's theory of General Relativity, which treats dimenisions as real, physical entities which can bend, warp, and move, seems rather extreme.

Your essay has received quite a lot of votes, so perhaps we can yet rid ourselves of Gravity, moving dimensions, and Einstein's General Relativity if enough people vote against it. I understand that Baez is in tight with the physics fanboy community, so seeing his name on your web-page is surely worth a few votes. But yet, it's hard to believe that there are that many people our there who oppose Einstein's General Relativity and dimensions that can bend, warp, amd move.

Einstein's General Relativity is founded upon a physical reality in which the *physical* dimensions can bend, warp, and move.

Your essay begins with, "The only observed relationship of time to space is a reciprocal relation, in the equation of motion. However, it seems absurd to think of space, defined as a set of points satisfying the postulates of geometry, as the inverse of time."

Now, if you are going to talk about time, space, and *geometry*, it makes little sense to refute Einstein's General Relativity--a well-tested *physical* theory which is built upon the fact that dimenions bend, warp, and move.

http://en.wikipedia.org/wiki/Tests_of_general_relativit
y

I hope that you get a chance to read Einstein's work "The Meaning of Relativity" and realize that General Relativity treats dimensions as *physical* entities with dynamical properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's The Meaning of Relativity

Particularly, I hope you get to read chapter XXVII: THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM

Also read CHAPTER XXVII, "In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made with the aid of clocks has by no means the same degree of plausibility in as in the special tehory of relativity."

Well Doug, I hope that you no longer deny the fact that as matter moves through space, it bends and twists the dimensions--and thus the dimensions can and do move.

Einstein himself states, in the Meaning of Relativity: "CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein

One of the fun things that MDT is doing is going on back to the foundational papers and showing how MDT agrees with all of them--with Einstein, Dirac, Newton, Teller, Galileo, Bohr, Schrodenger, Feynman--while so many modern physicists do not agree with the Greats, nor *physical* reality; as physical reality has a tendency to get in the way of fiat empires and postmodern groupthink tryannies.

Best,

Dr. E (The Real McCoy)

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I prefer to reserve this forum for the discussion of my essay. Therefore, I have posted responses to Dr. E’s and Narendra’s comments in their own respective forums, and prefer to discuss those issues there, rather than here.

However, in regards to how our RST-based theory of gravity relates to Einstein’s general relativity, or covariant theory, as applied to cosmology, and the...

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I prefer to reserve this forum for the discussion of my essay. Therefore, I have posted responses to Dr. E’s and Narendra’s comments in their own respective forums, and prefer to discuss those issues there, rather than here.

However, in regards to how our RST-based theory of gravity relates to Einstein’s general relativity, or covariant theory, as applied to cosmology, and the standard model, the easiest way to understand it is through the difference between the definition of distance-based space, which is the set of spatial (x, y, z) locations that satisfies the postulates of geometry, and the definition of motion-based space, which is the inverse progression of the time progression, s/t = c.

Obviously, distance is only a measure of the space aspect of past, or contemplated, motion; that is, d = s/t * t. In the case of the motion of objects, this is necessarily one-dimensional motion. In the case of radiation, it is motion in more than one dimension, but the motion, in all but one of the dimensions involved, the dimension of propagation, is oscillatory motion.

This leads to what is called electroweak symmetry breaking, when EM motion is measured relative to a fixed reference system, but in relativity theory, there is no fixed reference system. There are only relative inertial frames, so how do we measure the oscillation of a propagating photon in isolation, to see if it’s oscillating in only two dimensions, and not in the propagating dimension?

The only way an observer would be able to view an isolated photon in propagation is to be motionless relative to the photon, which requires the changing of the observer’s location at the speed of light, something impossible to do.

Yet, if it were possible to do this, as Einstein used to like to imagine it were, what would the observer’s speed be measured relative to? A stationary observer left behind? What, then, is the stationary observer stationary to? The departing moving observer?

Clearly, if the observer traveled with the photon, for a given unit of time, and then reversed course and traveled back to the stationary observer, at the same speed, the distance required to travel back to the stationary observer would have to be equal to the distance traveled out from the observer, which would equal half of the distance traveled by the photon, in the same amount of time.

Hence, in the time traveled by the photon, the total distance traveled by the moving observer is the same as the distance traveled by the photon, even though the distance between the stationary and the moving observers would be zero, while the distance between their location and the photon would be equal to the total distance traveled by the moving observer, out and back, in the same amount of time.

Certainly, we can represent these relative magnitudes of space, time and motion mathematically, and plot them on a graph. The speed of the moving observer and the photon is the same, c-speed. The distance traveled by the moving observer is the same as the distance traveled by the photon, but the direction reversal by the moving observer reduces the effective distance traveled, relative to the stationary observer, to zero. Yet, if we divide the time and distance traveled by the photon in half, it will equal the time and distance traveled by the moving observer in two directions. Therefore, the ratio of time to distance is the same, 2/2, in both cases, but in terms of the moving observer’s roundtrip, it took two halves of the total time to complete the trip, or a ratio of 1 roundtrip to 2 halves of the total time traveled by the photon.

Now, instead of changing his location in space, what if the observer could change his location in time, in order to observe the propagating photon? To do this requires a stationary observer, but one stationary in time, not stationary in space, in order to measure the distance traveled by the moving observer and the photon in terms of temporal distance.

In this case, time would necessarily be defined as a set of temporal locations (x, y, z) satisfying the postulates of temporal geometry, and the speed of the photon would be defined as time per unit of space, t/s, instead of space per unit of time, s/t. The temporal distance between locations would then be a measure of the time aspect of the motion of an “object,” given by d = t/s * s, which is, again, necessarily one-dimensional distance, in the case of the motion of these temporal “objects.”

And, again, in the case of radiation, it is motion in more than one dimension, but the motion, in all but one of the dimensions involved, the dimension of propagation of the photon, is oscillatory motion. Thus, nothing has changed, except for the inversion of s/t to t/s.

Using the same analysis as before, then, we see that, again, the ratio of the time to distance, in terms of the moving observer’s roundtrip, is 1 trip per two halves of the total temporal distance traveled by the photon. The ratio of temporal distance to space traveled by the photon is the same as the ratio of spatial distance to time in the former case: It is 2 units of temporal distance per 2 units of space, t/s = 2/2, which of course is unit speed in both cases.

So, what does this ansatz teach us, besides the perfect symmetry of space/time? Does it not teach us to distinguish between “space” as distance, and space entering into the speed of the photon? The fact that the temporal distance traveled by the moving observer in one roundtrip is equal to the temporal distance traveled by the photon in the same amount of space, and the spatial distance traveled by the moving observer in one roundtrip is equal to the spatial distance traveled by the photon in the same amount of time, are just the inverses of one another, suggests the possibility that time can be thought of as three-dimensional, as well as space, in the laws of motion.

The only difference is that, relative to the other, the moving observer’s one-dimensional roundtrip, out and back, in one system, appears four times the “speed” of the other, no matter which system is selected as the reference, because the inverse of the magnitude of the space/time ratio 1/2 = .5 is four times the inverse time/space ratio 2/1 = 2, and vice versa.

Of course, the implications of this symmetry are that there is a law of conservation associated with it, and that FTL limitation of objects only applies to objects with spatial extent. It would not apply to objects with temporal extent. But what in the world would an object of temporal extent be, anyway? Stay tuned for some thoughts on that, but in the meantime, it’s important to note that there is no conflict with the concept of relativity theory’s spacetime, as a four-dimensional continuum, and the concept of four-dimensional space/time, since the former is merely generated by the latter, when the idea of temporal and spatial distances are understood.

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Doug,

You write,

"What I have a problem with is your use of Einstein’s concepts to justify your confused notion that the DIMENSIONS of spacetime are warped, bent and moved. Notice that, no matter how hard you try, you will not be able to find Einstein saying that the DIMENSIONS of spacetime are warped, bent or moved."

This is getting funny.

In THE MEANING OF...

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Doug,

You write,

"What I have a problem with is your use of Einstein’s concepts to justify your confused notion that the DIMENSIONS of spacetime are warped, bent and moved. Notice that, no matter how hard you try, you will not be able to find Einstein saying that the DIMENSIONS of spacetime are warped, bent or moved."

This is getting funny.

In THE MEANING OF RELATIVTIY, Einstein writes, "the geometrical properties of space are not independent, but they are determined by matter." Egro mass bends spacetime dimensions. Ergo spacetime dimensions bend and move.

And this is backed by empirical evidence:

http://en.wikipedia.org/wiki/Tests_of_general_relat
ivity

As a mass moves through space, it warps and bends the dimensions. The dimensions bend and move around it.

I hope that you get a chance to read Einstein's work "The Meaning of Relativity" and realize that General Relativity treats dimensions as *physical* entities with dynamical properties.

"CHAPTER XXXII: THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY: According to the general theory of relativity, the geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe only if we base our considerations on the state of matter as being something that is known." --Einstein's The Meaning of Relativity

Here is an awesome video, starring David Duchovney playing Brian Greene, in which you can see the dimensions moving!

http://www.youtube.com/watch?v=0rocNtnD-yI

Start it at 6:15. When the sun is introduced onto the spacetime at approx 6:22, watch the dimensions move! This is produced by Columbia University, NSF, and one of the world's leading string theorists! Surely they would not mislead us about moving dimensions!

Then watch the Harvard physicist talk, and at around 6:35, you can see that as the earth moves through spacetime, it stretches the dimensions! Ergo dimensions can move!

Then, my favorite part--at 7:20 David Duchovney makes the sun dissapear! And how the dimensions move and then some! Look at the dimensions bending, warping, and moving!

And then, at about 0:36 into this next video, watch the dimensions themselves bend and move as the masses move through them!

http://www.youtube.com/watch?v=fxwjeg_r5Ug&feature=rela
ted

And if ths sun ceased to exist, watch what would happen to the dimensions--they would warp, bend, and move!

http://www.youtube.com/watch?v=T884m5_QzWM&feature=rela
ted

And check out the movement of the dimensions around two oribiting stars!

http://www.youtube.com/watch?v=sUyrPDmh4rI&feature=rel
ated

As you might know, Joseph Taylor won the Nobel Prize for observing such orbiting stars and finding more experimental evidence supporting the fact that dimensions can bend, warp, and move! I had Taylor for experimental physics at Princeton, but did not know that his middle name is Hooton:

http://en.wikipedia.org/wiki/Joseph_Hooton_Taylor_Jr.


"Taylor has used this first binary pulsar to make high-precision tests of general relativity. Working with his colleague Joel Weisberg, Taylor has used observations of this pulsar to demonstrated the existence of gravitational radiation in the amount and with the properties first predicted by Albert Einstein. He and Hulse shared the Nobel Prize for the discovery of this object."

Again, this is kindof boring after all the cool animations above with David Duchovney, but you can see how the earth would curve spacetime--how it would make the dimensions curve and move, as it revolved about the sun, tramping through spacetime.

http://en.wikipedia.org/wiki/Spacetime

http://commo
ns.wikimedia.org/wiki/Image:Eclipse-test-of-relativity.jpg

Pl
ease do not ignore this experimental evidence and all of Einstein's hard, grueling work in developing General Relativity, by stating that "dimensions" cannot bend, warp, and move. It is rather insulting, when you think about it, to Einstein. GR demonstrates irrefutably that dimensions are capabale of motion and that dimensions move.

If you really, really believe that "dimension is an adjective," I would encourage you to free your mind by reading about General Relativity, starting with Einstein's The Meaning of Relativity and progressing to:

http://www.amazon.com/Gravitation-Physics-Charles-W-Misne
r/dp/0716703440/

http://www.amazon.com/Journey-Gravity-Spacet
ime-Scientific-American/dp/0716760347/ (I highly recommend this book Doug! It is writen for laymen and a more general audience & too, my name is in the acknowledgements--the only time I have ever shared a paragraph with Einstein--haha)

You are refusing to watch, listen, think, read, and understand; preferring word games, and yet, I have faith that you might grasp the fact that dimensions can bend, warp, and move!

"According to Einstein's general theory of relativity, mass and energy warp spacetime. The undulations then affect the trajectories of passing objects, producing the effects we call gravity. In Einstein's theory, spacetime is a stretchy, dynamical entity." --http://focus.aps.org/story/v14/st13

Spacetime is a dynamical entity in Einstein's theory. Ergo, dimensions move.

So it is that MDT is small extension of something we already knew! The fourth dimension is expanding relative to the three spatial dimensions at c, in units of the Planck length!

With an heroic spirit, MDT takes us back to origin of modern physics--to the original papers on relativity and QM, and it humbles itself upon that mountaintop. And when it comes on down, off the shoulders of relativity and QM's giants, MDT presents us with a fundamental view of reality that conforms to all experimental evidence, while not only resolving the paradoxes of the non-locality of the EPR effect and seemingly frozen time in Godel’s block universe, but also unifying the resolution of both physical curiosities within a simple physical postulate--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. In a sense, this is the first theory to predict QM's nonlocality and entanglement, by postulating that the fourth dimension is inherently nonlocal via its expansion--an empirical fact that the timeless, ageless, nonlocal photon agrees with, as the photon surfs the fourth expanding dimension. And not only does MDT predict this, but it also provides a *physical* model for entropy and time and all its arrows and assymetries throughout all realms. And finally, all of relativity may be derived from MDT's simple postulate, as it is in my paper--the fourth dimension is expanding relative to the three spatial dimensions--dx4/dt = ic. A postulate and an equation representing a novel *physical* feature of our universe--a fourth expanding dimension--and the natural, subsequent prediction of all of relativity, qm's nonlocality, entropy, time's arrows and assymetries in all realms, and quantum entanglement.

The great thing about Moving Dimensions Theory is that it allows us to keep all of relativity while also granting us free will and liberating us from the block universe.

Wish I could buy everyone a beer to celebrate our newfound free will! Perhaps now they can no longer argue that string theory and loop quantum gravity are our fate for the next four thousand years, as they are pre-embedded in the future of our block universe.

And too, in addition to exploding the block universe myth and unfreezing time, MDT provides a *physical* model accounting for change, entropy, relativity, quantum mechanics' nonlocality and entanglement, and time and all its arrows and assymetries across all realms. Furthermore, Huygens' principle, which manifests itself in all realms from classical waves to Feynman's many-paths interpretations of quantum mechanics, is given a deeper foundation--a raison d'etre--a fundamental source--and this is the same fundamental source underlying relativity and quantum mechanics' nonlocality and thus QM's probabilistic nature, as the fourth expanding dimension distributes locality.

MDT's great uniter and unifier is a fundamental invariant of the universe that has hitherto been unsung--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic.

Too, too many postmodern theories suggest that we should get rid of time, free will, nonlocality, causality, change, and even space! Yes--too, too many modern theories suggest that we should get rid of *physics* and *physical reality*, so that we can keep funding bureuacracies! Too, too many postmodern physicists have long ago given up trying to explain entanglement, nonlocality, entropy, and time and all its arrows and assymetries with a *physical* model. Too, too many physicists have chosen to ignore Godel's problems with the block universe and time, while losing the sense of wonderment when considering action-at-distance, nonlocality, and the EPR Paradox.

"The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed." --Albert Einstein

Yes--entanglement, entropy, time, nonlocality, Huygens' Principle, relativity--how mysterious are all these! And yet if you ask foundational questions such as *why* entanglement, *why* entropy, *why* time, *why* nonlocality, *why* Huygens' Principle, *why* relativity, the richest, wealthiest establishment in the history of physics, which also happens to be the establishment which has contributed the least (perhaps money cannot buy physics and philosophy?), sends forth anonymous postdocs and grad students to launch the snarky, ad-hominem attacks they perfect under the guidance of their pseudo-physicist political mentors.

But hey--everyone's got to make a living.

Behold MDT--the great unifier and invariant source underlying all these *physical* phenomena--in relativity and quantum emchanics--in statistical mechanics and entropy.

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Narendra,

I’m sorry. I didn’t mean to ignore your specific questions. It’s only a matter of available time and energy that I must prioritize. You wrote:

“1. Your basis of discussing Physics is based purely on fundamental mathematics, using scalars, pseudoscalars and their extension on the physical symmetry considerations. Thus, you attempt to provide geometrical...

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Narendra,

I’m sorry. I didn’t mean to ignore your specific questions. It’s only a matter of available time and energy that I must prioritize. You wrote:

“1. Your basis of discussing Physics is based purely on fundamental mathematics, using scalars, pseudoscalars and their extension on the physical symmetry considerations. Thus, you attempt to provide geometrical representations for the fundamental particles. You then convert physical parameters into dimensionality numbers in dealing with fundamental physics. In short your hope is to describe physical phenomenon/processes in terms of frequencies of vibrations of space-time dimensions that implicitly involve

mass/energy and the interaction force-fields!

To me, Maths in Physics is a mere tool and certainly not a dictating factor. Observations and experimental facts control the conditions that govern mathematical parameters/expressions, not the other way around!”

I completely agree with you, but the mathematics enables us to formulate the relationships of space and time, which can get quite complicated. In terms of physical processes, historically we have had to add mass to the dimensions of space and time in order to formulate the fundamental laws of physics.

This is because, even though we know that f = ma can be written in terms of space and time only, so that t/s^2 = t^3/s^3 * s/t^2, we don’t know how to write 2(t/s^2) = 2(t^3/s^3) * s/t^2, since we can’t equate the kilogram units to space and time units.

So, what I’m doing with “scalars, pseudoscalars and their extension on the physical symmetry considerations,” is trying to change that,

You wrote:

“2.You have stopped far short of discussing any physical process or phenomenon in your model developed thus far. I doubt if you can go much further this way.”

The most difficult challenge I faced was what to put in a 5000-word essay. I chose to write about the mathematical aspects, because that’s easiest to succinctly communicate in context, but that doesn’t mean that there wasn’t a whole list of physical processes that I would have dearly loved to include.

You wrote:

“3.Physics thus far has developed on the basis of precepts and concepts that are physical in nature and not mathematical to start with. Mathematical expressions follow the conceptual picture one evolves after due considerations of observations/measurements available and intuitive and critical assessment of the same.”

True, but this has always been out of necessity, because the intuitive basis for mathematics that match the physics have been missing from science, due to the dichotomy between discrete numbers and continuous magnitudes. It appears that the new system finally promises to resolve this difficulty, so it can begin with the math.

You wrote:

“4. In my view, your mystic of four is a special case of Mathematical involvement, devoid of physical conditions prevalent to discuss the physical universe and processes undergoing therein. It is more a dream and less of reality or may i say, relative truth as seen in scientific phenomenon.”

As already explained above, this only appears to be the case, because the mathematical principles serve to introduce the physical principles, which is an unfamiliar approach, because it has never been possible to do it before. The fundamental “physical conditions prevalent to discuss the physical universe and processes undergoing therein,” starts with harmonic motion, in the new system, just as it does in the case of familiar physics.

I hope this helps. I certainly didn’t mean to imply that your inquisitiveness is “’childish’ foolishness.” To the contrary, I very much appreciate your questions.

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Doug,

"In other words, it’s not until the second measurement is made that the past has any meaning. A series of measurements in the present defines the past, which otherwise not only remains undefined, but undefinable."

So we are basically describing the same thing, that the past emerges from the present. We don't know what is going to happen, until it does, then it recedes into...

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Doug,

"In other words, it’s not until the second measurement is made that the past has any meaning. A series of measurements in the present defines the past, which otherwise not only remains undefined, but undefinable."

So we are basically describing the same thing, that the past emerges from the present. We don't know what is going to happen, until it does, then it recedes into the past.

"I think it does make some sense, but I don’t know how to work with it. In my development of an RST-based theory, the present doesn’t materialize as an event, until a measurement is made, and since the measurement potentially can be made at any point on the surface of the expanding pseudoscalar, the path from the past to the present doesn’t materialize until the measurement in the present is made in relation to a past measurement."

The relationship between the digital and the analog is a matter of perspective. It is impossible to measure anything, unless there are distinctions, but unless these differences have a fundamental connection, then it is equally impossible to describe their relationship.

"With two events, it is impossible not to define the line between them,"

What if they simply have no connection, are in alternate universes, not recorded, etc. That's where the analog unity is essential.

"But what is just mind boggling to my mind is that there is no way to define the future or the past with a succession of measurements on the progression, since if one waits long enough between measurements, the possibility exists that any two or more measuring events can spatially coincide!

This means that distance cannot be definitely correlated with the passage of time, nor that spatial proximity can be confidently correlated with temporal proximity. The implications of this are immense, but inescapable. Causality is not sacrificed, it’s just that it is indeterminate!"

You are describing why a purely digital reality is impossible.

I've been trying to make a point to Dr. E, with his MDT, that as Einstein described the speed of light as the constant, then it is what we think of as this three dimensional reality which is shrinking, ie, receding into the past. Since all that really exists is this field of energy, whether it is traveling in relatively straight lines as light, or bound up in nuclear mass, it's still the same energy field, so the very concept of this four dimensional reality is borderline illusionary as the three dimensional space coordinate system is dependent on a speculative center point that is receding into the past along with the frame it anchors. It doesn't seem this way, as we function as the neural centerpoint of our own reality, but given the overwhelming nature of this field, our minds function by quantizing thoughts into a series, like frames of film, otherwise it's a blurr of energy. So our thinking requires this distinct series of thought, but the process is continuous. Think in terms of a factory; The product goes from beginning to end, while the production line faces the other direction, consuming raw material and expelling finished product. Our minds are a process of consuming raw information and expelling the quantized units of thought. When we are young, time seems to move very slowly, as we need to accumulate more information to form each thought and they seem disconnected. When we get older, the thoughts happen much faster, as each grows from the previous, so they are much more linear and connected. It is only when we develop this connection between thoughts that memory starts.

Taking it a step deeper, raw consciousness rides this wave of energy, while the process of thinking is that collapsing wave of the past. We exist, like individual thoughts, being formed from this raw consciousness, then collapse into ever more structured thinking, until, like a hardened crust, we can no longer grow with this wave and peel away into the past. Yet without a structured past, the future would be equally featureless. So mortality is essential to creating life. It cannot grow, unless it consumes the essence of the past.

Knowledge is that digital information receding into the past, while consciousness is that analog awareness proceeding into the future. When we loose that connection between thoughts, we lose the memory that came when the connection first developed.

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In the latest post in his forum, Philip Gibbs writes:

“A central idea of the thesis in my essay is that symmetry is still important in going beyond our current understanding of physics. Actually it is a dual message. One half of it is that time reversal symmetry (or CPT at least) should not be ignored in deeper theories of quantum gravity or cosmology. In other words we should not be...

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In the latest post in his forum, Philip Gibbs writes:

“A central idea of the thesis in my essay is that symmetry is still important in going beyond our current understanding of physics. Actually it is a dual message. One half of it is that time reversal symmetry (or CPT at least) should not be ignored in deeper theories of quantum gravity or cosmology. In other words we should not be looking at models where temporal causality running in one direction is fundamental. The other half is that there is a huge gauge symmetry in string theory that includes all other known symmetries in physics including spacetime symmetries.”

The reason that this latter half is important is that it is precisely what superstring theory is missing. It is the lack of this super, over all, symmetry that M theory implies, but does not explicitly define, in terms of “a universal group that could encompass all these symmetries as subgroups.”

This inability to find the gigantic group of string theory, if you will, has led many physicists to forsake the faith in applying symmetry principles to theoretical physics, but not Philip, who asserts that if “you redo string field theory starting from a discrete set of events,” the problem can be solved. The discrete set of events comes from Philip’s principle of “event-symmetric spacetime,” leading to event-symmetric physics and cosmology that explains the universe in terms of a phase transition of spacetime, in which a gas of interacting strings condenses into continuous spacetime.

Thus, the principle of event-symmetry can be applied to develop a quantum theory of gravity through string theory, because it supplies the all-embracing symmetry that superstring theory lacks. Gibbs explains in his essay:

“It would be natural to try to explain the underlying structure of string theory using principles of symmetry. This would put it on an equal footing with general relativity and gauge theories that have been successful in the past. Yet the search for the symmetries of string theory has been abandoned by string theorists some time ago. It has been said that dualities in string theory show that symmetries are not of fundamental importance because different dual formulation have different symmetries. Yet the dualities themselves contain groups of self dual structures. The challenge is to understand why the unknown overall symmetry breaks in different ways.”

Gibbs goes on to outline the intricacies of various mathematical approaches that have been explored in connection with this challenge, culminating in the M(atrix) theory model of M theory, a form of which can be used to develop the “event-symmetric string field theory,” which includes a “superlie algebra” generating the symmetry of the theory.

His argument for preserving the role of symmetry in answering fundamental questions is persuasive. As he shows in his paper, historically it has always been the case that our intuitive view of reality is expanded, only when we discover the underlying symmetry that was hiding in our former view of the world. Applying this to the asymmetry in the arrow of time, it’s a good bet that our view of reality will once again be expanded, when we discover that, like before, the asymmetry of time is only an illusion produced by our limited perspective. He writes:

“Our experience also tells us that time proceeds in one direction from past to future and not in reverse. The laws of physics at the subatomic level tell us that this rule is not fundamental. Once again it is only a local effect which may not be supported on the largest scales of the universe.”

However, he then concludes, like practically everyone else in our world, that the origins of the arrow of time “are found in the large cosmological singularity that we know as the big bang.” Nevertheless, unlike most other theoretical physicists, he finds “in these extreme corners of spacetime a huge symmetry shapes the universe bringing order to the flow of information. Far beyond the horizon of our observable region in the cosmos there may be other singularities some of which push the flow of time in the opposite sense. [If so,] temporal causality as an explanation of our existence must be abandoned.”

I added the “if so,” because that’s how I read what he is saying here. In other words, as Carlo Rovelli also asserts, we must “forget time.” Gibbs concludes:

“The universe must be described by a vast ensemble of events devoid of spacetime structure. These events are linked by a web of possibilities allowed by the huge underlying of symmetry of string theory. Time emerges only because a solution fits in which the Lorentzian signature of spacetime prevails.”

This suggestion that the fundamental symmetry of spacetime demands that, since the flow of time is connected with a single event in the past, then it must be connected somehow to another single event, beyond our event horizon, in which the events of time flow in the opposite direction, contrasts sharply with the fundamental symmetry principle introduced in my own essay.

In an RST-based theory, the fundamental symmetry of the universe, hidden from our view by the arrow of time, is the symmetry of the space and time progression itself. From this simple relation, not only does spacetime emerge, but matter and radiation as well. However, the asymmetry of the arrow of time in an RST-based theory does not proceed from a primordial, universal, singularity, in a manifestation of global symmetry, but from many instances of a local oscillation in a global symmetry, a reverberation, a fundamental vibration, combined and multiplied in a myriad of ways, out of which proceeds a greater and more complex collection of local symmetries and dualities.

But nevertheless and notwithstanding this, I really like Philip’s essay.

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Hello Doug,

I'm not sure if you have been keeping up with the literature, but String Theory isn't really a physical theory, nor is M Theory. Five years ago you might have won a first place prize simply by talking about them, but after thirty years of doing nothing to advance physics, String Theory and M Theory are on their way out.

And "Symmtrey" as an oft abused notion, as Nobel...

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Hello Doug,

I'm not sure if you have been keeping up with the literature, but String Theory isn't really a physical theory, nor is M Theory. Five years ago you might have won a first place prize simply by talking about them, but after thirty years of doing nothing to advance physics, String Theory and M Theory are on their way out.

And "Symmtrey" as an oft abused notion, as Nobel Laureate Robert Laughlin reminds us in A DIFFERENT UNIVERSE: "Symmetry is an important, if often abused, idea in physics. An example of symmetry is roundness. Billiard balls are round, and this allows one to make some predictions about them without knowing exactly what they are made of, for example they will roll in straight-line paths across the table when struck with a cue. But roundness does not cause them to move. The underlying laws of motion do that.. . For this reason there is a tradition in physics of ascribing to symmetries an overriding importance even though they are actually a consequence, or property, of the equations of motion."

What Moving Dimensions Theory accomplishes is to provide an underlying *physical* mechanism for time and all its arrows across all realms. MDT weaves change into the fundamental fabric of spacetime with dx4/dt=ic, where change needs to be, as change pervades every realm of physics, for without change, no measurement can be made!

MDT's simple postulate--the fourth dimension is expanding relative to the three spatial dimensions at c--shows that the fixed velocity of light emerges from a deeper principle--photons are but matter that surf the fourth expanding dimension.

http://fqxi.org/community/forum/topic/238

Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

It is interesting that Einstein introduced relativity as a principle--as a primary law not deduced from anything else.

Well, I guess I was dumb enough to even ask, "why relativity?"

And I found the answer in a more fundamental invariance--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. Change is fundamentally embedded in space-time. And not only can all of relativity be derived from this, but suddenly we had a *physical* model for entropy, time and its arrows and assymetries in all realms, free will, and quantum nonlocality and entanglement. MDT accounts for the the constant speed of light c--both its independence of the source and its independence of the velocity of the observer, while establishing it as the fastest, slowest, and only velocity for all entities and objects moving through space-time, as well as the maximum velocity that anything is measured to move. And suddenly we see a *physical* basis for E=mc^2. Energy and mass are the same thing--it's just that energy is mass caught upon the fourth expanding dimension, and thus it surfs along at "c."

On page 37 of "Einstein's Mistakes, The Failings of Human Genius," by Hans Ochanian, we read,

"Einstein acknowledged his debt to Newton and to Maxwell, but he was not fully aware of the extent of Galileo's fatherhood. In an introduction he wrote for Galileo's celebrated Dialogue Concerning the Two Chief World Systems, he faults Galileo for failing to produce a general mathematical proof. Galileo regarded relativity as an empirical, observational fact, that is, a law of nature, and Einstein's own formulation of the Principle of Relativity three hundred years later imitated Galileo's in treating this principle as a law of nature and not as a mathematical deduction from anything else."

Well, MDT provides a more fundamental law--a hitherto unsung universal invariant--with an equation: dx4/dt = ic, from which relativity is derived in my paper. And an added benefit are all the other *physical* entities dx4/dt=ic accounts for with a *physical* model, from Huygens' principle to entropy to quantum entanglement and nonlocality to time and all her arrows and assymetries.

"Rebellion to Tyrants is obedience to God"--Thomas Jefferson and Benjamin Franklin

And String Theory and M-Theory have devolved into snarky, physicless, handwaving tyrannies.

I expect MDT to bring additional boons for years to come!

It is certainly a greater theroy, with far more ranging consequences, than String Theory and LQG.

The first page of String Theory in a Nutshell states in a footnoted sentence:

THE CASE FOR STRING THEORY:

String Theory has been the leading candidate over the past two decades for a theory that consistently unifies all the fundamental forces of nature, including gravity. It gained popularity because it provides a theory that is UV finite.(1)

The footnote (1) reads: "Although there is no rigorous proff to all orders that the theory is UV finite, there are several all-orders arguments as well as rigorous results at low-loop-order. In closed string theory, amplitudes must be carefully defined via analytic continuation, standard in S-matrix theory. When open strings are present, there are diveregences. However, they are interpreted as IR divergences (due to the exchange of massless tsates) in the dual closed string channel. They are subtracted in the "Wilsonian" S-matrix elements."

So you see, String Theory is not a finite theory, but this is generally kept to the footnotes, when mentioned at all.

A lot of Nobel Laureates have problems with String Theory:

""WE DON'T know what we are talking about." That was Nobel laureate David Gross at the 23rd Solvay Conference in Physics in Brussels, Belgium, during his concluding remarks on Saturday. He was referring to string theory. . ." --http://www.newscientist.com/channel/fundamentals/mg1882529
3.700

It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself." -Einstein to Paul Ehrenfest

String theorists don't make predictions, they make excuses. -Richard Feynman, Noble Laureate

String theory is like a 50 year old woman wearing too much lipstick. -Robert Laughlin, Nobel Laureate

Actually, I would not even be prepared to call string theory a "theory" rather a "model" or not even that: just a hunch. After all, a theory should come together with instructions on how to deal with it to identify the things one wishes to describe, in our case the elementary particles, and one should, at least in principle, be able to formulate the rules for calculating the properties of these particles, and how to make new predictions for them. Imagine that I give you a chair, while explaining that the legs are still missing, and that the seat, back and armrest will perhaps be delivered soon; whatever I did give you, can I still call it a chair? -Gerard `t Hooft, Nobel Laureate in String Theory

"It is tragic, but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. So when one person spends 30 years, it's a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious." -Sheldon Glashow, Nobel Laureate

"I don't like that they're not calculating anything. I don't like that they don't check their ideas. I don't like that for anything that disagrees with a n experiment, they cook up an explanation-a fix-up to say, "Well, it might be true." For example, the theory requires ten dimensions. Well, maybe there's a way of wrapping up six of the dimensions. Yes, that's all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there's no reason whatsoever in superstring theory that it isn't eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn't produce anything; it has to be excused most of the time. It doesn't look right." -Richard Feynman, Nobel Laureate in Physics

"But superstring physicists have not yet shown that theory really works. They cannot demonstrate that the standard theory is a logical outcome of string theory. They cannot even be sure that their formalism includes a description of such things as protons and electrons. And they have not yet made even one teeny-tiny experimental prediction. Worst of all, superstring theory does not follow as a logical consequence of some appealing set of hypotheses about nature. Why, you may ask, do the string theorists insist space is none-dimensional? Simply because string theory doesn't make sense in any other kind of space." --Sheldon Glashow, Nobel Laureate in Physics

Even String Theory's founder, Michio Kaku, has problems with the theory: "The great irony of string theory, however, is that the theory itself is not unified. To someone learning the theory for the first time, it is often a frustrating collection of folklore, rules of thumb, and intuition. (IN OTHER WORDS IT IS NOT PHYSICS!!!) At times, there seems to be no rhyme or reason for many of the conventions of the model. For a theory that makes the claim of providing a unifying framework for all physical laws, it is the supreme irony that the theory itself appears so disunited!!"

Chapter 1. Path Integrals and Point Particles: Why Strings?

" --"Introduction to Superstrings and M-Theory," page 5. -Michio Kaku

"If Einstein were alive today, he would be horrified at this state of affairs. He would upbraid the profession for allowing this mess to develop and fly into a blind rage over the transformation of his beautiful creations into ideologies and the resulting proliferation of logical inconsistencies. Einstein was an artist and a scholar but above all he was a revolutionary. His approach to physics might be summarized as hypothesizing minimally. Never arguing with experiment, demanding total logical consistency, and mistrusting unsubstantiated beliefs. The unsubstantial belief of his day was ether, or more precisely the naïve version of ether that preceded relativity. The unsubstantiated belief of our day is relativity itself. It would be perfectly in character for him to reexamine the facts, toss them over in his mind, and conclude that his beloved principle of relativity was not fundamental at all but emergent-a collective property of the matter constituting space-time that becomes increasingly exact at long length scales but fails at short ones. This is a different idea from his original one but something fully compatible with it logically, and even more exciting and potentially important. It would mean that the fabric of space-time was not simply the stage on which life played out but an organizational phenomenon, and that there might be something beyond." -A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.

"[String Theory] has no practical utility, however, other than to sustain the myth of the ultimate theory. There is no experimental evidence for the existence of strings in nature, nor does the special mathematics of string theory enable known experimental behavior to be calculated or predicted more easily. Moreover, the complex spectroscopic properties of space accessible with today's mighty accelerators are accountable in only as "low-energy phenomenology"-a pejorative term for transcendent emergent properties of matter impossible to calculate from first principles. String theory is, in fact, a textbook case of Deceitful Turkey, a beautiful set of ideas that will always remain just barely out of reach. Far from a wonderful technological hope for a greater tomorrow, it is instead the tragic consequence of an obsolete belief system-in which emergence plays no role and dark law does not exist."

-A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.

MDT delivers an ultimate theory, whereas Loop Quantum Gravity and Sring Theory only sustain a myth of an ultimate theory. And thus we are commanded from on high--from the pinnacles of the ani-theory regimes--to ignore MDT and Nobel Laureates such as Robert Laughlin, F.A. Hayek, Feynman, Einstein, Planck, and others I quote above. Welcome to the dark ages.

I apologize for the length of this post, but I am working on a book: HERO'S JOURNEY PHYSICS: FROM BRUNO, TO GALILEO, TO EINSTEIN--AND YET IT MOVES!

Best,

Dr. E (The Real McCoy)

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Elliot,

I don’t know why you keep insisting on using the forums for other people’s essays to discuss MDT, even though you have been asked repeatedly and politely to cease and desist.

I’ve told you before, the fact that time and space are expanding is a very good bet, but to say that x4 is a moving dimension, without saying a dimension of what, and making it expand over time is...

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Elliot,

I don’t know why you keep insisting on using the forums for other people’s essays to discuss MDT, even though you have been asked repeatedly and politely to cease and desist.

I’ve told you before, the fact that time and space are expanding is a very good bet, but to say that x4 is a moving dimension, without saying a dimension of what, and making it expand over time is just nonsense, and everyone but you knows it.

For this reason, I don’t want to discuss the claims you make for MDT in your own forum, let alone in my forum.

If you want to discuss my understanding of the nature of time, as the reciprocal of expanding space, then, by all means, let’s do it. In an RST-based theory, x4, is the fourth time variable. It is a scalar expansion, the reciprocal of the 1D, 2D and 3D pseudoscalar expansion. However, there’s no need to equate it to ict. Einstein did this in order to equate Minkowski spacetime with expanding Euclidean space. The i variable serves to make the term negative in the Pythagorean equation, which, in turn, is used to define the radius of expansion. When ict is squared, as used in the Pythagorean equation, i makes the whole term negative, rotating it on the number line effectively equating the time expansion with the space equation.

But there is no need to do this to understand the expansion itself. The radius of a c expansion will always be c times t, the time of the expansion. But to specify the same point to which the radius is measured from the origin, on the surface of the expanding sphere, in terms of x, y, z, coordinates, the base and height of the Pythagorean triangle, corresponding to the radius, which constitutes the hypotenuse, cannot be 1, when the radius is 1. These two magnitudes will always be less than 1, when r = 1.

Or else, if they are set to 1, then the radius, r, must be > 1. This indisputable mathematical fact gives us two choices for defining a unit expansion: One choice constitutes the real circle, corresponding to r = 1, while the second choice constitutes the complex circle, corresponding to r = a + bi = 1. Einstein’s field theory uses the first, while quantum field theory uses the second, as the basis of their respective physical theories.

What my essay discusses is that there exists a mathematical symmetry, consisting of these two circles and the inverse of the real circle, with radius r = 2. That the symmetry underlies a field, consisting of the group of integers, under addition, and the rationals, under multiplication, is very important, because it means that an algebra exists that the operations of addition, subtraction, multiplication and division (except division by zero) may be performed in a way that satisfies some familiar rules from the arithmetic of ordinary numbers.

This puts us in the integral domain, or what’s known as a commutative ring, which is important, because there are no zero divisors in it! Thus, if we can identify physical entities, with these mathematical entities, we accomplish a great deal, as can be understood from what has already been said: particle theory suffers from non-dimensional points, string theory from extra-dimensional loops.

The theoretical physics of matter, of particles, charges and spins, defines the relationship of these in terms of fixed spacetime. The theoretical physics of gravity defines the relationship of it and matter in terms of dynamic spacetime, but even if this incompatibility were overcome, the fact would remain that properties of particles, charges, and spins have to be put into the theory, making it in the end, “ugly, unsatisfactory and ad hoc,” as Hawking puts it, as a unified theory.

What I would like to discuss in this forum are the merits, or lack thereof, of this approach, not the consequences of rotating light-speed by ninety degrees (i.e. ic), which is something that, to me, is not even wrong enough to argue about it, with all due respect.

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Physics Nick,

Are you a sock puppet? Your writing style and sentiment are so close to Elliot’s that it’s difficult to tell you apart. In fact, I will assume that you are the same, unless you care to identify yourself and give me some reason to believe otherwise.

You write: “I find Dr. E's MDT far more appealing than your theory on numerous levels. For starters he actually...

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Physics Nick,

Are you a sock puppet? Your writing style and sentiment are so close to Elliot’s that it’s difficult to tell you apart. In fact, I will assume that you are the same, unless you care to identify yourself and give me some reason to believe otherwise.

You write: “I find Dr. E's MDT far more appealing than your theory on numerous levels. For starters he actually focuses on a new physical model and mechanism, not just a bunch of neither-here-nor-there words pretending to be physics/maths.”

“Focuses” is the key word here. Obsesses is another word that comes to mind. The essay is supposed to be on “the nature of time,” but his essay has nothing to say about time other than to substitute x4 = ict for it. He asserts that “time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c,” and states that this constitutes a postulate.

But is not a postulate of anything, because it makes no sense to refer to a dimension as if it were an entity in and of itself. A physical dimension denotes a degree of freedom. Physical entities have magnitude, dimension and direction. If we define physical space as a set of points, or locations, satisfying the postulates of geometry, then that geometry may be Euclidean or non-Euclidean. If it is the geometry of Euclidean space, three degrees of freedom define space only, if it is the geometry of Minkowski, four degrees of freedom define spacetime, where another dimension, the dimension of time, is added to the three dimensions of Euclidean space.

If we consider the fourth dimension of spacetime, x4, as Einstein did, the subscript 4 denotes that it is “space like.” Not that it is a fourth dimension of space, but that it is mathematically unified with space such that metrical spacetime is something substantive. However, without the metric, or without the distance relations of spacetime, it is nothing. The metric is inseparable from the concept of dynamic spacetime, and it is in this sense of measure that we speak of dimensions: The magnitudes of spacetime distance relations have four dimensions, four independent numbers that must be specified in order to define a spacetime location.

Now, when Elliot proposes to replace the time of spacetime, with ict, we should call it spaceict, not spacetime, because Elliot asserts that time emerges from spaceict. So, then, the question becomes, what is the nature of ict? It is no longer a question of what is the nature of time. In fact, because ict has now become a metric, a distance measure, Elliot must now employ time as a measure of change in that measure, and does so with the equation ic = icdt/dt. But since c is a magnitude of constant velocity, cdt is a measure of distance, or length, so we now get idL/dt; that is, without the i factor in the term, ct is a line growing over time, the radius of an expanding sphere.

However, we must ask what is the meaning of the i factor in the term? If i is the square root of –1, i^2 is a 180 degree rotation on the number line, meaning i is a 90 degree rotation wrt the number line, but what is the meaning of this rotation in this context? Any radius of the expanding sphere will serve to define it. Its direction, hence its rotation, is meaningless. If we drop the i factor, nothing changes. Therefore, x4 = dL/dt = c is no different than dx4/dt = ic.

Consequently, the expanding sphere is simply a measure of the expanding volume of Euclidean space over time, or a three-dimensional, constant, motion. Of course, I don’t have any problem with this concept, if it is correctly characterized. It is only the characterization of it as a new, fourth, dimension that moves and replaces time that I have a problem with. Not only is there is no need to introduce this confusion into the theoretical picture, it actually makes it impossible to treat it seriously, in my opinion.

Given this is the case, Elliot, your hostility towards the theoretical physics community is also unwarranted. Instead of trying to force-feed your conclusions on all those who disagree with your characterization of x4, using an endless barrage of rhetoric, I recommend that you try to work out your arguments analytically, including your arguments against the assertions of others, as well as those supporting your own conclusions.

For instance instead of just asserting that my essay is “just a bunch of neither-here-nor-there words pretending to be physics/maths,” or writing, “Your words are worse than the Sokal Hoax,” you could take issue with something specific in my words, showing the error that you have found, like I have done above in regards to your characterization of x4. A pastiche, consisting of one small paragraph, should be easy enough for a seasoned and accomplished physicist, such as you are, to dispatch succinctly and concisely, in my opinion. Why not take a shot at it, Elliot?

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Hello Doug,

I am not "physics nick," although I appreciate the support!

I love the theoretical physics community--Einsetin, Wheeler, Bohr, Dirac, Fermi, Feyman, Born, Heisenberg, Maxwell, Faraday. I love reading their original papers and marveling at their eloquent use of language, which is used to make clear and elucidate eternal equations, while you use it to confound the simple...

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Hello Doug,

I am not "physics nick," although I appreciate the support!

I love the theoretical physics community--Einsetin, Wheeler, Bohr, Dirac, Fermi, Feyman, Born, Heisenberg, Maxwell, Faraday. I love reading their original papers and marveling at their eloquent use of language, which is used to make clear and elucidate eternal equations, while you use it to confound the simple and obscure beauty! Doug--do you have a physics degree? It doesn't seem so. Other than John Baez, who hasn't really ever advanced physics, have you read foundational papers of *real* physicists?

You write, "“Focuses” is the key word here. Obsesses is another word that comes to mind. The essay is supposed to be on “the nature of time,” but his essay has nothing to say about time other than to substitute x4 = ict for it. He asserts that “time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c,” and states that this constitutes a postulate.""

YES! My essay is *ALL ABOUT* the *VERY NATURE OF TIME!*

Time is not the fourth dimension, but rather it is a parameter that emerges because the fourth dimension is expanding relative to the three spatial dimensions.

My essay provides a *physical* mechanism accounting for time and all its arrows and assymetries across all realms!!:

The fourth dimension is expanding relative to the three spatial dimensions at the rate of c, as a wavefront with wavelength of the Planck length.

The MDT essay states, "The time on a watch or clock, whether linked to an oscillating circuit, quartz crystal, or unwinding copper spring, is based on changes in energy, which is based on the emission and propagation of photons. Photons surf the fourth expanding dimension, and thus time inherits properties of the fourth dimension, but time is not the fourth dimension. Past, present, and future are but states contained in our mind—past is what we remember—order stored in our brains. The present is physical change that creates the order in our brain. The future is but in our imaginations—changes we can potentially effect which will be recorded in the order of our memories. In relativity we often equate one second of time with 3x108 meters—the distance traveled by a photon in one second. This is because photons are matter surfing the fourth dimension which expands at c." --http://fqxi.org/community/forum/topic/238

How can you dismiss these revolutionary insights, Doug? It is interesting that you defend the absolute failure of string theory and the current "theoreticl physics community," who have never advanced physics, and have actually impeded advancement over the past thirty years via snarky fundraising games, while rejecting the simple elegance and beauty of MDT. This is quite an intellectual feat, you are pulling off, and I imagine that it must require one to have no advanced degree in physics, as that is who the string theory regimes and quantum gravity gangs have resorted to recruiting these days.

"Come support our regime with your handwaving, physicless, degreeless snark, and we will give you a postdoc and tenure as physics dies!"

I stand by my paper, as does Einstein:

"In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time’s physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify."

"The primary invariant is c—all matter and/or photons—be it propagating through space or time, or some combination thereof, always move at the rate of c through space-time, and this reality arises because of the deeper physical invariance of a fourth dimension that is expanding relative to the three spatial dimensions at the rate of c. To be stationary in the three spatial dimensions means to propagate at the rate of c through the fourth dimension, as a stationary clock ticks away this distance at a maximal rate, as the photons in the unwinding clock’s spring travel at c relative to the stationary clock. To be stationary in the fourth dimension means to propagate at the rate of c through the three spatial dimensions, as does the ageless photon. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions."

Doug--you write, "Consequently, the expanding sphere is simply a measure of the expanding volume of Euclidean space over time, or a three-dimensional, constant, motion. Of course, I don’t have any problem with this concept, if it is correctly characterized. It is only the characterization of it as a new, fourth, dimension that moves and replaces time that I have a problem with. Not only is there is no need to introduce this confusion into the theoretical picture, it actually makes it impossible to treat it seriously, in my opinion."

No. No. No. No. The spacetime of General Relativity--of which special relativity is a special case of--is non-Euclidean. Your words crack me up as they remind me of the papers produced by one of those random buzzword generators--it's as if you typed in a bunch of Baez's work into one of these random-essay-generating programs, and it spat out your essay.

And MDT does not create confusion! No! It introduces clarity and order while providing a massive unification, all based on a simple *physical* model, marking it as a most unique essay in this conest, as it provides a *physical* mechanism for time and change, based on a hitherto unsung universal invaraint--the fourth dimension is expanding relative to the three spatial dimensions.

Postmodern physicists write a lot about the "Time axis" in their papers and coffee-tabel books, but you need to keep in mind that the time axis is a human construct, and that we do not live in a block universe wherein time is frozen. The block universe is also a human construct, which Godel had problems with. Also, Einsetin never said that time is the fourth dimension in his 1912 paper, but rather he wrote x4=ict, and t and ict are very different things. It is amazing how many physicists have thrown away the ic in front of the t, and gotten tenure while conceiving of time machines they never build, and wormholes they never see, not to mention multiverses and parrallel universes and tiny little vibrating strings in their block universe wherein funding is an established part of the future which has already happened, but you get the point. All the pop-sci books and texts always have those pictures of light cones, but what they forget is that photons do not travel in straight lines, but rather quantum mechanics tells us that photons travel as expanding spherical wavefronts of probality in our 3D. And in doing so, they maintain a locality in the fourth expanding dimension.

Those who argue with MDT's postulate that the fourth dimension is expanding relative to the three spatial dimensions are actually arguing with the photon. And yet, the photons keep right on travleing at c--billions upon billions upon billions of them--every second, as they surf the fourth expanding dimension, while yet retaining a locality in time and the fourth expanding dimension. I would not be surprised if photons start protesting all the tenured elite who are trying to freeze them and emprison them in their block universe, wherein time and progress in theoretical physics must remain frozen, so as to keep their perpetual-motion funding machines printing cash day and night for thier non-theories and ani-theories.

Now of course we can forgive Einstein for not noting all this in his 1912 paper, as he never quite accepted quantum mechanics' reality, but for all those of us who passed undergrad and grad quantum, and for all of us who use computers which were built upon nonlocality's reality and wave/particle duality--it is time for all of us to admit that the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, and that this fundamental universal invariant gives rise to the time we measure on our watches, which we we also enjoy designating as an axis in diagrams when writing coffee-table physics books that have frozen time so as to write chapter after chapter about time travel.

Both Einstein and Minkowski wrote x4 = ict, but they never saw that this naturally implied dx4/dt = ic. All of relativity is right--it's just that change is now forever wedded into the fundamental fabric of spacetime with dx4/dt = ic. I know they will ignore this and continue to raise tens of millions for mytholgies, while training grad students in the art of sycophancy, thuggery, and anonimity, and picking the best to reward with a few pennies now and then from their millions, as senior citizen physicists dictate the questions, banning those who were born with their own curiosities, like Einstein, Newton, Bruno, Galileo, and every other scientist and artist who has ever contributed to art and science.

And Einstein's Relativity may be derived from dx4/dt= ic, which represents a more fundamental invariance of this universe--the fourth dimension is expanding relative to the three spatial dimensions. Einstein introduced relativity as a principle--as a law of nature not deduced from anything else, and well, I guess I was dumb enough to ask, 'why relativity?' And I found the answer in a more fundamental invariance--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic.

And not only can all of relativity be derived from this, but suddenly we are liberated from the block universe and time and progress in theoretical physics are unfrozen. And change is seen in a most fundamental equation that *weaves* change into the very fabric of space-time, where it needs to be, as change pervades every realm of physics and all acts of *physical* measurement. And suddenly we have a *physical* model for entropy, time and its arrows and assymetries in all realms, free will, and quantum mechanics' nonlocality, entanglement, and wave-particle duality. The fourth expanding dimension distributes locality, fathering time. MDT accounts for the constant speed of light c--both its independence of the source and its independence of the velocity of the observer, while establishing c as the fastest, slowest, and only velocity for all entities and objects moving through space-time, as well as the maximum velocity that anything is measured to move. And suddenly we see a *physical* basis for the dualities--for space/time, wave/matter, and energy/mass or E=mc^2. Energy and mass are the same thing--it's just that energy is mass caught upon the fourth expanding dimension, and thus it surfs along at "c."

Finally Doug, you write, "Given this is the case, Elliot, your hostility towards the theoretical physics community is also unwarranted. Instead of trying to force-feed your conclusions on all those who disagree with your characterization of x4, using an endless barrage of rhetoric, I recommend that you try to work out your arguments analytically, including your arguments against the assertions of others, as well as those supporting your own conclusions."

DOUG! DOUG! DOUG! PHYSICAL REALITY naturally and logically supports all of MDT's contentions! To keep it short, I will not repeat them here, but please read my paper when you get a chance.

AND DOUG! STOP SHOOTING TRUTH'S MESSENGER!! I have no hostility towards the theoretical physics community, but rather, I am but quoting the Nobel Laureates who have noted the supreme failure of the quantum gravity regimes and string theorists, whose most famous and lasting contribution to physics has been John Baez's crackpot index. We must ask, is Baez's crackpot index really worth billions of taxpayers' dollars, especially when it is used as a tool to kill physics so as to shore up funding for regimes of failure?

I am not speaking out against quantum gravity and string theory, but Baez is! As you will se below.

String Theorists and Quantum Gravitationists generally ban you from quoting Nobel Laureates in physics and talking about physics and physical reality. When you do, they shoot you--the messenger.

They do not like you talking about time, space, and causality, as they insist that such things are not real, while tiny, vibrating strings, ten to forty additional dimensions, and atoms of spacetime and "bouncing" universes *are* real. Basically it's an entire program of replacing physical reality, science, and physics with groupthink, mysticism, tyranny, PR hype, and well-funded, snarky bureaucracies--it's a cash-driven conquest. Today success is considered having one's anti-theory hyped on Fox News, while perhaps signing a book deal before one's fifteen minutes of fame expires--even though their theories state that time does not flow and isn't real. The math never adds up, and even the great John Baez has finally given up, and is jumping off the train after riding it for ten years in the block universe that MDT has freed us from:

http://www.edge.org/q2008/q08_5.html

"Loop quantum gravity was less ambitious than string theory. Instead of a "theory of everything", it only sought to be a theory of something: namely, a theory of quantum gravity.

So, I jumped aboard this train, and for about a decade I was very happy with the progress we were making. A beautiful picture emerged, in which spacetime resembles a random "foam" at very short distance scales, following the laws of quantum mechanics.

We can write down lots of theories of this general sort. However, we have never yet found one for which we can show that General Relativity emerges as a good approximation at large distance scales — the quantum soap suds approximating a smooth surface when viewed from afar, as it were.

I helped my colleagues Dan Christensen and Greg Egan do a lot of computer simulations to study this problem. Most of our results went completely against what everyone had expected. But worse, the more work we did, the more I realized I didn't know what questions we should be asking! It's hard to know what to compute to check that a quantum foam is doing its best to mimic General Relativity.

Around this time, string theorists took note of loop quantum gravity people and other critics — in part thanks to Peter Woit's blog, his book Not Even Wrong, and Lee Smolin's book The Trouble with Physics. String theorists weren't used to criticism like this. A kind of "string-loop war" began. There was a lot of pressure for physicists to take sides for one theory or the other. Tempers ran high. . .

I realized I didn't have enough confidence in either theory to engage in these heated debates. I also realized that there were other questions to work on: questions where I could actually tell when I was on the right track, questions where researchers cooperate more and fight less. So, I eventually decided to quit working on quantum gravity.

It was very painful to do this (so painful that Baez created a crackpot index to snark physicists with ad hominem attacks), since quantum gravity had been my holy grail for decades. After you've convinced yourself that some problem is the one you want to spend your life working on, it's hard to change your mind. But when I finally did, it was tremendously liberating."--John Baez: http://www.edge.org/q2008/q08_5.html

Yes--string theory and quantum gravity seem to be on their way out, after thirty years of absorbing hundreds of millions of dollars, with nothing to show for it, but snarky groupthink regimes fighting for their version of unreality, non-theories, quotes on TV shows such as the Big Bang, and mythology.

Now I agree that it is good to fund science, such as the artificial retina I worked on for my dissertation: http://elliotmcgucken.com/dissertation.html (where the first treatment of MDT appeared in the appendix--please find a figure from the dissertation attached)

So it is DOUG, that I am not against the theoretical physics community by any means, as MDT is leading it to a brand new day, in a most heroic, and traditional way. But rather, I am against your snarky handwaving and high-school debating tacticts by which you guys advance your pseudo-science, at the expense of Einstein, Borh, Newton, and physics.

It is not I who oppose your snarky reign of handwaving hype, but the GIANTS OF PHYSICS, and physical reality:

The first page of String Theory in a Nutshell states in a footnoted sentence:

THE CASE FOR STRING THEORY:

String Theory has been the leading candidate over the past two decades for a theory that consistently unifies all the fundamental forces of nature, including gravity. It gained popularity because it provides a theory that is UV finite.(1)

The footnote (1) reads: "Although there is no rigorous proff to all orders that the theory is UV finite, there are several all-orders arguments as well as rigorous results at low-loop-order. In closed string theory, amplitudes must be carefully defined via analytic continuation, standard in S-matrix theory. When open strings are present, there are diveregences. However, they are interpreted as IR divergences (due to the exchange of massless tsates) in the dual closed string channel. They are subtracted in the "Wilsonian" S-matrix elements."

So you see, String Theory is not a finite theory, but this is generally kept to the footnotes, when mentioned at all.

A lot of Nobel Laureates have problems with String Theory:

""WE DON'T know what we are talking about." That was Nobel laureate David Gross at the 23rd Solvay Conference in Physics in Brussels, Belgium, during his concluding remarks on Saturday. He was referring to string theory. . ." --http://www.newscientist.com/channel/fundamentals/mg1882529
3.700

It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself." -Einstein to Paul Ehrenfest

String theorists don't make predictions, they make excuses. -Richard Feynman, Noble Laureate

String theory is like a 50 year old woman wearing too much lipstick. -Robert Laughlin, Nobel Laureate

Actually, I would not even be prepared to call string theory a "theory" rather a "model" or not even that: just a hunch. After all, a theory should come together with instructions on how to deal with it to identify the things one wishes to describe, in our case the elementary particles, and one should, at least in principle, be able to formulate the rules for calculating the properties of these particles, and how to make new predictions for them. Imagine that I give you a chair, while explaining that the legs are still missing, and that the seat, back and armrest will perhaps be delivered soon; whatever I did give you, can I still call it a chair? -Gerard `t Hooft, Nobel Laureate in String Theory

"It is tragic, but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. So when one person spends 30 years, it's a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious." -Sheldon Glashow, Nobel Laureate

"I don't like that they're not calculating anything. I don't like that they don't check their ideas. I don't like that for anything that disagrees with a n experiment, they cook up an explanation-a fix-up to say, "Well, it might be true." For example, the theory requires ten dimensions. Well, maybe there's a way of wrapping up six of the dimensions. Yes, that's all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there's no reason whatsoever in superstring theory that it isn't eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn't produce anything; it has to be excused most of the time. It doesn't look right." -Richard Feynman, Nobel Laureate in Physics

"But superstring physicists have not yet shown that theory really works. They cannot demonstrate that the standard theory is a logical outcome of string theory. They cannot even be sure that their formalism includes a description of such things as protons and electrons. And they have not yet made even one teeny-tiny experimental prediction. Worst of all, superstring theory does not follow as a logical consequence of some appealing set of hypotheses about nature. Why, you may ask, do the string theorists insist space is none-dimensional? Simply because string theory doesn't make sense in any other kind of space." --Sheldon Glashow, Nobel Laureate in Physics

Even String Theory's founder, Michio Kaku, has problems with the theory: "The great irony of string theory, however, is that the theory itself is not unified. To someone learning the theory for the first time, it is often a frustrating collection of folklore, rules of thumb, and intuition. (IN OTHER WORDS IT IS NOT PHYSICS!!!) At times, there seems to be no rhyme or reason for many of the conventions of the model. For a theory that makes the claim of providing a unifying framework for all physical laws, it is the supreme irony that the theory itself appears so disunited!!"

Chapter 1. Path Integrals and Point Particles: Why Strings?

" --"Introduction to Superstrings and M-Theory," page 5. -Michio Kaku

"If Einstein were alive today, he would be horrified at this state of affairs. He would upbraid the profession for allowing this mess to develop and fly into a blind rage over the transformation of his beautiful creations into ideologies and the resulting proliferation of logical inconsistencies. Einstein was an artist and a scholar but above all he was a revolutionary. His approach to physics might be summarized as hypothesizing minimally. Never arguing with experiment, demanding total logical consistency, and mistrusting unsubstantiated beliefs. The unsubstantial belief of his day was ether, or more precisely the naïve version of ether that preceded relativity. The unsubstantiated belief of our day is relativity itself. It would be perfectly in character for him to reexamine the facts, toss them over in his mind, and conclude that his beloved principle of relativity was not fundamental at all but emergent-a collective property of the matter constituting space-time that becomes increasingly exact at long length scales but fails at short ones. This is a different idea from his original one but something fully compatible with it logically, and even more exciting and potentially important. It would mean that the fabric of space-time was not simply the stage on which life played out but an organizational phenomenon, and that there might be something beyond." -A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.

"[String Theory] has no practical utility, however, other than to sustain the myth of the ultimate theory. There is no experimental evidence for the existence of strings in nature, nor does the special mathematics of string theory enable known experimental behavior to be calculated or predicted more easily. Moreover, the complex spectroscopic properties of space accessible with today's mighty accelerators are accountable in only as "low-energy phenomenology"-a pejorative term for transcendent emergent properties of matter impossible to calculate from first principles. String theory is, in fact, a textbook case of Deceitful Turkey, a beautiful set of ideas that will always remain just barely out of reach. Far from a wonderful technological hope for a greater tomorrow, it is instead the tragic consequence of an obsolete belief system-in which emergence plays no role and dark law does not exist."

-A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.

MDT delivers an ultimate theory, whereas Loop Quantum Gravity and Sring Theory only sustain a myth of an ultimate theory. And thus we are commanded from on high--from the pinnacles of the ani-theory regimes--to ignore MDT and Nobel Laureates such as Robert Laughlin, F.A. Hayek, Feynman, Einstein, Planck, and others I quote above. Welcome to the dark ages.

All this will be in HERO'S JOURNEY PHYSICS & MOVING DIMENSIONS THEORY: FROM BRUNO, TO GALILEO, TO EINSTEIN--AND YET IT MOVES!

Best,

Dr. E (The Real McCoy)

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Elliot,

Thank you for reading and rereading my essay and asking for clarification. You write:

“I have now read your essay twice. It has very little in common with MDT, if anything at all. What similarities do you see between your non-theory and MDT?”

The similarity is found in the reciprocal relationship of space and time. In Larson’s reciprocal system of physical theory...

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Elliot,

Thank you for reading and rereading my essay and asking for clarification. You write:

“I have now read your essay twice. It has very little in common with MDT, if anything at all. What similarities do you see between your non-theory and MDT?”

The similarity is found in the reciprocal relationship of space and time. In Larson’s reciprocal system of physical theory (RST), everything starts with a one-for-one space/time expansion. Since space is three-dimensional (a pseudoscalar), and time is zero-dimensional (a scalar), this space/time expansion takes the form of a spherical expansion; that is, just as in MDT, every location is expanding relative to every other location. The difference is that the fourth dimension that is expanding, relative to the three spatial dimensions, is the time dimension, not some unknown dimension.

However, this is the initial condition, before matter and radiation enter into the theoretical situation. At this point in the theory, there is nothing but the perfect symmetry of this motion. In order for something to exist, this state, where nothing is perfect, has to be elegantly organized in someway that entails the breaking of the initial symmetry. The s/t = 1/1 unit progression has to be displaced, from unity, to less than (s/t = 1/n), or greater than (s/t = n/1), unity (n/n, where n > 1).

You write:

“MDT has a simple postulate and equation representing a hitherto unsung physical reality form where relativity and other physical phenomena naturally emerge, including time and all its arrows and assymetries. Your antitheory lacks any such substance. It lacks a simple postulate and equation:

’The fourth dimension is expanding relative to the three spatial dimensions at c: dx4/dt=ic .’”

This equation is not valid, Elliot, and positing a “moving dimension” makes no sense. Look, I’m just trying to help you here, not fight you. The changing coordinate, x4, designates a point, x, y, z, on the surface of the expanding sphere at a given time, t. If we freeze the expansion at some point in time that we designate elapsed unit time and draw a line from the origin to any point, x, y, z, on the surface, the length of the radius will be a unit line, r, that corresponds to the unit time, t, of the expansion, if the rate of the expansion is constant. One way we can mathematically represent the length of the line, r, using the time, t, is by employing the Pythagorean theorem, like we normally do.

But the length of the line, r = 1, corresponding to the elapsed time, t = 1, is just ct, or s/t * t1 - t0 = s, where s is space (in this case length) and t is time. This is simply the physics everyone is familiar with. The distance of the radius of the expansion is equal to the speed (c-speed in our case) multiplied by the elapsed time. No big mystery, no big deal. Note that nothing is changing “position” here, nothing is “moving” in the sense of changing locations in space or time along the radius. It is only the magnitudes of spacetime itself that are changing. The three positive magnitudes, x, y and z, and the one negative magnitude, t, are continuously growing larger and larger.



Remember, this is a description of flat spacetime, before mass, or radiation, are introduced into the theory. Of course, in currently accepted theory this is an impossible state of affairs, but not in your theory and not in my “anti-theory.”

You write:

“You yet deny Einstein's general relativity which states that dimensions can warp, bend, and move. Until you accept physical reality and one of the greatest contributions to modern physics, it will be hard to take your ideas seriously.”

The spacetime metric (say, + + + -) constitutes the set of directions inherent in its four dimensions. These four dimensions are the independent magnitudes required to specify the spacetime locations. They are abstractions. We don’t “warp, bend and move” these little positive and negative signs. They stay put. Only their magnitudes change dynamically, as they interact with matter, in GR. I have been trying to clarify that point with you for some time, but you continue to misunderstand it, for some reason.

Now, the acknowledged trouble with current cosmological theory, based on the standard model and general relativity is how to get started. You simply can’t start the big bang as things now stand in current theory. Of course, your MDT theory faces the same difficulty, I believe, but, unlike current cosmology, your theory doesn’t have to begin with a singularity, because, again, like the RST, the space/ict expansion that you postulate in MDT expands everywhere, everywhen. The movement of the moving dimension of MDT does not necessarily start from a single point in the past, if I understand correctly.

Nevertheless, you are stuck just as much as current cosmology, because, just like it, you have to introduce matter into your theory somehow, or else your moving dimension isn’t very useful to you. In the RST-based theory development, on the other hand, this is not the case, since the RST posits the following:

First Fundamental Postulate: The physical universe consists of one component, motion, existing in discrete units, with two reciprocal aspects, space and time.

The entire theoretical development in the new system follows, as the consequences of this postulate are deduced. The first consequence to be deduced from it is that, in order for anything to exist, the symmetry of unit motion, s/t = 1/1, has to be broken. As I mentioned in the beginning, there are exactly two ways the symmetry of this unit space/time ratio can be broken: A space/time displacement that constitutes a motion magnitude that is less than unit motion breaks the symmetry in one “direction,” while a space/time magnitude that constitutes a motion magnitude that is greater than unit motion breaks the symmetry in the opposite “direction.”

The question is how does this change in the ratio of changing space and time happen and what are the mathematics of it? My essay explains a little of this. However, I had to cut out the equations and their explanations, due to the essay contest constraints, but if you are interested, we can certainly discuss them.

Regards,

Doug

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Doug,

You write, "What makes this argument so hard for me to continue to press is that I agree with you in that the fourth dimension is expanding, relative to the three spatial dimensions!"

DOUG! YOU AGREE WITH MDT'S POSTULATE! O HAPPY DAY!

MDT: The fourth dimension is expanding relative to the three spatial dimensions at the race of c.

dx4/dt=ic

WELCOME HOME...

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Doug,

You write, "What makes this argument so hard for me to continue to press is that I agree with you in that the fourth dimension is expanding, relative to the three spatial dimensions!"

DOUG! YOU AGREE WITH MDT'S POSTULATE! O HAPPY DAY!

MDT: The fourth dimension is expanding relative to the three spatial dimensions at the race of c.

dx4/dt=ic

WELCOME HOME DOUG! Today is a great day, as you have been liberated from the block universe, and joined us with your newfound freewill granted by MDT, which weaves change into the fundamental fabric of spacetime.

Einstein introduced relativity as a principle--as a law of nature not deduced from anything else, and well, I guess I was dumb enough to ask, 'why relativity?' And I found the answer in a more fundamental invariance--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. Change is finally fundamentally embedded in space-time, for teh first time in all of history.

MDT simplifies our universe in an elegant, logical manner, uniting hitherto disparate phenomena, across multiple realms, in a simple physical model representing a hitherto unsung universal invariant: dx4/dt=ic. MDT gives us a *physical* mechanism powering light, time, and relativity and thus MDT naturally gives us everything relativity gives us--time dilation, length contraction, and the equivalence of mass and energy--while also libertating us from a timeless, block universe, as well as providing a *physical* model for time, entropy, quantum entanglement and nonlocality, and the equivalence of mass and energy.

You write, "Clearly, there is no fourth space coordinate in Euclidean space, and real time is certainly not a coordinate in Euclidean space,"

As I stated, Einstein's spacetime is non-Euclidean.

Read chapter XXVII of Einstein's Relativity, which is titled "THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM."

Doug--you write: "However, what I am arguing, fervently, is that the way Einstein used “ict” to make Minkowski spacetime ANALOGOUS to Euclidean space, does NOT IMPLY MDT’s equation. This is my argument here, ok?"

As I stated, Einstein's spacetime is non-Euclidean, so your argument is hollow.

Read chapter XXVII of Einstein's Relativity, which is titled "THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM."

now, 4D is a tough entity to envision, and i don't know if my theory improves on previous treatments.

but, it does do the following:

1. recognizes that time is not the fourth dimension, but x4 = ict, as Einstein and Minkowski agreed.

2. shows all of time's arrows from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

3. shows all of time's assymetries from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

4. derives relativity from a simple postulate/equation: dx4/dt = ic

5. presents a physical model for QM's nonlocality & entanglement, relativity's silumtaneity, and entropy

6. unifies the dualities with a common postulate: wave-particle duality, space-time duality, and matter-energy duality are all natural results of a fourth expanding dimension, which distributes nonlocality via its expansion. note that entanglement always occurs between two particles that were formerly in contact, and thus all nonlocality emerges from a common point or locality--another clue.

7. provides a physical model for time's fundamental assymetry in this universe

8. shows that time, as measured on our watches and witnessed in the world around us, emerges from a deeper reality dx4/dt = ic.

Relativity implies a block, timeless universe. "And yet it moves," as Galileo said. "Eppur si muove"

http://en.wikipedia.org/wiki/E_pur_si_muove!

And yet, we continue to ask questions--those questions which keep us up at night, searching for a *physical* reality and model that might answer them.

Why entropy? Why time's arrows? Why time's asymmetries? Why is c the maximum velocity and why is c independent of the source? Why the dualities? Why does physics present us with the mass-energy, space-time, and wave-particle dualities? Why entanglement, length-contraction, nonlocality, and time dilation? Why *time*? All of these phenomena can be traced to a simple principle--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c: dx4/dt = ic, from which Einstein's relativity is derived.

Energy does tend to radiate outwards, and MDT accounts for this with a *physical* model--as the fourth dimension is expanding relative to the three spatial dimensions at c, and as photons (energy) are but matter caught on the fourth expanding dimension, the photon appears as a spherically-symmetric expanding wavefront, as it surfs the expanding fourth dimension. All of nature rests upon this fundamental reality, and all of time's arrows and entropy derive from this simple premise, as does nonlocality, entanglement, and the agelessness of the photon.

Relativity proposes a block universe. Godel pointed out the paradoxical "timeless" implications of this, as well as its inability to account for time as we experience it, and this problem has largely been swept under the rug, along with curiosities such as quantum entanglement, nonlocality and all the dualities--space/time, energy/mass, and wave/particle. Today we are told that that is "just the wya things are" and not to worry about it. Perhaps this helps explains why physics has not really advanced in the past thirty years... for Einstein stated, "curiosity is more importnat than knowledge."

And thus MDT's center and circumference rests upon asking and answering fundamental questions with a simple, elegant *physical* model that comes with both a postulate of a fourth expanding dimenson.

Doug--you write, "What makes this argument so hard for me to continue to press is that I agree with you in that the fourth dimension is expanding, relative to the three spatial dimensions!"

What makes the argument so hard for you is that you have seen the light, and you now agree with the simple, unifying elegance of MDT!

Best,

Dr. E (The Real McCoy)

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Elliot,

You are only seeing what you want to see, and this makes intelligent discussion so hard! I’m not saying anything new here. I’m just rephrasing what I have always said. Let me try again (!).

The term “ic” makes no sense. The concept of the imaginary number is an ad hoc invention concocted to deal with the fact that (–1)^2 = +1. Just as Brian explains in his...

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Elliot,

You are only seeing what you want to see, and this makes intelligent discussion so hard! I’m not saying anything new here. I’m just rephrasing what I have always said. Let me try again (!).

The term “ic” makes no sense. The concept of the imaginary number is an ad hoc invention concocted to deal with the fact that (–1)^2 = +1. Just as Brian explains in his wonderful essay, concerning the wavefunction of quantum mechanics:

“Wavefunctions in quantum physics provide chance predictions for what classical physics predicted with certainty. The Copenhagen interpretation postulates the unsquared wavefunction as a mathematical object with no physical significance. The wavefunction is a superposition of imaginary bases states.

Ψ(x,t) = C[a1ψ(1)+ a2ψ(2) +…+ anψ(n)] (7)

All physical predictions in quantum mechanics must be real probabilities. Imaginary numbers become real numbers by squaring them.“

Even so, the “i” factor in Einstein’s “ict” term makes no sense, if it is not squared. Indeed, we may take our clue from Brian’s observation about the wavefunction and say that the unsquared “ict” term is a mathematical term with no physical significance.

So, bear with me now and take a second look at your equation, considering, for the sake of argument, that the expansion of the three spatial dimensions means that the radius of the expanding sphere is simply ct, instead of ict.

We would write this as x4 = ct, contrary to Einstein, but not with the intent to do what Einstein was trying to do, as I explained previously. Since the constant c is a velocity, we can write it as c = ds/dt, or changing space over changing time. Thus, ct = s/t * t = s. In this case, s is one-dimensional length, the radius r of the expanding sphere.

This distance r could represent the one-dimensional path of a photon, but we are choosing to interpret it as a representation of the radius of the three-dimensional expansion, and in one unit of time, that would be one unit of length, as I have already explained. What this means is that the change in time is numerically equal to the radius of the change in space, in one unit of space/time change.

But since the dimensions of space are three, each with two directions, while time doesn’t have directions in space, meaning it doesn’t have a dimension, or, to put it another way, its potential directions are null, c = s/t, for the expanding sphere, should be written as c = s^3/t^0.

On this basis, when we write ct, we get s^3/t^0 * t^0 = s^3, a sphere. See? I’m just saying, you don’t need to introduce the confusion of dict/dt = ic in order to weave change into your physical theory. You can have everything that you theoretically have now, without offending the logical consistency of your theory. The only difference is that “x4” is not considered a “space coordinate,” borrowed from the concept of imaginary time, in a Euclidean analogy of Minkowski spacetime, but instead is real time, moved to the denominator of c, where real time belongs.

Of course, this doesn’t invalidate Einstein’s work, nor his attempt to promote its understanding through the Euclidean analogy with Minkowski spacetime. It just puts the basis of MDT on a sounder footing.

Peace,

Doug

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Doug--you write "The term “ic” makes no sense. The concept of the imaginary number is an ad hoc invention concocted to deal with the fact that (–1)^2 = +1."

How dare you stipulate that ic makes no sense?!?

Instead, one must ask, "what is the *physical* meaning of ic?" as MDT does. And the answer to that leads us to a brand new physical invariant--the fourth dimension is...

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Doug--you write "The term “ic” makes no sense. The concept of the imaginary number is an ad hoc invention concocted to deal with the fact that (–1)^2 = +1."

How dare you stipulate that ic makes no sense?!?

Instead, one must ask, "what is the *physical* meaning of ic?" as MDT does. And the answer to that leads us to a brand new physical invariant--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic.

Einstein wasn't kiding when he stated, "Curiosity is mor eimportant than knoweldge." Curiosity is also more important than arrogant snark wild handwaving.

You will find that humble curiosity is a far greater force in advancing physics than the snarky imposition of one's lack of curiosity and humility on the beauty of physical reality--simple curiosity is far greater than the methodology of the antitheory regimes who have built billion-dollar, televised groupthink regimes of censorship, snark, and intimidation while killing progress in physics.

MDT explains the vast and profound significance of ic in x4 = ict. It means the fourth dimension is expanindg relative to the three spatial dimensions, in a manner perpendicular to the three spatial dimensions!

dx4/dt = ic is what MDT states, which comes straight from Einstein's work.

x4 = fourth dimension

i = imaginary number

c = velocity of light

t = time

Suppose I told you x4 = ict and asked you to draw x4 at t=1, t=2, t=3 . . . etc.

Would you not draw x4 in different places for different t's?

Then, since Einstein and Minkoswki agree that the fourth dimension x4 = ict, does it not make sense that the fourth dimension moves over time?

Towards the bottom of page 6 of my paper, i write:

"Einstein definitively states x4 = ict, and time and ict are very different entities. Einstein states, “One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as x4) is always purely imaginary.” It is imaginary because the expansion of the fourth dimension is orthogonal to the three spatial dimensions in every direction,"

i represents an orthogonality, so I would infer that i represents a perpendicularity--the fourth dimension is perpenidular to the three spatial dimensions. This makes sense!! For is this not what a dimension ought be--perpendicular to the other dimensions, providing an independent degree of freedom? x2 is perpendicular to x3 and x1, and x4 is perpendicular to x1, x2, and x3! That is why the i showed up! For when one goes into calculations, and an i pops out, it means that we need to think of a brand new perpendicularity in our system!! i has so very much significance, and ic has ven more! x4=ict means that the fourth dimension is expanding relative to the three spatial dimensions at the rate of c!

now einstein writes x4 = ict, so that dx4/dt = ic.

let me illustrate the meaning of this.

consider a 2D x-y plane and an expanding 3D sphere. the expansion of the sphere would appear as an expanding circle in the 2D plane. now, the surface of the sphere would be perpendicular to every point in the 2D plane. instead of writing the third coordinate as z, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 2d plane.

now, let us consider the above with an extra dimension, so:

consider a 3D space and an expanding 4D surface. the expansion of the 4D surface would appear as an expanding sphere in the 3D space. now, the surface of the 4D surface would be perpendicular to every point in the 3D space. instead of writing the fourth coordinate as x4, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 3D space.

now, 4D is a tough entity to envision, and i don't know if MDT improves on previous treatments.

but, it does do the following:

1. recognizes that time is not the fourth dimension, but x4 = ict, as Einstein and Minkowski agreed.

2. shows all of time's arrows from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

3. shows all of time's assymetries from various realms derive from a common physical reality--the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

4. derives relativity from a simple postulate/equation: dx4/dt = ic

5. presents a physical model for QM's nonlocality & entanglement, relativity's silumtaneity, and entropy

6. unifies the dualities with a common postulate: wave-particle duality, space-time duality, and matter-energy duality are all natural results of a fourth expanding dimension, which distributes nonlocality via its expansion. note that entanglement always occurs between two particles that were formerly in contact, and thus all nonlocality emerges from a common point or locality--another clue.

7. provides a physical model for time's fundamental assymetry in this universe

8. shows that time, as measured on our watches and witnessed in the world around us, emerges from a deeper reality dx4/dt = ic.

MDT agress 100% with Einstein's and Minkowski's relativity. The fourth dimension is a dimension that is orthogonal to the three spatial dimensions. All that MDT states is that the fourth dimension is expanding relative to the three spatial dimensions. In his 1912 paper Einstein just states x4 = ict. MDT begins at a more fundamental level: dx4/dt=ic, which also provides a physical model accounting for entropy, entnaglement, quantum mechanics' nonlocality, and time and its arrows in all realms, in addition to relativity.

MDT contends that the fourth dimension is very much like the spatial dimensions, except that it is expanding relative to them! dx4/dt = ic.

Now, regarding i, i does not imply "imaginary" in the sense of "it doesn't really exist." But rather i implies a very real perpendicularity.

i is an imaginary number, but it can define very real entities!

For instance, in a complex plane, we can designate the x axis to be real and the y axis to be imaginary. This is a mathematical tool, but the y axis is very real! Imaginary numbers are very useful in describing oscillations and rotations. When we solve an equation and we see one, that is math's way of lettig us know--"hey there is something going on here that is perpendicular to where you started."

If we were called upon to draw i, we would draw it perpendicular to the real number line. i^2 would be -1 on the real number line i^3 would be -i--it would point "south" along the y axis. And i^4 is 1 on the real number line. So multiplying by i rotates something by 90 degrees! Multiplying by i makes something perpendicular to its former self! Now although i is "imaginary," the y-axis is a very real entity. So i has a reality to it.

So if we're solving an equation, and an i pops out, all of a sudden we need to start thinking of an orthogonal space.

Now the way I interpret x4 = ict is that x4 is perpendicular to the three spatial dimensions, and that as t advances on our clock or watch, it moves.

Consider a 2D x-y plane and an expanding 3D sphere. We could then say that the sphere will also expand in the imaginary direction, which is directed along the z axis. The expansion of the sphere would appear as an expanding circle in the 2D plane. Now, the surface of the sphere would be perpendicular to every point in the 2D plane. instead of writing the third coordinate as z, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 2d plane.

Now, let us consider the above with an extra dimension, so:

consider a 3D space and an expanding 4D surface. The expansion of the 4D surface would appear as an expanding sphere in the 3D space. now, the surface of the 4D surface would be perpendicular to every point in the 3D space. instead of writing the fourth coordinate as x4, we could associate it with i--the imaginary number, which would represent the orthogonal surface at every point in our 3D space.

more clues are discussed in the paper, where towards the bottom of page 6, i write:

"Einstein definitively states x4 = ict, and time and ict are very different entities. Einstein states, “One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as x4) is always purely imaginary.” It is imaginary because the expansion of the fourth dimension is

orthogonal to the three spatial dimensions in every direction, just as the radii of an expanding sphere are perpendicular to its surface at every point."

The fourth dimension is very, very real.

All motion rests upon its fundamental expansion relative to the three spatial dimensions: dx4/dt = ic. Every object moves at but one speed through space-time--c. This is because space-time moves at but one speed through every obeject--c. Catch up with the fourth expanding dimension, and you'll be going close to c relative to the three spatial dimensions. Remain stationary in the three spatial dimensions, and you'll be traveling at close to c relative to the fourth dimension. And isn't it cool that the faster an object moves, the shorter it is in the three spatial dimensions? This is because it is physically being rotated into the fourth dimension--the fundamental source of all motion by its never-ending motion, which sets the universe's maximum velcoity at c.

Relativity implies a frozen, timeless, block universe. But as Galileo said, "Yet it moves!" *Why* is this? Because dx4/dt = ic! And the spherically-symmetric expansion that the expanding fourth dimension manifests itself as--this smearing of locality--jives perfectly with the motion of a photon as well as its nonlocal properties, setting its velocity to c independent of the source and rendering it timeless and ageless--stationary in the fourth expanding dimension, which would also explain entanglement with other photons with which it once shared a common origin! And we also get a *physical* model for entropy and time.

The block universe froze eternity,

'til MDT rose to set us all free!

Best,

Dr. E (The Real McCoy)

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Hi Tom,

That’s an interesting comment. I guess it constitutes the argument on the other side of the coin so-to-speak. However, to say that something exists, such as Einstein’s spacetime, it merely has to be defined, as something with physical effect, yet also as something not effected by physical conditions, is a heavy concept.

I’m not sure I understand things in the same way....

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Hi Tom,

That’s an interesting comment. I guess it constitutes the argument on the other side of the coin so-to-speak. However, to say that something exists, such as Einstein’s spacetime, it merely has to be defined, as something with physical effect, yet also as something not effected by physical conditions, is a heavy concept.

I’m not sure I understand things in the same way. I would say that if something can be acted upon, then it exists physically. I’m not sure that motion per se, i.e. a change of space and time, can be acted upon, unless the change of space that enters into the motion is defined as a change in the location of something that exists, a physical object.

In this way, we say that a photon exists, because it can be acted upon, but how can we act upon the constant c, apart from the photon that enters into it? It turns out that we can calculate c-speed, apart from the measurements of the photon’s change in location, using Maxwell’s equations, like we can calculate the zero timelike separation between physical bodies, but I’m not sure that means either one can be acted upon.

On the other hand, in an RST-based theory, we start by assuming a continuous increase of space and time exists, not a continuum of locations, but a scalar increase in a zero-dimensional quantity. Together, due to their reciprocal relationship, the increase of these two quantities defines a magnitude of scalar motion, by definition, like the B and E fields in Maxwell’s equations.

However, these quantities do not change locations, like the B and E fields. In fact, they don’t have the property of locations, as in x, y, z, or t in a continuum. They only have the property of dimension (i.e. scalar quantities with two, opposite, directions).

The fact that numbers, if also defined in terms of dimensional quantities, can be used to define exactly the same sort of a magnitude, again, by definition, is of deep fundamental significance.

But given this initial condition in the RST-based theory, we have to assume that a constant, uniform, change in the “direction” of increase, is just as permanent a condition as is a constant, uniform, non-change in the “direction” of increase, just as simple harmonic motion is just as permanent as translational motion, all things considered.

Though this is analogous to saying, “Let there be light, and there was light,” it is inescapable, and, truth be told, every physical theory has to be incomplete like this, as shown by Gödel.

Yet, once this new condition of equilibrium is admitted, the symmetry of the space/time relationship is locally broken, which is tantamount to “quantizing” the continuous increase, but without contradicting it; that is, the uniform change in scalar “direction” is analogous to the uniform change in vectorial direction that is inherent in an orbiting object: The object continues its forward motion even though it only goes round and round, never getting anywhere, “quantizing” both the space and time aspects of its motion, without compromising its continuity.

The thing is Tom, even though I know of no other way in which so much of what needs to be accomplished in theoretical physics, in the sense of uniting the discrete with the continuous, can be accomplished, without violating the principles articulated by Peter, it forces me to admit that it fits Einstein’s definition perfectly; that is, it requires a concept of something the physical properties of which are independent, but is independent of physical conditions. Go figure!

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Hello Doug,

You write "I guess it constitutes the argument on the other side of the coin so-to-speak. However, to say that something exists, such as Einstein’s spacetime, it merely has to be defined, as something with physical effect, yet also as something not effected by physical conditions, is a heavy concept."

It isn't just a definition. When Einstein speaks of spacetime as...

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Hello Doug,

You write "I guess it constitutes the argument on the other side of the coin so-to-speak. However, to say that something exists, such as Einstein’s spacetime, it merely has to be defined, as something with physical effect, yet also as something not effected by physical conditions, is a heavy concept."

It isn't just a definition. When Einstein speaks of spacetime as "independent in its physical properties, having a physical effect but not itself influenced by physical conditions," he is describing the kinematics of gravity and thus the basis for inertia. These effects are measurable.

You write:

"I’m not sure I understand things in the same way. I would say that if something can be acted upon, then it exists physically."

We act upon the real line of positive integers when we do arithmetic. Does it exist physically?

"I’m not sure that motion per se, i.e. a change of space and time, can be acted upon, unless the change of space that enters into the motion is defined as a change in the location of something that exists, a physical object."

We measure motion by changes in relative positions of mass points. Do points exist physically? Can you draw one?



"In this way, we say that a photon exists, because it can be acted upon, but how can we act upon the constant c, apart from the photon that enters into it?"

The photon's speed in a vacuum is never less than c. What it means to act on it, is to impose a medium by which that speed is slowed, or in which the photon is absorbed. Time has no meaning to a beam of immortal photons. They are not influenced by physical conditions. Particles, even massless ones, are real in a scientifically objective sense.

"It turns out that we can calculate c-speed, apart from the measurements of the photon’s change in location, using Maxwell’s equations, like we can calculate the zero timelike separation between physical bodies, but I’m not sure that means either one can be acted upon."

Again, it depends on what one means by acting on. Our mathematical results are representations of a physically measurable phenomenon, not the phenomenon itself.

"On the other hand, in an RST-based theory, we start by assuming a continuous increase of space and time exists, not a continuum of locations, but a scalar increase in a zero-dimensional quantity."

I can't understand how something that has no magnitude increases in magnitude.

"Together, due to their reciprocal relationship, the increase of these two quantities defines a magnitude of scalar motion, by definition, like the B and E fields in Maxwell’s equations.

"However, these quantities do not change locations, like the B and E fields. In fact, they don’t have the property of locations, as in x, y, z, or t in a continuum. They only have the property of dimension (i.e. scalar quantities with two, opposite, directions).

"The fact that numbers, if also defined in terms of dimensional quantities, can be used to define exactly the same sort of a magnitude, again, by definition, is of deep fundamental significance.

"But given this initial condition in the RST-based theory, we have to assume that a constant, uniform, change in the “direction” of increase, is just as permanent a condition as is a constant, uniform, non-change in the “direction” of increase, just as simple harmonic motion is just as permanent as translational motion, all things considered.

"Though this is analogous to saying, “Let there be light, and there was light,” it is inescapable, and, truth be told, every physical theory has to be incomplete like this, as shown by Gödel."

I am going to have to pass on commenting about RST theory,

since I don't know anything about it. However, Godel's

incompleteness theorem does not obviate a mathematically complete physical theory. The theorem addresses the limitations of any formal axiomatic system to prove all mathematical statements that are true using only the system of axioms. Considering this forum, I think it's especially appropriate to quote from Paul Davies' foreword to Gregory Chaitin's collection of essays, Thinking about Godel and Turing. Davies notes that in a finitely-resourced universe, a generic entangled state of just 500 quantum particles requires a list of 2^500 amplitudes, one for each branch of the wavefunction, which exceeds the theoretical maximum information capacity of the entire universe. However, Davies also notes that "...if one accepts Landauer's principle that only cosmic-computable functions should be invoked to describe the real physical cosmos, then the distinction between Turing and cosmic computability could lead to definite and potentially observable consequences." Davies agrees with Chaitin's claim that "perhaps mathematics and physics are not so different as most people think."

You continue:

"Yet, once this new condition of equilibrium is admitted, the symmetry of the space/time relationship is locally broken, which is tantamount to “quantizing” the continuous increase, but without contradicting it; that is, the uniform change in scalar “direction” is analogous to the uniform change in vectorial direction that is inherent in an orbiting object: The object continues its forward motion even though it only goes round and round, never getting anywhere, “quantizing” both the space and time aspects of its motion, without compromising its continuity."

Again, I'll have to defer comment.

"The thing is Tom, even though I know of no other way in which so much of what needs to be accomplished in theoretical physics, in the sense of uniting the discrete with the continuous, can be accomplished, without violating the principles articulated by Peter, it forces me to admit that it fits Einstein’s definition perfectly; that is, it requires a concept of something the physical properties of which are independent, but is independent of physical conditions. Go figure!"

Well, I certainly do prefer to go figure rather than rely on philosophy. Peter's principle, however (to coin a phrase), seems to deny that measurability is an objective property of the real universe. In such a universe, only philosophy happens.

Tom

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Hi Everyone,

Yes, NN, time IS short and I’m way behind in the discussion here. The thing is, we still cannot calculate the speed of light, Planck’s constant, or the electron’s mass, from first principles, let alone the stages of the universe’s existence. It’s so obvious that we yet lack answers to many fundamental questions.

But let me try to focus on the question of the...

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Hi Everyone,

Yes, NN, time IS short and I’m way behind in the discussion here. The thing is, we still cannot calculate the speed of light, Planck’s constant, or the electron’s mass, from first principles, let alone the stages of the universe’s existence. It’s so obvious that we yet lack answers to many fundamental questions.

But let me try to focus on the question of the existence of the “point,” first. Tom asks, “Do points exist physically? Can you draw one?”

Then Peter answers, “That's analogous to arguing that unicorns exist because you can draw one. Points exist in a platonic sense, but they don't physically (as distinct from representations in pictures, graphs etc).”

To which Tom replies, “Right. A point does not even physically exist as a representation of anything physical; it's a pure abstraction. It's long been known that physical phenomena that appear continuous can be analyzed discretely by treating points as lines. That requires a two dimensional method; i.e., complex analysis.”

Here we have the crux of the problem: How can we say what a physical point is then? Clearly, it’s not a line in the complex plane, even though the ad hoc invention of the imaginary number enables us to mathematically transform it into one.

It’s such a conflicted and contradictory concept that Einstein is reported to have opined, “It would be enough, if we just understood the electron.” Who can explain how can a point particle be charged, without flying apart? We can invent ad hoc concepts such as Poincaré stresses that enable us to go on theoretically, but who can feel confident with this expedient?

String theory was seen as a way out of the same kind of dilemma in terms of energy exchange, because it eliminates the point, the vertex, of the Feynman diagrams, but, so far, it’s only led us into a quagmire, a swampland of theoretical confusion and speculation.

Peter’s point is not that the concept of a point doesn’t exist and shouldn’t be used in physics, but that the concept cannot logically be employed to define the motion of an object in terms of changing space and time, if one looks closely enough, just as it cannot be logically employed to define an electron, or a vertex of a Feynman diagram, if one looks closely enough.

Tom, the invention of Poincaré stresses, to hold the electron together, and the invention of virtual particles, to enable energy exchanges, at a point in time and space, are the particle physicists way of avoiding the philosophical impasse that Peter raises in his essay, following the arguments of the Greeks. To insist that the current concept of the point is an illusion, is not just a non-scientific, philosophical, point; It is a physical point as well! (sorry LOL)

My answer to Peter’s challenge is that the discrete interval is an illusion all right, but it is nevertheless real in its effect. By assuming that there is no discrete interval in which there is no change, but there IS a discrete interval in which there exists a change in direction as well as in magnitude, we are able to escape the dilemma, having our cake and eating it too.

I wish I could go on, but I have to leave it at that for now. Maybe that’s good, because this is point that needs to be deeply pondered and soberly considered: All the trouble with physical theory, from the days of the ancients to our own day, when the proliferation of ad hoc inventions has gotten so out of hand, is founded in this mystery of the discrete versus the continuous.

As always, the philosophers have to keep the feet of the physicists grounded. We need more like Peter to make their voices heard, in my opinion.

Peace,

Doug

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Peter, I have read your paper, and I will reply to it just once more here, so as not to wear out my welcome in Doug's forum. You write: "I am beginning to question if you properly read my essay. It is time (and space and space-time), instants (and spatial points), and instantaneous magnitudes, that I am arguing do not exist, nothing more. Furthermore, showing how change is only possible due to...

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Peter, I have read your paper, and I will reply to it just once more here, so as not to wear out my welcome in Doug's forum. You write: "I am beginning to question if you properly read my essay. It is time (and space and space-time), instants (and spatial points), and instantaneous magnitudes, that I am arguing do not exist, nothing more. Furthermore, showing how change is only possible due to these things not existing (and that calculus [frozen] has its limits when applied to Nature [dynamic]) is the central thesis of my essay. That is, change is very much the major player in it."

Of course, mathematics is static. However, the representation of dynamic motion in mathematical symbols--through limit and function, domain and range, operation and correspondence--is no more outside the representation of nature than a representation of a state of dynamic relations represented in a painting or a pictorial diagram. The map is not the territory, but a map that corresponds to the territory leads one to predicted outcomes at specific points. As those outcomes are only measured in the territory to which the map refers, the non-existence of points (of which the manifest map is composed) would obviate any mathematical model to accompany your philosophy. Hence, my demonstrable claim that your philosophy is outside science.

I wrote earlier "When you deny that discrete instants exist, you obviate measurability of energy, because that measure depends on an exchange of particles between other particles and that exchange requires an interval, an instant."

And you replied, "No it doesn't. It simply requires a clock. Any mathematical value representing a reading of a clock (or meter) naturally represents an interval (and as such, two instants or spatial points to bound and determine such an interval), but it does not mean that such intervals or points exist. Indeed, one can show that if they did exist, one could forget about change, motion, energy and clocks altogether. Once again, your comment makes me wonder if you have given any real thought to my essay."

A clock marks a time interval, Peter. A meter stick marks a spatial interval. Einstein has been all through this. When you claim that your philosophy of motion obviates time and change, you are saying in essence that there is no exchange of energy between particles. Measuring a change in energy state is in fact how we objectively know that anything changes at all. For example, one can define a faster than light particle as a particle that changes direction without changing velocity; the statement is true, but there's no physics in it. By the same token, there's no physics in which motion is defined out of existence by disallowing an interval to measure it.

You continue, "Finally, you acknowledged that points do not physically exist, and yet, claim that instants do. As instants are obviously just points – point of time – you seem to be going around a little bit in circles."

Well, you said that instants are points, not I. Brushing aside your straw man, what I actually said was that points are pure abstractions. A point of time is an endpoint to an interval, initial condition t, or future condition t'. We use abstract symbols to express variables that are unknown until we make a calculation or take a measurement.

Doug wrote:

"Here we have the crux of the problem: How can we say what a physical point is then? Clearly, it’s not a line in the complex plane, even though the ad hoc invention of the imaginary number enables us to mathematically transform it into one."

This is a common misconception of complex analysis. I don't want to get bogged down in this; I would refer the reader to Barry Mazur's delightful treatment of the history and meaning of complex analysis in his book, Imagining Numbers. I will only go so far as to say, as Mazur makes clear, that we understand algebra through the geometry of the complex plane. To quote Jacques Hadamard quoting Paul Painleve, "The shortest path between two truths in the real domain passes through the complex domain."

Doug, I apologize for not replying more completely in your forum. I can't address your points without more knowledge.

Tom

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No worries Tom. To me, this is a significant, relevant and worthwhile discussion. Both you and Peter are defending your views vigorously, but politely. Feel free to keep it right here, if you like.

Peter, I don’t think there is a conflict here, if you understand what I’m saying. I agree with you that “There is no such thing as an instant in time, and regardless of how small the time...

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No worries Tom. To me, this is a significant, relevant and worthwhile discussion. Both you and Peter are defending your views vigorously, but politely. Feel free to keep it right here, if you like.

Peter, I don’t think there is a conflict here, if you understand what I’m saying. I agree with you that “There is no such thing as an instant in time, and regardless of how small the time interval or slowly a body is moving, its position is constantly changing and undetermined. If its position were not constantly changing, it could not be in motion.”

However, if we think of a continuous rotation as a constant change of space/time (e.g. a planet’s orbit), the continuous change of location, and the simultaneous change in direction, ultimately divides the orbital period into two halves.

Projection of the rotation onto the diameter of the orbit “folds” the motion, if you will. It folds it into two, discrete, halves, or into two intervals. These two intervals constitute a cycle of vibration, yet this happens without violating the continuity of the rotational motion, which never ceases; that is, two, discrete, intervals of space/time are formed from the constantly changing and undetermined motion of the rotating body.

Thus, in this sense, discrete intervals of motion emerge from the continuous motion, without paradox, as at some instantaneous point, a boundary is defined, when the “direction” at either end of the projected diameter is changed instantaneously (changed from more positive (negative) to less positive (negative), or changed from positive (negative) to negative (positive), when crossing zero).

On the other hand, while I concur that “Time, space, and space-time too, as commonly conceived as actual physical things, do not exist, [but] physical continuity (i.e. the capability for events to be continuous), and as such, motion and change, do exist,” I do not agree that we should therefore conclude that there is no flow of time (expansion of space), because “there is nothing there to measure.”

We can measure an interval of space, given the “basic and fundamental” physical continuity of substance, but only as an aspect of that continuous change by which we measure it. Similarly, we can measure an interval of time, but only as an aspect of that continuous change by which we measure it. Intervals of space (time) are simply measures of past (or contemplated) motion (change).

The problem comes when we seek to “divide” time (space) into indivisible, discrete, units, by defining interval as the distance between points, without recognizing that the act of dividing (measuring) is itself impossible without change. While such a procedure (division into intervals) cannot be conceived outside the definition of change, without contradiction, as you so correctly point out, it does not follow from this that it can’t be done in another manner that escapes the contradiction, i.e. by defining discrete intervals through a procedure in which change never ceases.

Hence, let me ask you a few questions: When we think of the directional change in an orbital path, as a constituent of continuous, 2D, rotational motion, does change occur in the two dimensions simultaneously? If not, in which dimension does the change occur first, and how can we tell? If so, what does this imply, if anything?

Since the “points” on the path of this 2D change are not ordered, we can choose any one as a “point” of reference, immediately determining the “point” diametrically opposite it. Does the next instance of motion, then, necessarily decrease the distance between the points, while the previous instance necessarily increased it, or is there an interval between these, when (where) the distance between them neither increased nor decreased?

Really, keep up the good work you guys!

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Dear Tom,

"As those outcomes are only measured in the territory to which the map refers, the non-existence of points (of which the manifest map is composed) would obviate any mathematical model to accompany your philosophy. Hence, my demonstrable claim that your philosophy is outside science."

You seem very keen to dismiss my work as philosophy. As it deals with questions of the...

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Dear Tom,

"As those outcomes are only measured in the territory to which the map refers, the non-existence of points (of which the manifest map is composed) would obviate any mathematical model to accompany your philosophy. Hence, my demonstrable claim that your philosophy is outside science."

You seem very keen to dismiss my work as philosophy. As it deals with questions of the existence of time, instants etc, a large part of it naturally is. However, it also has significant and direct relevance to a number of deeply fundamental questions and problems in physics. To be a bit bold, I should also note that the argument contained in my essay doesn't represent another solution to Zeno's paradoxes. As it is the assumption of instantaneous position that causes the paradoxes to result, it is the solution.

You are correct that my conclusions can have no mathematical model to back them up. As I mentioned in the essay, because the main point of the work was to show that calculus has limits when applied to the physical universe, trying to use calculus itself to demonstrate this would be impossible. Considering this, I don't think it can really be used as a criticism of the work though!

"A clock marks a time interval, Peter. A meter stick marks a spatial interval. Einstein has been all through this. When you claim that your philosophy of motion obviates time and change, you are saying in essence that there is no exchange of energy between particles..."

I can only assume that you completely ignored what I just said. I should also add that despite the quote often being attributed to him, it doesn't seem that Einstein said that time is what a clock measures. Being Einstein, he was a bit too clever for that. His original quote ("Zeit ist das, was man an der Uhr abliest") actually translates to "Time is what one reads off the clock." Although the difference seems tiny, as the first says that interval exists, while the actual quote neither affirms or denies its existence (although it leans towards that latter), the difference is quite big.

"Well, you said that instants are points, not I. Brushing aside your straw man, what I actually said was that points are pure abstractions."

This has gotten a little bit silly Tom, as you are not playing by the rules.

Dear Doug,

Thanks. I find your attitude very refreshing. I think what I just said about the measuring of intervals above (and in my essay), applies to what you just said on the topic as well.

"While such a procedure (division into intervals) cannot be conceived outside the definition of change, without contradiction, as you so correctly point out, it does not follow from this that it can't be done in another manner that escapes the contradiction, i.e. by defining discrete intervals through a procedure in which change never ceases."

I think the problem with that is, as soon as you define such an interval, you naturally invoke the existence of instants to bound and determine it as an interval. Because, if change is to be possible, instants cannot exist, no such interval can exist either. If you haven't read it already, some of the material in the notes linked to from my essay is related to this issue.

To try to answer your questions, I think the change would occur in the two dimensions simultaneously. In relation to your second question, the first, although the motion would be continuous, so that it is somewhat unphysical to talk about instances of motion. With the example, I can see what are you saying, but I do no think there is any sense in which the motions are physically discrete, as, with the motion being continuous, there can be no instant at which "the "direction" at either end of the projected diameter [instantaneously] changed."

Best wishes

Peter

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Peter, you write, quoting me:

T: "As those outcomes are only measured in the territory to which the map refers, the non-existence of points (of which the manifest map is composed) would obviate any mathematical model to accompany your philosophy. Hence, my demonstrable claim that your philosophy is outside science."

P: You seem very keen to dismiss my work as philosophy. As it deals...

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Peter, you write, quoting me:

T: "As those outcomes are only measured in the territory to which the map refers, the non-existence of points (of which the manifest map is composed) would obviate any mathematical model to accompany your philosophy. Hence, my demonstrable claim that your philosophy is outside science."

P: You seem very keen to dismiss my work as philosophy. As it deals with questions of the existence of time, instants etc, a large part of it naturally is. However, it also has significant and direct relevance to a number of deeply fundamental questions and problems in physics. To be a bit bold, I should also note that the argument contained in my essay doesn't represent another solution to Zeno's paradoxes. As it is the assumption of instantaneous position that causes the paradoxes to result, it is the solution.

"You are correct that my conclusions can have no mathematical model to back them up. As I mentioned in the essay, because the main point of the work was to show that calculus has limits when applied to the physical universe, trying to use calculus itself to demonstrate this would be impossible. Considering this, I don't think it can really be used as a criticism of the work though!"

It can't? You've got to be the first person I have ever encountered who claims that the language of science is unnecessary to settle scientific problems. Language may be independent of meaning, but no meaning is communicated without correspondence to linguistic symbols. And even though it is true (though exceedingly tedious and impractical) that any mathematically symbolic language can in principle be translated to literary language--for you to obviate the possibility of any such model to make your theory scientifically comprehensible, and then to say you can't be criticized for it, is...well...I don't know what it is if you don't call it philosophy. You certainly cannot call it science.

T: "A clock marks a time interval, Peter. A meter stick marks a spatial interval. Einstein has been all through this. When you claim that your philosophy of motion obviates time and change, you are saying in essence that there is no exchange of energy between particles..."

P: I can only assume that you completely ignored what I just said. I should also add that despite the quote often being attributed to him, it doesn't seem that Einstein said that time is what a clock measures. Being Einstein, he was a bit too clever for that. His original quote ("Zeit ist das, was man an der Uhr abliest") actually translates to "Time is what one reads off the clock." Although the difference seems tiny, as the first says that interval exists, while the actual quote neither affirms or denies its existence (although it leans towards that latter), the difference is quite big."

Reading what you please into Einstein isn't going to help your case, when Einstein's physics career was largely devoted to the science of measure. He was, after all, a classical physicist. The "quite big" difference in the reading of clocks refers to Einstein's discovery that clock readings are not absolute--moving clocks run slower. Now what was that theory?--oh, yes, it was called special relativity.

T: "Well, you said that instants are points, not I. Brushing aside your straw man, what I actually said was that points are pure abstractions."

P: This has gotten a little bit silly Tom, as you are not playing by the rules.

T: I must have missed seeing the rule that reciting facts is disallowed. Please provide a rule book.

Tom

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Tom and Peter,

I see that sarcasm is starting to creep into your debate. It would be a shame to let your differences degenerate into hostility at this point. Tom’s argument is that the concept of instants and instantaneous positions must be valid, in order for physics to work, while Peter’s point is that the only way the concept of change can be logically consistent is by rejecting the...

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Tom and Peter,

I see that sarcasm is starting to creep into your debate. It would be a shame to let your differences degenerate into hostility at this point. Tom’s argument is that the concept of instants and instantaneous positions must be valid, in order for physics to work, while Peter’s point is that the only way the concept of change can be logically consistent is by rejecting the validity of the concept of instants and instantaneous positions.

Peter’s position is arrived at philosophically, while Tom’s position is arrived at physically. Hence, Tom blames Peter’s epistemology, appealing to Einstein’s statement that time is what a clock measures, while Peter asserts that Tom is misconstruing Einstein’s statement to reinforce his argument by appealing to authority.

Thus, it appears that an impasse has been reached. In the meantime, however, I have stated that I agree with Peter that constant change and instantaneous position are inconsistent, since any interval of time in which change does not occur makes continuous change impossible, while admitting change during any interval, no matter how small, implies that yet smaller intervals must exist, by virtue of the definition of change.

But the identification of this impasse is precisely the reason that I would choose Peter’s essay as the contest winner in my book. Not that I think that he SOLVES the problem, mind you, but that I think that he identifies it so clearly and articulately. Meanwhile, Tom’s competence, in defending the implication that Peter’s argument can have no connection with science, is powerful and clear.

However, it was Einstein who describes this fundamental debate the best, I believe. He states:

“The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent upon each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is - insofar as it is thinkable at all - primitive and muddled. However, no sooner has the epistemologist, who is seeking a clear system, fought his way through to such a system, than he is inclined to interpret the thought-content of science in the sense of his system and to reject whatever does not fit into his system.

“The scientist, however, cannot afford to carry his striving for epistemological systematic that far. He accepts gratefully the epistemological conceptual analysis; but the external conditions, which are set for him by the facts of experience, do not permit him to let himself be too much restricted in the construction of his conceptual world by the adherence to an epistemological system.

“He therefore must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as the free inventions of the human spirit (not logically derivable from what is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research.”

I hope this helps Peter and Tom understand each other’s motivation better. However, here we are more interested in the impasse itself, than cooling the ardor of the contestants. What is the solution? Is it necessary that there be a solution? What is to be gained from it, if one does exists? Is it worthwhile to pursue it?

Of course, in the schools, as Lee Smolin, in his article, “A Crisis in Fundamental Physics,” has pointed out, the mantra “Shut up and calculate!” demonstrates the historic difficulty and the practical response to the question, which has been forced upon the educators, who must train scientists. But now FQXI, taking advantage of the new world classroom offered by the Web, which transcends the historic limitations of space and time, making it practical to undertake the discussion, has thankfully provided this discussion forum to take up the debate in earnest.

I, for one, couldn’t be more delighted. It is my desire to try to break the impasse by addressing the concept of change in the expanded context that includes the notion of “direction” in its definition, as indicated in my previous comment. I think that this may point to a fundamental aspect of the debate that has yet to be considered.

Doug

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Hi Doug,

You write,

"While I agree with you that the universe is organized from “pure space and time,” I must confess that I do not understand the conjecture in your essay, much less its mathematical support."

Do you mean my extension of Kepler's 2nd law of planetary motion to complex analysis? What I means is that, insofar as Kepler's law conserves angular momentum, a...

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Hi Doug,

You write,

"While I agree with you that the universe is organized from “pure space and time,” I must confess that I do not understand the conjecture in your essay, much less its mathematical support."

Do you mean my extension of Kepler's 2nd law of planetary motion to complex analysis? What I means is that, insofar as Kepler's law conserves angular momentum, a generalized n-dimensional conservation principle (n> 3) allows dissipative energy to drive orbital speed change (negatively) in imaginary time in the same way that conservation of angular momentum drives orbital speed change positively in real time. In other words, we measure angular momentum as a conserved quantity, only because excess energy is carried away as what we would perceive as negative entropy, into hyperspace. I say "perceive" because any (indirect)measurement of negative entropy would appear to us as temporal-reversed, just as we can interpret anti-particles in high energy experiments as traveling backward in time. I hope you can see from my paper that this effect is very tiny. Even so, consider the example that for the two bodies referenced--sun and Earth--the difference between 1.00000448 seconds in one direction and 0.99999552 in the other, about 9 X 10^-7 seconds, is still sufficiently large to measure. I haven't been on task yet to devise a thought experiment to test the conjecture, but I plan to. Perhaps some enterprising reader here has an idea.

You may be familiar with the physicist Mordehai Milgrom, who proposes an alternative theory to the dark matter model, in which Newton's familiar F = ma is modified with a term that makes dark matter superfluous to the explanation for flattening the galactic rotation curve. Milgrom calls the theory Modified Newtonian Dynamics (MOND). Milgrom's colleague Jacob Bekenstein devised a relativistic version of MOND called TeVeS (for tensor-vector-scalar), in which he calculated an equivalent theory in the non-relativistic limit which predicts gravity lensing. You can google all this, but I brought it up to make the following points:

MOND has been criticized for ad hoc-ness. The premise is that dark matter is a superfluous assumption, invented to explain the observed flat rotation curve; however, MOND is open to the same criticism, having not been developed from first principles.

My model does not obviate dark matter, but I think it does explain from first principles why the Milgrom and Bekenstein models are correct. That is, we don't need dark matter to explain local interactions or cosmic parameters. I think we do need it to explain the origin of inertia; the halo of dark matter that astronomers invented to flatten the rotation curve is, I think, spent inertial energy, i.e., mass, weakly interacting. To explain:

Recall that excess energy to which I referred earlier. Where did it come from? Because my model is a complex system of interacting nodes, it has the advantage of feedback effects--I explain in my ICCS 2007 paper that negative feedback informs the present, while positive feedback informs the future. Gravity being a universal negative feedback system, controlled information in a chaotic but metastable universe requires an energy throughput of just the barest difference in potential between between the future and the present. Where does that potential exist?--just as Hawking told us decades ago, just outside the black hole event horizon!

If we are staring right into the face of a huge primordial black hole, dark energy is no more than the event horizon and dark matter a high entropy mass slowly (by our relativistic measure)fading from view and interacting but weakly with low entropy matter--yet enough--to produce inertia for the whole universe of our 3+1 domain.

My excess energy term is derived from first principles, and not "by hand," and the math is not difficult--just a little algebra, analysis and topology. I would refer the reader to my ICCS 2006 and 2007 papers, and my longer proposed article to the InterJournal of complex systems. Link addresses are provided at my Comcast site:

home.comcast.net/~thomasray1209/site/

Doug, I appreciate your noble effort to mediate between Peter Lynds and me. However, having twice been called silly and told that my theory has no physical basis (?), I will have nothing further to say. Parenthetically, though, I will relate this anecdote:

Having just noted that the distinguished David Finkelstein has submitted an essay here, I was reminded that years ago I submitted a paper containing a germ of my present thought, to the prestigious journal he edited. I received back a short handwritten rejection with the words, "interesting and plausible physical ideas, not accompanied by a mathematical theory which would incorporate them." It was a kindness, and a lesson, I shall never forget.

Shut up and calculate, indeed. (Actually, I thought that was Feynman's line.)

Tom

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Hi Everyone,

Well now that the contest is closed there is nothing left but the voting for the best of the 126, or so, 10 page essays! I see Carlo’s essay, which was the first to receive 2 restricted votes, has now received 3 restricted votes. It makes me wonder if this early lead reflects a tendency in the community to favor the “End of Time.” If so, I guess we can expect to see...

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Hi Everyone,

Well now that the contest is closed there is nothing left but the voting for the best of the 126, or so, 10 page essays! I see Carlo’s essay, which was the first to receive 2 restricted votes, has now received 3 restricted votes. It makes me wonder if this early lead reflects a tendency in the community to favor the “End of Time.” If so, I guess we can expect to see Julian Barbour’s essay receiving many votes as well.

In the meantime, I’m still sticking with Peter Lynds’ essay, because, in my opinion, he returns to the most fundamental issue of all. The challenge of discovering how nature combines the discrete and the continuous is by far the most important task, facing theoretical physics, and it is the key to redefining our understanding of the nature of space and time, in the coming revolution of physics, prognosticated by David Gross and others.

The new essay of David Hestenes has to be my second choice, at this point, because, in my opinion, his conviction, following Einstein and many others, that it is to the laboratory of the electron to which we should turn, if we are to understand the foundation of quantum mechanics, is right on.

His report of the new experimental data showing evidence that the electron is indeed a clocked system, enabling him to extend his model of the electron, based on his Zitter concept, and to explain many quantum mechanical mysteries that have been intractable before now, is just a plain exciting development to me.

Finally, because symmetry is so important, as a foundational principle of physics, indicating where to find its laws of conservation, I have to vote for Phillip Gibb’s essay too.

It’s not that I agree with the conclusions of any of these three authors, or that other essays aren’t equally, or even more, impressive in some ways. It simply boils down to the fact that it is my conviction that time is simply one aspect of change, and, as they say, it takes two to tango.

With this thinking, since we know that the universe changes inexorably, whether or not we are present in body or mind to observe it, then we must conclude that the most likely candidates for the fundamental dancing couple are space and time, or at least what we have called space and time.

It’s very clear, upon reflection, that we cannot measure either of these two without the other. Space, as distance, is just the history, or just the calculation, of the space aspect of the motion, or changing space/time, needed to measure it, nothing else. Likewise for time, it is just the aspect of the motion needed to measure it, having no significance apart from its reciprocal relationship with space, in the equation of motion (i.e. we can ‘forget time’ as an independent entity, but not as the reciprocal aspect of space, in the equation of motion).

However, to measure anything requires the determination of unit intervals of change, and while, for us, those units may be arbitrary, they certainly are not arbitrary for Mother Nature. At the same time, though, we have learned that units of measure, including the units of space and time measure, are relative, not absolute, in terms of inertial reference systems. But, surprisingly, this is nothing new, since the ancients knew it as well, when Western civilization was just a gleam in the eye of mankind.

However, what we have yet to fully recognize is that there is a definite order in these relative magnitudes, ultimately making them absolute magnitudes, relative to the unit space/time ratio, and this is where the principle of symmetry first comes in.

Einstein’s limit on the speed of light is easily understood in terms of symmetry, where unity is the lightlike curve, but also the combination of spacelike and timelike curves, which are nothing more than the space/time ratios that are less than and greater than the unit space/time ratio, respectively, in the same way that the sides of a square are related to its diagonal.

Such symmetry, in the changing space/time ratios, clearly suggests that it is the space/time system itself, which is most likely to be the fundamental system of the universe, a fundamental system of motions, if you will. In such a system, the “fabric” of spacetime, radiation, matter, gravity, galactic formation and recession, entropy, the arrow of time, etc, all emerge as complex subsystems/phenomena of the fundamental, space/time system.

Of course, the devil is in the details, but the fact that, in this case, the fundamental symmetry is between two, inverse, entities, which corresponds to the rational number system, is a phenomenal discovery of fundamental significance. Though this unification of kinematics and mathematics has long been suspected, until now it has not been possible to make the identification.

Moreover, the fact that the physical space/time system and its corresponding system of rational numbers, fits perfectly into the system of abstract algebra, without the need of employing ad hoc inventions, giving us a whole new insight into the meaning of the so-called reals, complexes, quaternions and octonions, simply boggles the mind with the portent of things to come.

We knew the magic of combining dimensions with numbers, but to behold it in such a perfect, harmonious, state, being one with the spectrum of space/time magnitudes, was something too glorious to have even been anticipated. Now, when we see that the inverse of all this emerges, when space/time becomes time/space, our appetites are irresistibly whetted, because, like kids on a teeter-totter, we can see how one face of the universe, is just the inverse of the other face, and we can see how the two can be interchanged; Which one is on our left hand, and which one is on our right hand, is entirely dependent upon our point of view.

From this perspective, we can see that, while the expansion of space creates an irreversible arrow of time, in the context of the low-speed side of the universe, the expansion of time creates an irreversible arrow of space, in the context of the high-speed side of the universe, one side mirroring the other side. Now we see that what is space on one side, is time on the other side, and what is time on one side, is space on the other side, so one cannot tell which is which, except from across the unit boundary;

When crossing the boundary, nothing seems to change, even though looking from across the boundary, it seems that there is a huge difference in magnitude, where one side is much lower than the other side, and its magnitudes increase to infinity, but, in reality, this is only an illusion; One side’s zero is just the other side’s infinity, and vice-versa that’s all.

It’s elementary to see how this works, when we understand that space/time becomes time/space on the other side of unit speed, even though without this knowledge, it must be impossible to think that the spacetime of one side of the universe becomes the timespace on its inverse side.

But as Baez said, “It takes guts to do theoretical physics.”

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Having commented a lot about the importance of instants and intervals that drove me to vote for Peter’s essay, and the principles of symmetry that drove me to vote for Philip’s essay, I now want to write about why I voted for Hestenes’ essay. Here is the first of two parts of a lengthy explanation:

One of the reasons I voted for Hestenes’ essay is that I agree with him that the...

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Having commented a lot about the importance of instants and intervals that drove me to vote for Peter’s essay, and the principles of symmetry that drove me to vote for Philip’s essay, I now want to write about why I voted for Hestenes’ essay. Here is the first of two parts of a lengthy explanation:

One of the reasons I voted for Hestenes’ essay is that I agree with him that the electron should be the focus of study, if someday we want to understand the foundations of quantum mechanics. Another reason that I voted for it is because he refers to the new experimental results, which he explains, showing the existence of an intrinsic frequency in the electron.

But I want to comment on his analysis too somewhat, because it shows some important dimensional confusion that is relevant to my RST-based approach. As mentioned in my essay, it has been shown by Larson, and independently by Borg, that the units of all physical entities can be expressed in terms of the four dimensions of space, s, and its reciprocal, time, t.

When this is combined with Larson’s procedure for quantizing space and time, as explained in my essay, via the two constants of velocity and frequency, the dimensions of Planck’s constant become the dimensions of momentum, t^2/s^2, not the dimensions of action, t^2/s.

This is relevant in Hestenes’ essay, because his point of departure is the work of de Broglie, who deduced that matter is associated with periodic waves, that massive point particles each have an associated frequency of oscillation, which, for the electron, Hestenes shows to be .77634 x 10^21s^-1.

After noting this, the author points out the remarkable fact that, probably due to the inaccessibility of such a high frequency oscillation, no one, until recently, even thought about testing the de Broglie result. Indeed, no one but the French has ever even taken the idea of intrinsic electron oscillation seriously. So much so that they had to resort to a stratagem in order to get the funding to perform an experimental test of the de Broglie hypothesis!

But when they managed to do it, and found the positive result, they had no theoretical basis to explain it, even though, unbeknownst to them, Hestenes had developed a theoretical model describing the oscillation, based on his 3D geometric algebra, or rather his 4D spacetime algebra, called geometric calculus.

Now Hestenes’ work has always been important to me, because he was the first to bring to light the work of Clifford, in connection with Grassmann and Hamilton, which led to the understanding of the independent spaces of the tetraktys, interpreted in terms of operational, as well as quantitative, values of numbers. This fundamental mathematical discovery led Hestenes’ to his unusual idea, following Clifford, of combining scalars and vectors into the geometric product, the pillar of geometric algebra.

However, Hestenes’ use of the operational interpretation of number comes in the form of rotation, where multivectors are formed by interpreting the imaginary number ‘i’ as a rotation, defining the “orientation” of the bivectors in the third of the tetraktys’ four linear spaces, while the trivector pseudoscalar of the fourth space becomes the unit imaginary number, designated ‘I,’ used for inversions.

As, can be seen from my essay, I do not use the idea of an operational interpretation of number in this way, but, instead, use it to define the scalar speed-displacements of the RST. In this way, a new, 4D, scalar algebra emerges from the four independent spaces of the tetraktys, which does not employ the concept of vector at all, much less the imaginary number ‘i’.

In this manner, we are able to arrive at basis “scalars,” rather than basis “vectors,” and thus quantize the speed displacements of the RST. Hence, we can now make sense of an equation like f = ma, in terms of space/time dimensions, so that t/s^2 = t^3/s^3 * s/t^2 now makes sense quantitatively, as well as dimensionally.

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Part 2 of commentary on Hestenes vote.

With this much understood, we can now look at Hestenes’ introduction of de Broglie’s equations, and try to clarify some of the dimensional/conceptual confusion that the RST approach brings to light.

When we consider Planck’s constant, we see that it has the dimensions of action, t^2/s, which, when multiplied by frequency, nu, with...

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Part 2 of commentary on Hestenes vote.

With this much understood, we can now look at Hestenes’ introduction of de Broglie’s equations, and try to clarify some of the dimensional/conceptual confusion that the RST approach brings to light.

When we consider Planck’s constant, we see that it has the dimensions of action, t^2/s, which, when multiplied by frequency, nu, with dimensions 1/t, yields the dimensions of energy, t/s.

As Hestenes introduces the fundamental equations in his essay, he annotates them with remarks, indicating the familiar interpretations, such as “Energy is frequency” (Planck’s equation, E = hv), “Mass is energy” (Einstein’s equation, E = mc^2), and then the less familiar, “Mass is frequency” (de Broglie’s equation, ωB = mec^2/hbar).

However, in the first and last equation, unlike in the second, the dimensions are not the dimensions of energy, mass and velocity alone, where velocity merely seems to act as the mysterious conversion constant between mass and energy, but they also include the dimensions of Planck’s constant, h, and since the dimensions of h are the dimensions of action, which are the dimensions of area times mass per unit of time, or (s^2 * t^3/s^3)/t = t^2/s, which really are the dimensions of inertia, t^3/s, times frequency, 1/t, we can rewrite the de Broglie frequency equation as the energy equation:

E = Iω^2,

where ‘I’ is inertia, and ω^2 is the 1/t term in Planck’s constant h, times nu, times 2π.

Nevertheless, as noted by Larson, frequency, as cycles per second, 1/t, is really a velocity, s/t, in space and time terms, where the “direction” of the motion reverses every 180 degrees, and as such the term 1/t is actually an auxiliary device, used as a mathematical expedient to express the units of periodicity in rotational motion.

When this fact is recognized, and the proper space/time dimensions of velocity are substituted for the dimensions of frequency, in the radiation equation of energy, the dimensions of Planck’s constant become the dimensions of momentum, not the dimensions of action: Thus, the energy equation of radiation becomes t^2/s^2 * “s/t” = t/s, in space/time terms, where “s/t,” the velocity term, is the “velocity” of oscillation, in which the “direction” of the motion is periodically changing; It is not the uniform translational velocity, as indicated by the quotation marks.

In the same way, the energy of the de Broglie equation can be viewed as t^3/s^3 * “s^2/t^2” = t/s, conforming to the dimensions of the Einstein equation, when the periodic “velocity” term is substituted for the frequency term.

Consequently, we see that the use of the mathematics of frequency hides the fact that these three equations are not all that different. The radiation equation, E = hv, can be rewritten as E = Iω^2, which in space/time terms is equivalent to E = mc^2, when the “velocity,” ω, has the value c (in units of 2π). Likewise, the de Broglie equation, ωB = mec^2/hbar, can be rewritten as E = Iω^2, where the same thing holds, when the “velocity,” ωB, has the value c; That is to say, there appears to be only one, underlying, energy equation, not three.

Ironically enough, however, equating translational c-speed, with oscillating c-speed, is mathematically problematic, when “direction” reversals of c-speed are used to define the quanta of speed-displacement, as we do in our RST-based theory. This is due to the fact that, upon reflection, we can see that this “folding” of c-speed through oscillation means that ω, the frequency of the oscillation, in terms of units of 2π, can never really equal c-speed, since by definition, oscillation can only be achieved in one or two ways: Either the space aspect of the motion has to oscillate (the oscillating spatial pseudoscalar), or the time aspect of the motion has to oscillate (the oscillating temporal pseudoscalar), while the reciprocal aspect (the temporal or spatial scalar) continues to increase uniformly.

In the former case, the frequency of the oscillation is 1/2 c-speed, and, in the latter case, the frequency is 2/1 c-speed. Hence, if we double 1/2, we get 2 * 1/2 = 2/2 = 1, and, if we divide 2/1 in half, we get 1/2 * 2/1 = 2/2 = 1, but, in terms of cycles, this makes no sense, because, under this familiar mathematical operation, the number of cycles is doubled, while the number of time (space) units required to complete these two cycles is not. The number of reciprocal units, time or space, in each case does not change, under the doubling (halving) operation. The same number of scalar units is required to complete two cycles as is required to complete one cycle.

Clearly, something is wrong with this. If the number of cycles is doubled, then the number of time (space) units to complete those cycles must be doubled as well, when we are adding these ratios together as units of oscillation. So, the only thing we can do, to be mathematically consistent, in doubling (halving) the 1/2 and 2/1 space/time ratios as units, is to multiply both the numerator and the denominator by 2; that is, in both cases, the operator must be 2/2, not 2/1 and 1/2: In this way, we get 2/2 * 1/2 = 2/4, and 2/2 * 2/1 = 4/2, which, in effect, conserves the frequency, since 2/4 = 1/2, and 4/2 = 2/1.

But, then, if the frequency is conserved, what changes, when the number of these pseudoscalar oscillations is doubled (halved)? Well, obviously, given the energy equations just discussed, the only thing that can change is the energy/mass term, but in terms of the pseudoscalar oscillation’s geometric properties, the SIZE of the pseudoscalar changes.

Under the doubling operation, the radius of the sphere, isomorphic to the scalar (either 0D time or 0D space) is doubled and, consequently, so is the diameter of the sphere, which is always twice the size of the radius and generates the 1D, 2D and 3D pseudoscalars, increasing them exponentially, according to their dimensions.

In Hestenes’ model, when the energy/mass of a particle changes through interaction, the radius and zitter frequency vary, in order to maintain the velocity of light. Now we can see that, in the RST model, it is the 1:2 ratio of the pseudoscalar’s radius and diameter that is maintained, as the properties of the system change, which is tantamount to maintaining the speed of light, only in this case, it’s the “velocity” of light in the periodic variation that is maintained.

In a former paper, Hestenes writes:

‘The zitterbewegung, if it turns out to be physically real, is belated confirmation of de Broglie’s original hypothesis that the electron has an internal clock with period precisely equal to twice the zitter period, precisely the relation between the period of a rotor and that of a vector it rotates. As we have seen, the physical signature of zitter is a rotating electric dipole with ultra high frequency. If this exists, its implications for quantum mechanics will be far-reaching.”

Indeed.

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Hi Larry,

No, not at all, but what I am saying is that his attribution of the electron’s properties to a “clock,” a zitter frequency, supports the RST-based model as well, since it also consists of oscillations, though oscillations of very different kind.

Hestenes’ model is based on a circulating point charge of very high frequency, and the figure in his essay shows its world...

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Hi Larry,

No, not at all, but what I am saying is that his attribution of the electron’s properties to a “clock,” a zitter frequency, supports the RST-based model as well, since it also consists of oscillations, though oscillations of very different kind.

Hestenes’ model is based on a circulating point charge of very high frequency, and the figure in his essay shows its world line chart. Thus, as time marches on, the free particle, rotating around a point at light-speed, traces a helical pattern.

The equations of motion for this approach were first worked out by Myron Mathisson in the late 30’s, then extended by Weyssenhoff and Raabe in the 40’s. It started with the assumption of intrinsic angular momenta as an approach to spin particles, but it eventually included spin particles with dipole and quadrupole momenta, investigated by Średniawa, in the form of something call “a bilocal model.”

The whole idea goes back once again to the problems with discrete points. Physicists need a field theory to escape the enigma of elementary point particles, and the bilocal theory of Yukawa was very popular in the 50’s, as an alternative to a point particle with no internal structure. According to Rzewuski, the Yukawa theory describes a particle in terms of two four-vectors. One is at the center of rotation, while the other is at the circumference. The trouble is, in order to make the volume of the sphere spacelike and covariant, it is necessary to introduce a mysterious, timelike, unit vector, pointing towards the future, he says.

But I think Hestenes calls this the “time parameter,” and though it had to be introduced ad hoc into the bilocal theory, he finds that one can attribute it to the spin observable, in his theory:

“As proper time cannot be defined on a lightlike curve, a physical definition of the time parameter τ must be determined by other features of the model. We shall see that an intrinsic definition of electron time derives from the assumption that the electron has an intrinsic angular momentum or spin.”

The intrinsic angular momentum was also the idea of the early investigators mentioned above, I think, but they had no physical justification for the particle’s bilocality, which, together with the ad hoc time vector, pretty much killed the idea, according to Rzewuski.

I’m still not sure I understand how Hestenes gets around this, and, unfortunately, he hasn’t engaged at all yet in the discussion in his essay’s forum, so we don’t get a chance to ask him questions (one of the main virtues of FQXI initiative, in my opinion).

At any rate, the RST-based theory is nothing like this bilocality model, as, first of all, it’s strictly a model of kinematics initially, starting with nothing but the continuous increase of space and time, with no concept of mass, momentum or force to work with until they emerge from the theoretical development.

In other words, the RST-based theory’s dynamics must emerge from its kinematics, but even this description falls short, given that the scalar motion of the system has no cause; It is assumed in the fundamental postulates of the system.

I hope this helps.

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Hi Larry,

I appreciate your probing questions. You’re right. I ought to give the reasons why one should vote for my essay. To say that it quantizes time, without violating Lynds’ arguments, that it is based on underlying symmetry principles, as is Gibbs’ article, and that its model of the electron and other particles constitutes a high-frequency clock, in a similar fashion to...

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Hi Larry,

I appreciate your probing questions. You’re right. I ought to give the reasons why one should vote for my essay. To say that it quantizes time, without violating Lynds’ arguments, that it is based on underlying symmetry principles, as is Gibbs’ article, and that its model of the electron and other particles constitutes a high-frequency clock, in a similar fashion to Hestenes’ findings, is not enough.

To vote for an essay in this contest, I think one should be sure that it has something revealing to say about the nature of time. My essay does that. It says that the most important feature of the nature of time is that it is the reciprocal of space, in the equation of motion; that is, it asserts that time does not exist, apart from its relation to space.

This is a highly significant proposition for several reasons. First, it is something that is observable. We cannot measure space without time, and we cannot measure time without space. To measure space, as distance, or time, as duration, requires motion. Without it, neither space nor time can be observed.

Conversely, the observation of space and time, the measurement of them, implies the existence of motion. All the separate objects in a room, lying in various locations, imply the existence of the past motion that separated them. Indeed, this is the very basis of the big bang theory, except that, in it, spacetime also moves (a spatial point expands into a spatial “room,” expanding the original material in the point, i.e. the objects don’t separate out into a pre-existing room).

However, what is important to realize is that if we observe the incessant march of time, intrinsic to objects at rest, bound together in a gravitational field, then this implies the continual existence of motion that is NOT measured by the motion of objects between space and time locations.

There is no escaping this conclusion. The mere existence of the zitter frequency, or the de Broglie frequency, implies that a universal motion exists, forming the basis of the electron and the other so-called elementary particles. The passage of time requires that a complementary, incessant, march of space also exists, which must be the reciprocal of the observed march of time, and oscillations in this universal motion are the prime candidates for explaining matter and radiation.

The fact that a universal motion does indeed exist, at great distances, as observed in the universal recession of the galaxies, and in the expansion of the space between them, is a great confirmation of this compelling conclusion. Unfortunately, however, the two conclusions, the one that implies that the past motion, separating the galaxies, is a globally reversible motion of universal expansion from a single point in the past, and the one that implies that it is not a globally reversible motion at all, but only a locally reversible motion, a local manifestation of broken symmetry, are difficult to distinguish.

But even raising the possibility of the alternative conclusion gives us a way out the dilemma that every other leading approach in this essay contest suffers from: The necessity to introduce matter into space and time, eventually leads us to the paradoxes Peter delineates, because, given matter as separate from space and time, no way has been found to quantize space and time without inconsistencies, as Sadykov points out (although Rylov has an interesting mixed approach.)

The way out of this ancient dilemma is to recognize that each space/time magnitude (observable) intrinsically has two directions, and, while no instantaneous change in position can exist without contradiction, a change in direction cannot be other than instantaneous.

The profundity of this fact opens the door to understanding the fundamental nature of space and time in way that has never before been possible: We can now see how all things must consist of motion, combinations of motions, or relations between them.

This is good news on all fronts, especially as one becomes aware of the mathematical consequences of the concept. For example, it immediately becomes apparent, from the considerations of symmetry and the mathematics of motion, that an irreversible arrow of space progression, as well as an irreversible arrow of time progression, must exist, given the symmetry of a universal motion equation.

But once one realizes that identifying the nature of time, as simply one aspect of a universal motion, and that to satisfy the demands of symmetry, an irreversible arrow of space must exist, to compliment the observed, irreversible, arrow of time, our entire cosmology changes dramatically.

With this much understood, it’s not long before we can fully appreciate that the prognosticated revolution in our understanding of the nature of space and time could not be more profound in its impact on our understanding of particle physics and gravity. The enigma of discrete particle physics is swallowed up in the harmonics of local space and time vibrations, while the concept of proper space, accompanying the concept of proper time, swallows up the enigma of smooth relativity.

The trouble is, that confusing the universal expansion of space, as just one aspect of an unrecognized universal motion, which constitutes the measurement datum of an infinite and eternal universe, consisting of nothing but motion, with a more familiar motion that supposedly separated an infinitesimally small, infinitely dense, lump of pre-existing matter, almost 14 billion years in the past, is only to be expected, at first.

But now it’s time to move on. It’s time to thaw the frozen river of time, before it’s too late. What more could you ask of an essay, Larry?

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In his essay, Sean Carroll writes:

“What if time exists, and is eternal, and the state of the universe evolves with time obeying something like Schrödinger’s equation? This is a point of view that has by no means become obsolete, and may ultimately prove to be indispensable. We will find that, by taking time seriously, we can conclude a great deal about the deep architecture of...

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In his essay, Sean Carroll writes:

“What if time exists, and is eternal, and the state of the universe evolves with time obeying something like Schrödinger’s equation? This is a point of view that has by no means become obsolete, and may ultimately prove to be indispensable. We will find that, by taking time seriously, we can conclude a great deal about the deep architecture of reality.”

In other words, Sean suggests that we entertain the notion that there is no big bang singularity to block the progression of time from eternity to eternity; that is, let’s assume that time is what it is observed to be, an eternally flowing river, not a frozen river.

What a novel idea! However, Sean’s challenge, in invoking “something like Schrödinger’s equation,” is that the equation is reversible, while the entropy of the big bang universe, the observed arrow of time, is not reversible. To reconcile the disparity, one has to reconcile the old assumption that the lowest entropy state of the universe began with a bang, with the new assumption that there is no beginning, implying that there could not have been a single starting point of lowest entropy in the past.

So the question becomes, “How can the arrow of time be explained without the big bang?” In Sean’s words, “Can the observed arrow of time be explained by the apparently reversible physics embodied in the Schrödinger equation?” His novel approach to this task is to take the cycle out of the wave equation!

Actually, a non-periodic wave is a logical contradiction, so it’s not the rotation per se that he removes from the wave equation, but, rather, he takes the view of projective geometry, where the spatial rotation in the complex plane is transformed into the unit temporal spiral that is dual to the unit linear advance. In this way, the unit rotations of phase space (the basis of the gauge transformations) never return to the same point in space, but spiral eternally forward in time.

Thus, Sean transforms the finite-dimensional Hilbert space into an infinite-dimensional Hilbert space, which he dubs a “Heraclitean” universe, a universe in which change is the primary, or fundamental, concept.

While this produces a “state of the universe [that] evolves with time obeying something like Schrödinger’s equation,” the problem is that combining it with ordinary quantum mechanics leads to the prediction that the observed universe is dead!

To get around this obstacle, an ad hoc invention is needed to make the Heraclitean universe of eternal, non-recurrent, change, in which there can be no end, since there was no beginning, conform to a universe in which an end can be imagined. This ad hoc invention takes the form of “an accumulation point of energy eigenvalues.”

In other words, somehow, in this view of the eternal river of change, there must be a disturbance that temporarily backs up the ever increasing entropy of the universe, like a boulder that temporarily backs up the flowing water, in the middle of a Rocky Mountain stream.

That just such a “boulder” seems available in the unstable de Sitter space has driven the speculation so far, but as Sean admits, “We are a long way from understanding the details of such pictures, or indeed whether they make much physical sense at all.” However, that’s not the point. The point is that such thinking provides a roadmap for investigators. Sean writes:

“But there are robust features of the models that may very well survive as part of a better-developed understanding. The crucial point is that the universe finds itself in a state that will never settle down into equilibrium. In such a situation, the kind of entropy gradient we currently find ourselves in is perfectly natural; entropy is growing because entropy can always grow.”

If I had another vote, I think I would vote for Sean’s essay, not because I agree with his conclusions, any more than I agree with Peter’s, or Philip’s, or David’s, but because I agree with his observation that “entropy is growing because entropy can always grow.”

Given the arguments based on the discrete versus continuous paradox, the demands of symmetry, the de Broglie frequency of mass, and now the argument that the most reasonable view of time is that it is an eternal increase, with no beginning and no end, there is only one essay that reflects the characteristics of the one solution that answers all these requirements in an eloquent, beautiful, and compelling manner.

What Sean needs now is an infinite-dimensional Hilbert “time,” to go along with his infinite-dimensional Hilbert space, where the low entropy of the arrow of time is actually the high entropy of the arrow of space, and vice-versa. But that's another story.

If he's ever interested, though, someone tell him to call me.

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Hi Doug,

I much appreciate this reply, as it finally gives me a handle on your theory in language that I can understand.

A scalar, by definition, is a magnitude without direction. Time is a scalar in general relativity because it is a simple parameter of reversible direction. When you define scalar as a magnitude increasing in all directions of space and time, this is not what...

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Hi Doug,

I much appreciate this reply, as it finally gives me a handle on your theory in language that I can understand.

A scalar, by definition, is a magnitude without direction. Time is a scalar in general relativity because it is a simple parameter of reversible direction. When you define scalar as a magnitude increasing in all directions of space and time, this is not what mathematicians generally mean. What your operation requires is an infinity of vectors expressing the same scalar magnitude of spacetime from a fixed point.

When you assumed from the outset that a unified space and time are expanding at a constant rate in discrete dimension spheres, you forgot one critical point: after 3 dimensions, we are in hyperspace. Because of this crucial omission, and because you assume that n-dimensional motion is continuous in both space and time (in contradiction to your treatment of discrete dimension spheres), your mathematics is inconsistent. Here’s why:

What you call the “1D component of spherical expansion” is actually a topological 1-sphere, i.e., a 1-dimensional sphere in 2 dimensions. How do I know this?—because what you call the “space-time ratio=6” is a sphere packing in 2 dimensions, and the maximal kissing number. Why does this have to be so?—because you start out with the assumption of discrete Euclidean dimensions combined with time. Then your next space-time ratio=12 is the sphere packing & kissing number of the 2-sphere, i.e., a 3-dimensional sphere. You’re okay, then, for dimensions 1, 2 & 3. What happens when you move up to dimension 4? That’s the inconsistency in your technique. You’ve forgotten that of the 16 components of the Riemann tensor metric (remember, you have assumed a space-time combination, or Minkowski space, Euclideanized in d= 1,2,3 from the beginning), 6 components are redundant. With the 3-sphere, i.e., a 3-dimension sphere in 4 dimensions (skipping a lot of technical details here), the sphere packing & kissing number is 24. These packings, in dimensions 1—4 (also in d=8 & 24) are known and proved. The “3D expansion” compatible with your Euclidean model is then 8 + 2 (=10, or 16-6); i.e., 8 components of space and 2 of time. This works for continuous functions in general relativity, but not for your discrete treatment of dimensional spheres, and not for infinite-dimension Hilbert space.

At last, I understand why you took Peter Lynds’ essay—which is completely empty of physics—so seriously. Your universe is massless, and assumes mass created by a fundamental motion of space and time, while Lynds assumes motion without space and time. Both of these views obviate the exchange of mass –energy between bodies, which defines motion and makes the analysis of mechanics possible.

You write that “…mass and energy should be quantifiable, in terms of …changing space and time quantities.” Well, of course they are quantifiable, and quantified, in special relativity (E=mc^2), which treats only uniform motion. General relativity incorporates the change properties by dealing with acceleration. That’s what acceleration is, a change in the direction of motion.

Fotini Markopoulou has an interesting theory of time without space. See my question in her forum, which hints at why I prefer 10-dimensional supersymmetry to explain the continuation of time’s arrow in hyperspace.

All best,

Tom

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Hi Tom,

I appreciate your willingness to earnestly engage. You write:

“A scalar, by definition, is a magnitude without direction. Time is a scalar in general relativity because it is a simple parameter of reversible direction. When you define scalar as a magnitude increasing in all directions of space and time, this is not what mathematicians generally mean. What your operation...

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Hi Tom,

I appreciate your willingness to earnestly engage. You write:

“A scalar, by definition, is a magnitude without direction. Time is a scalar in general relativity because it is a simple parameter of reversible direction. When you define scalar as a magnitude increasing in all directions of space and time, this is not what mathematicians generally mean. What your operation requires is an infinity of vectors expressing the same scalar magnitude of spacetime from a fixed point.”

You are right about the definition of the scalar, but you are mistaken when you think I define it differently. It is the pseudoscalar magnitude that increases in all directions. In the case of the spatial pseudoscalar, the increase is in all directions of space, as the reciprocal temporal scalar increases. In the case of the temporal pseudoscalar, the increase is in all directions of time, as the reciprocal spatial scalar increases.

The equation for pseudoscalar expansion is the same as the equation for linear distance, except for the dimensions of the quantities involved. The equation for the spatial pseudoscalar expansion is:

s^3/t^0 * nt^0 = ns^3,

where n is the number of discrete units of elapsed time. The inverse of this is the equation of the temporal pseudoscalar expansion:

t^3/s^0 * ns^0 = nt^3,

where n is the number of discrete units of elapsed space.

Thinking in terms of “an infinity of vectors expressing the same scalar magnitude of spacetime from a fixed point,” is a spacetime perspective in which the infinite number of vectors are 1D paths of vector motion, or potential vector motion, but the realization of any one vector path must be defined as the motion of something changing locations from the origin to the spherical surface.

However, the strict definition of motion, a change of space per change of time, requires no change of an object’s location, only the changing quantities of the equation. Since we assume in the new system that the nature of time is that it is simply one of two, reciprocal, aspects of motion, this requires the existence of a “flow of space,” corresponding to the observed “flow of time.” Another way to say the same thing is to say that we assume the existence of a space clock as well as a time clock.

You write:

“When you assumed from the outset that a unified space and time are expanding at a constant rate in discrete dimension spheres, you forgot one critical point: after 3 dimensions, we are in hyperspace. Because of this crucial omission, and because you assume that n-dimensional motion is continuous in both space and time (in contradiction to your treatment of discrete dimension spheres), your mathematics is inconsistent.”

I don’t think so. Here’s why: The fourth dimension, time (space), is the reciprocal of the three spatial dimensions, in the equation of motion. Only when we want to define motion in terms of a 1D change of locations does the fourth dimension appear as a coordinate in spacetime, but this is not the concept of pseudoscalar expansion. Neither is it correct to imagine the space/time expansion as occurring in “discrete dimension spheres.”

It is only when we seek to measure the expansion, by picking a spacetime point in the expansion, does the “discrete dimension sphere” materialize. The motion is a continuous expansion without contradiction, because the quantization doesn’t appear until we introduce scalar changes of “direction” in the expansion.

Once these “direction” reversals are admitted, for a given point in the progression, the unit pseudoscalars follow, as oscillating pseudoscalars. In the case of the spatial pseudoscalar, the physical expansion/contraction is spherical, which means that our dimensions are necessarily expressed in terms of π. The 1D parameter is the circumference of the sphere (there are three orthogonal ones), the 2D parameter is the area of the sphere (three of these may also be defined), and there is one expanded volume, the inverse of the contracted point (the scalar).

Of course, these numbers conform to the mathematics of the binomial expansion in four dimensions, and we can therefore exploit the Clifford algebra, or the geometric algebra, of the Euclidean space, albeit in an unfamiliar manner.

What I mean by that is that we don’t regard the four linear spaces of the algebra as n-dimensional vector spaces. We regard them as n-dimensional scalar spaces, components of the infinite dimensional Hilbert space, if you will, but without defining a scalar in terms of the inner product of vectors.

For example, in the unit spherical expansion,

s^3/t^0 * nt^0 = ns^3,

where n = 1, there are three components of the s^3 expanded pseudoscalar. There are three, orthogonal, 1D units, each with two “directions,” or six units altogether. There are also three, orthogonal, 2D units, each with two “directions,” or twelve altogether, and there is one set of eight 3D units.

Now, as these n-dimensional units are spherical, not cubical, there is a disconnect between the algebra and the geometry of the oscillating pseudoscalar, which the topological approach seeks to overcome, but this fact does not prevent us from exploring other approaches.

In fact, this disconnect is the familiar discrete versus continuous mystery that has plagued mankind from the beginning of science, and it is why I think Lynds’ essay is so important to this contest.

Regardless, however, you ask:

“What happens when you move up to dimension 4? That’s the inconsistency in your technique. You’ve forgotten that of the 16 components of the Riemann tensor metric (remember, you have assumed a space-time combination, or Minkowski space, Euclideanized in d= 1,2,3 from the beginning), 6 components are redundant. With the 3-sphere, i.e., a 3-dimension sphere in 4 dimensions (skipping a lot of technical details here), the sphere packing & kissing number is 24. These packings, in dimensions 1—4 (also in d=8 & 24) are known and proved. The “3D expansion” compatible with your Euclidean model is then 8 + 2 (=10, or 16-6); i.e., 8 components of space and 2 of time. This works for continuous functions in general relativity, but not for your discrete treatment of dimensional spheres, and not for infinite-dimension Hilbert space.”

The direct answer to your question is simple in structure, but complicated in detail, like a maze. Let me try to explain, but I don’t know how successful I will be. The pseudoscalar/scalar expansion is four-dimensional, from 0D to 3D. No higher dimensional magnitudes, with two “directions,” exist, as observation shows, even though mathematically, we can easily increase the powers of two ad infinitum.

However, as the oscillating pseudoscalar is a composite, n-dimensional, entity, up to the fourth dimension, its four component dimensional spaces (0, 1, 2, and 3, corresponding to the spaces of points, lines, areas, and volumes), can be repeated, or compounded, infinitely, in principle.

In this way, the next dimension (the fifth dimension in the binomial expansion of Clifford algebras), becomes the new 0D space, the sixth dimension becomes the new 1D space, the seventh dimension becomes the new 2D space, and the eighth dimension becomes the new 3D space. At this point, we have effectively doubled the tetraktys, to what we call the second tetraktys, which simply describes denser points, lines, areas and volumes, but still maintains the dimensions of the first tetraktys (that’s why I have always been fascinated with Carl Brannen’s density operators).

What’s important to recognize is that the new system is not based on understanding oscillation in terms of rotation, but in terms of pseudoscalar expansion/contraction. The difference is stark, not just in a switch from quadrantal functions to binary functions, but in terms of eliminating the need for imaginary numbers and thus the whole idea of what constitutes the reals, the complexes, the quaternions, and the octonions, let alone the septillions. However, the good news is that it explains the repeating function of 8 and the mystery of 1, 2, 4 and 8, together with 0, 1, 3 and 7, in the Russian doll like fashion of Bott periodicity that so mystifies the topologists.

While this may be too iconoclastic even for the brave hearts in here, it’s all an inescapable consequence of developing the consequences of the fundamental postulates of the reciprocal system, which has to be reassuring for the thoughtful.

You write:

“At last, I understand why you took Peter Lynds’ essay—which is completely empty of physics—so seriously. Your universe is massless, and assumes mass created by a fundamental motion of space and time, while Lynds assumes motion without space and time. Both of these views obviate the exchange of mass –energy between bodies, which defines motion and makes the analysis of mechanics possible.”

Your conclusion is premature, Tom, because the new system subsumes the legacy system. Once mass is manifest, all the known relations of mass and energy in mechanics emerge in the new system. What may cause some confusion, though, is the definition of energy in mechanics, from a 0D scalar, to a 1D “scalar” via the concepts of force and work.

Finally, you state:

“You write that “…mass and energy should be quantifiable, in terms of …changing space and time quantities.” Well, of course they are quantifiable, and quantified, in special relativity (E=mc^2), which treats only uniform motion. General relativity incorporates the change properties by dealing with acceleration. That’s what acceleration is, a change in the direction of motion.”

Again, one has to take into account the new system’s definition of scalar motion, where change in the “direction” of an increasing scalar quantity, to a decreasing scalar quantity, is not the same as a change in the direction of the vector of a moving mass. The difference is crucial to understand. Whereas acceleration, as a component of rest mass, is hard to come by (see Hestenes essay), acceleration of a moving mass is common place.

Merry Christmas,

Doug

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Hi Larry,

The confusion is due, in large part I think, to a lack of communication. When we speak of distance and direction, a vector, in 4D spacetime, we are dealing only with the surface of a sphere, not the volume. In fact, technically, the word sphere is used to refer to the surface of a ball. The word ball is used to refer to the interior volume, but I don’t always make the proper...

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Hi Larry,

The confusion is due, in large part I think, to a lack of communication. When we speak of distance and direction, a vector, in 4D spacetime, we are dealing only with the surface of a sphere, not the volume. In fact, technically, the word sphere is used to refer to the surface of a ball. The word ball is used to refer to the interior volume, but I don’t always make the proper distinction, which causes a lot of confusion.

In dealing with the curved surface of a sphere, the vectors in the plane tangent to a point on the surface are important. All the possible directions of the curved surface at this point can be defined in the plane that is tangent to the point. These are the tangent vectors of curved space geometry.

The tensor calculus is a way to deal with the tangent vectors of curved space and involves contravariants that behave as vectors and covariants that behave like gradients, or changing magnitudes. The thing is, tensors, called Riemann tensors, can be used to describe the curvature in all directions at a given point in space, but these tensors have 256 components in 4D spacetime!

Fortunately, most of these are redundant, or reduce to zero, and so the number of necessary components can be reduced to 20, which then can be used to calculate a Ricci tensor, but only 10 of the 20 Riemann tensor components are actually needed to do this. These are the 8+2 = 10 dimensions that Tom is referring to, which are the 10 out of the 4x4 = 16 elements of the Ricci tensor matrix that are actually independent (i.e. orthogonal).

Maybe now you can see why I didn’t want to get into it! The important thing to understand is that all this deals with differential geometry, which is irrelevant to the expanding/contracting pseudoscalar concept of my work, but Tom was thinking it shows that “A Mystic Dream of Four” is an illusory dream at best, since a discrete treatment of dimensional spheres such as mine can’t work with these 8+2 = 10, independent, dimensions, as do the continuous functions of general relativity.

Yet, this is a case of mixing apples and oranges, since what it takes to describe a location in 4D spacetime has little to do with the space/time ratios generated by the oscillating pseudoscalars that I am talking about.

I am trying to explain to Tom that this is not a valid argument, because we are now treating the four linear spaces of the 8 dimensional algebra, as four scalar spaces, not four vector spaces, and we are now dealing with scalar magnitudes of an expanding/contracting ball, not the vectors and gradients, used to describe the curved space of the sphere. However, it is possible to see the 10 dimensions, or the orthogonal directions, in the discrete 4D reciprocal algebra as well.

Normally, mathematicians refer to the fourth dimensional Euclidean algebra as actually having 2^3 = 8 dimensions, because, in the binomial expansion, the index of orthogonality for each linear space, as I call it, is 1, 3, 3, 1, which, together, sum to 8. Nevertheless, while the index of the 3D pseudoscalar space is 1, just like the index of the 0D scalar space, in reality, the two are not the same, since, unlike the 0D scalar, the 3D magnitudes of the pseudoscalar can be generated in three different ways, just as the magnitudes of the 2D planes and the 1D diameters can be.



To see this, we just need to see the six orthogonal 2^1 units (the three pairs of radii associated with the three intersecting, orthogonal, diameters of the ball) and the 12 orthogonal, 2^2 units (the three pairs of four quadratures associated with the three intersecting, orthogonal, planes of the ball, as together forming the 8 orthogonal 2^3 units (the three pairs of four octants associated with the three, orthogonal planes and the three orthogonal diameters).



In this manner, there are three, independent, ways to describe the pair of four 3D octants, constituting the volume, corresponding to the three, independent, ways to describe the 1D diameters and the 2D planes. Consequently, the total index of the 4D space is actually 1 + 3 + 3 + 3 = 10, only the first of which is the 2^0 = 1 time dimension.

Since no one has been much interested in studying oscillating pseudoscalars, this is unfamiliar territory, and unfamiliar territory is not inviting for many committed investigators. Nevertheless, the simple mathematics of these four linear spaces is straightforward for all those who can afford the time and effort to investigate the consequences, regardless of how its 10 dimensions have been thought of in the past.

With this much understood, we begin with the investigation of how these pseudoscalar oscillations combine to form observed particles of matter and how they interact in terms of energy conservation laws, using the 10 dimensions Tom is talking about to describe the change of position of these particles, or aggregates of them, in 4D spacetime, using functions of general relativity.

Also, the principles of sphere packing will become relevant at that point, since the eigenvalues of the oscillating pseudoscalars can be treated as combinations of spheres. This is a really interesting area of research that I’m approaching via simulation at the moment, but several FQXI essays have been helpful and stimulating in the process, including Tom’s.



I hope this helps.

Doug

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Hi Tom,

Thanks for deciding to not give up on our dialog just yet. I think there is a lot that is worth our while in pursuing it still.

You wrote, “for while an eternal space/time progression has attractive mathematical properties, it doesn't account for observational consequences of physical discontinuity, particularly quantum mechanical unitarity.”

The unitarity of QM is...

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Hi Tom,

Thanks for deciding to not give up on our dialog just yet. I think there is a lot that is worth our while in pursuing it still.

You wrote, “for while an eternal space/time progression has attractive mathematical properties, it doesn't account for observational consequences of physical discontinuity, particularly quantum mechanical unitarity.”

The unitarity of QM is inherent in the rotation of the complex plane. The 1D, 2D and 3D units are formed from the rotations of complex numbers, which mathematicians discovered are isomorphic to the rotations of real numbers, but are much richer in that they can be used to supply the units for three Lie groups, U(1), SU(2) and SU(3).

The problem is that the 1D complex rotations actually require the two real dimensions of R(2) that form the complex plane, while the 2D complex rotations require the three real dimensions of R(3), so by the time we get to the 3D unitarity, we’ve run out of real dimensions to generate it, and have to resort to higher, unobserved, or unreal, dimensions.

Of course, it turns out in the end that the consistency and usefulness of these internal symmetry spaces seem to make this extraordinary expedient irrelevant, since we know that the angular momentum of spin space is definitely real, which seems to imply that the symmetry of isospin and flavor spaces must be real in some sense as well.

But, in spite of the successes of these abstractions, it leaves us with a somewhat queasy feeling that, having invented a highly complex, abstract, accounting method for our physical theory, without any clear connection to real physical dimensions, we might be asking for trouble in the long run (apparently, trying the same type of approach in the financial world has led it ruin!)

Hence, maybe we shouldn’t resign ourselves into thinking that there is no way to account for these strange properties in a 3D physical space that we can understand, just because we haven’t been able to find it yet. The thought that the RST-based approach embraces is that the problem may be in the way we think of motion, rather than in the way we think of space.

Indeed, we have already seen a great illustration of this in the contrast between the dimensions of space, understood from the perspective of the scalar motions of the tetraktys, and the dimensions of space, understood from perspective of the vector motions on the surface of the sphere.

In the latter, the external kissing numbers are employed, but in the former, the internal index of orthogonality is used, which, at first glance seems to lead to the wrong number of dimensions. Yet, we see that the number is the same after all, when the nature of the concept of real dimensions is clarified: Real dimensions are independent dualities, or powers of two, and when independent magnitudes of motion can be described in terms of these independent dualities, the correspondence of the ten mathematical dimensions of algebra with the three physical dimensions of geometry, using these dualities, becomes child’s play compared to the use of tensor calculus and matrix operations to explain the same thing.

That is to say, using the dimensions of the tetraktys, we start with 3*2^1/2^0 = 6, 3*2^2/2^0 = 12, 3*2^3/2^0 = 24, the same number of dimensions as found with the kissing numbers, but we don’t have to leave real space and go into hyperspace, in order to obtain them.

Then, when we recognize the nature of n-dimensional motion, we are naturally led to divide each of these mathematical dimensions in the pseudoscalar spaces of the tetraktys, by the corresponding physical dimensions of those respective spaces, and we get the correct ratio in each case: 3*2^1/2^1 = 3, 3*2^2/2^2 = 3 and 3*2^3/2^3 = 3, which, when summed together with the 2^0/2^0 = 1, of the scalar space in the tetraktys, gives us the 10 dimensions we know are there, but in a much more straightforward and simple manner than doing it, using the concepts of Riemann, Minkowski and the tensor calculus.

In the same way, using the 1D, 2D and 3D space/time magnitudes of the tetraktys, generated by the pseudoscalar oscillations, gives us the unitarity needed to form the magnitudes corresponding to the three internal symmetry spaces of complex analysis in QM, but, again, we don’t have to leave the real physical space of three dimensions and go into the abstract space of higher dimensions, in order to do it.

In explaining the outer product, and the idea of directed numbers, in his geometric algebra, Hestenes’ points out that the fact that multiplying the trivector (3D pseudoscalar) by a fourth vector “fails to sweep out a four-dimensional space segment,” describes a real physical limit that we must respect, even though it’s clear that there is no abstract limit to the number of possible dimensions we can conjure up mathematically. He writes: “…this is a simple way of saying that space is 3-dimensional.”

So, while numbers are not limited to three dimensions, space is, and in the RST-based development of theory, so is time, but only when space is reduced to zero dimensions. However, just how such a transformation might take place is another fascinating journey into the true nature of physical dimensions that we might want to explore later.

Regards,

Doug

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Happy Holidays Doug!

I hope you have had the chance to study up on some general relativity and see that the dimensions bend, warp, and move. Indeed--dimensions even "wiggle." Do not take my word for it, but listen to Lee Smolin.

Hope all is well!

In this BBC video, Lee Smolin states, "Einstein taught us that space is not a background that things move in. Spoace is a network...

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Happy Holidays Doug!

I hope you have had the chance to study up on some general relativity and see that the dimensions bend, warp, and move. Indeed--dimensions even "wiggle." Do not take my word for it, but listen to Lee Smolin.

Hope all is well!

In this BBC video, Lee Smolin states, "Einstein taught us that space is not a background that things move in. Spoace is a network of relationships that are ever dynamical, ever evolving, part of the world. The geometry of space evolves and changes--WIGGLES--just like anything else==just like electromegnetism, just like particles."

http://www.youtube.com/watch?v=3bLwqnIfLRA&featur
e=related

So it is that dimensions move.

All that my theory--Moving Dimensions Theory--does is note that the fourth dimension is expanding relative to the three spatial dimensions, as attested to the photon which is ageless in relativity and nonlocal in quantum mechanics.

From MDT's simple postulate and equation dx4/dt=ic, all of relativity is derived.

Give me a universe wherein we have four dimensions x1, x2, x3, x4 and the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt=ic, and all of relativity arises.

This is a simple, buautiful postulate and principle--indeed, Einstein's principle of relativity descends form MDT's postulate. And MDT is more succinct than relativity, for from MDT's single postulate and equation comes both of relativity's postulate.

Also from MDT's simple postulate and equation comes a natural *physical* model for time and all its arrows and assymetries, as well as entropy, quantum nonlocality and entanglement, all the dualities--space/time, mass/energy, wave/particle--and both Heisenbergs' and Huygens' principles.

dx4/dt=ic (MDT's fundamental equation underlying relativity) suggests that the fourth dimension is expandingh at c.

xp-px = ih (underlying quantum mechanics) suggests that the wavelength of this expansion is Planck's length.

So it is that MDT sets both Planck's constant and the veloicty of light, while also maintaining the ocnstancy of the velocity of light by giving rise to all of relativity.

Lee Smolin also states in the video, "We've forgotten how audacious science is and how it rages sometime -- how the ideas that turn out to be true are so often outrageous... we've forgotten the lessons of the people like Einstein, who come from the outside but have exactly the right insight and right idea." --http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related
BBC Hard Talk

"Openness, the inclusion of different points of view, like in anything else, is essential to progress." --Lee Smolin http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related BBC Hard Talk

MDT's simple elegance accounts for the gravitational slowing of light and time, as well as the quantum nature of all measurement--the fourth dimension has a nonlocal, wavelike, quantized quality via its invariant expansion in units of the Planck wavelength--something that is attested to by every photon which 1) is timeless and ageless, 2) moves at the speed of light, 3) remains fixed in the fourth dimension, and 4) is described by a nonlocal, spherically-expanding wavefront.

More on this in the upcoming book! "HERO'S JOURNEY PHYSICS & MOVING DIMENSIONS THEORY: FROM HERACLITIS, TO PLATO, TO ARISTOTLE, TO COPERNICUS, TO BRUNO, TO KEPLER, TO GALILEO, TO NEWTON, TO PLANCK/EINSTEIN/BOHR/BORN--AND YET IT MOVES! Unifying relativity, quantum mechanics, entropy, and time's arrows and assymetries with a new universal invariant: dx4/dt=ic."

MDT allows us to keep all time and change by weaving change into the fundamental fabric of spacetime (for the first time in the history of relativity) with dx4/dt=ic. This means that come 2009, both time and progress in theoretical physics will be unfrozen, and we will be liberated from the block universe and granted free will!

Moving Dimensions Theory is bold, subtle, far-reaching, simple, and consistent. MDT agrees with all empirical evidence and all of relativity and quantum mechanics. MDT has come not to abolish the laws of the founding fathers of physics, but to unite them. MDT liberates us from the block universe and frozen time, while allowing us to keep space-time diagrams so as to sell coffee-table books on physics and time travel (although MDT shows that time travel into the past is impossible). MDT goes so far as to show that seeming paradoxes across all realms--from the paradoxes of Godel's block universe to the EPR paradox--can be expalined and accounted for with a novel universal invariant which underlies Einstein's Principle of Relativity, entropy, and emergent time and all its arrows and assymetries.

MDT resembles neither String Theory nor Loop Quantum Gravity, but this should not count against it.

Here is another passage pertaining to the fact that photons remain stationary in the fourth dimension:

From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS:

"Special relativity declares a similar law for all motion: the combined speed of any object's motion trhough space and its motion through time is always precisely equal to the speed of light. . . . Morover, the maximum speed through space is reached when all light-speed motion through time is fully diverted into light-speed motion through space--one way of understanding why it is impossible to go through space at a greater than light speed. Light, which always travels at light speed through space, is special in that it always achieves such total diversion. And just as traveling due east leaves no motion for traveling north, moving at light speed through space leaves no motion for traveling through time! Time stops when traveling at the speed of light through space. A watch worn by a particle of light would not tick at all. Light realizes the dream of Ponce de Leon and the cosmetics industry: it doesn't age." --From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS

Ergo, a photon experiences no motion through the foruth dimension. Ergo, a photon remains in one place in the fourth dimension. And as quantum mechanics describes a photon as an expanding spherically-symmetric probabilistic wavefront, the fourth dimension must be expanding as a sphecially-symmetric wavefront! The expansion of the fourth dimension at c underlies photon's invariant velocity of c, as well as the photon's nonlocality! And too, MDT accounts for the fact that a photon remains stationary in the fourth expanding dimension, while also provding a physical framework for time and all its arrows, all of relativity, quantum nonlocality and entanglement, and entropy!

Well Doug, in light of Smolin, Einstein, Wheeler, and General Relativity, I hope that you can come to terms with the fact that dimensions move in 2009.

Best,

Dr. E (The Real McCoy)

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Merry Christmas Tom,

As last night’s caroling is over, this morning’s presents unwrapped, and I’m sitting here sipping my hot chocolate, my thoughts turn to the meaning of this life and the life to come. In that context, the concepts of change and inertia have a special, if different, meaning, but I can’t help making comparisons.

If we define inertia, as the resistance of an...

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Merry Christmas Tom,

As last night’s caroling is over, this morning’s presents unwrapped, and I’m sitting here sipping my hot chocolate, my thoughts turn to the meaning of this life and the life to come. In that context, the concepts of change and inertia have a special, if different, meaning, but I can’t help making comparisons.

If we define inertia, as the resistance of an object to a change in its motion, and motion, as a change of position over time, then we have to define position, which isn’t easy.

Peter’s point is that an instantaneous position simply cannot be defined. We can only approximate it at best. Yet, things move, so obviously this is a measurement problem, a problem of describing an aspect of reality in a precise, philosophically consistent, manner.

But since we need discrete units to count the space and time magnitudes in a calculation, we have to find a way to overcome this conceptual obstacle. My point is that a discrete interval of time (or space) can only be defined precisely by instantaneous, periodic, changes in “direction,” which actually permit the description of vibrational (or rotational) motion, kinematically.

QM unitarity is based on rotational motion, while RST-based unitarity is based on vibrational motion. The difference is instructional, as I’ve already pointed out, but only in the latter case do matter and its properties emerge from the combinations of the described units of motion. On the other hand, these have to be put into the QM theories, as free parameters.

But in order to account for the inertial property of mass, and its gravitational behavior, it’s necessary to distinguish between the two “directions” of the new system’s units of motion. Scalar motion does not have direction, while pseudoscalar motion has two “directions,” inward and outward motion.

Since both the gravitational behavior of mass, and its inertial property, both resist outward motion, the clear implication is that mass consists of inward motion, or that some part of it does. So, the question arises, what is inward motion? Inward with respect to what?

The answer is clear from the nature of the oscillating pseudoscalar: Inward motion occurs with each contraction half of the cycle. But because we have defined time as the inverse of space, a contraction of a unit spatial pseudoscalar is the equivalent of the expansion of a unit temporal pseudoscalar, from the point of view of the number of units involved. So, when the two oscillations are combined in equal numbers, the net result is neither inward nor outward motion. Only when one of the pseudoscalars outnumbers the other, in the combination, is there a net inward effect.

Consequently, the all green color code of the neutrinos in the toy model of figure 1 in my essay, shows neutrinos with no inward motion (a null, or lightlike, worldline), while the all red color code of the electrons shows that they are imbalanced to the spatial pseudoscalar side, giving them a net inward spatial motion (a timelike worldline), while the all blue color code of the positrons shows that they are imbalanced to the temporal pseudoscalar side, giving them a net inward temporal motion (a spacelike worldline).

Of course, there are a lot of details that I have to skip, but I wanted to outline the argument that, in principle, it’s not true that “defining motion only in terms of itself fails at providing any means to introduce inertia,” even though I have to take exception with the assertion that we have defined “motion only in terms of itself.”

We have defined motion in the only way it can be defined, in terms of changing space and time. If there is another way, please let me know.

Regards,

Doug

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Hi Doug,

Let me begin at the end. You wrote: "We have defined motion in the only way it can be defined, in terms of changing space and time. If there is another way, please let me know."

I did let you know. Mach's principle, which is the philosophical foundation of general relativity, defines motion as the relative change in position among center of mass points. Space counts for...

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Hi Doug,

Let me begin at the end. You wrote: "We have defined motion in the only way it can be defined, in terms of changing space and time. If there is another way, please let me know."

I did let you know. Mach's principle, which is the philosophical foundation of general relativity, defines motion as the relative change in position among center of mass points. Space counts for nothing in Mach's mechanics and time is the measured interval between changes in positions, driven by changes in velocity. In Einstein's hands, Mach's principle is completed:

Mach assumed without justification that the universe is a closed and isolated system. He assumed this error with as much conviction as you and Lynds assume that motion is an independent physical property. Einstein recognized that no such closed system could cohere with the concept of a continuous field, which is the way we objectively experience physical reality. To combine experience with geometry and introduce inertia, Einstein applied a specific definition to "physically real" in order to accommodate the space-time continuum. Allow me to quote it again: "... independent in its physical properties, having a physical effect but not itself influenced by physical conditions ..." It appears that in contradiction to Mach, Einstein was indeed "... competent to predicate things about absolute space and absolute motion ..." because general relativity, in giving a primary role to the geometry of spacetime ("space tells mass how to move..." as John Wheeler elegantly put it) and keeping the kinetic properties of measured inertial effects ("...mass tells space how to curve") Einstein managed to preserve the idea of Mach's principle without the unphysical assumptions.

If it were just space and time that define motion, as you assume, or if motion were simply a primary property of the universe and space and time don't exist, as Lynds assumes--both special and general relativity would be falsified. Relativity predicts physical consequences, however, that are already experimentally validated.

That brings us to the beginning. You write, "Peter’s point is that an instantaneous position simply cannot be defined. We can only approximate it at best. Yet, things move, so obviously this is a measurement problem, a problem of describing an aspect of reality in a precise, philosophically consistent, manner." There's nothing at all obvious in that claim, and in fact it contradicts known experimental results. We very well know that position can be measured to arbitrary accuracy and that momentum can be measured to arbitrary accuracy. Physics doesn't care about philosophy; that it's possible that "things move" beyond any conceivable measurement limit only supports a continuous field theory of quantum mechanics that we believed was true all along.

You continue, "But since we need discrete units to count the space and time magnitudes in a calculation, we have to find a way to overcome this conceptual obstacle. My point is that a discrete interval of time (or space) can only be defined precisely by instantaneous, periodic, changes in “direction,” which actually permit the description of vibrational (or rotational) motion, kinematically." But there is no conceptual obstacle, and no kinetics there. Discrete intervals of time are well defined in measurement of momentum; discrete intervals of space are well defined in measurement of position. At the frontier of physics research we ask whether space might be quantized beyond the Planck limit, or if time might be an emergent property of classical mechanics rather than a fundamental property of a unified theory. The obstacles are theoretical and experimental, not conceptual.

So because I deny, with factual support, the primacy of "motion" on which your argument is based, your argument fails. The geometry may be beautiful--I don't know, I haven't studied it--yet I do know that the assumption of motion as a primary property of space and time is a false premise. You can't derive inertia from it, because when mass is defined in terms of geometry alone, not even an "oscillating pseudoscalar" (nor any geometric object) can impart energy to what is essentially a static--not kinetic--model. Compare this to Einstein's appropriation of Riemannian geometry to describe "curved" spacetime in general relativity. The geometry did not provide the kinetics; inertial mass was already there (through special relativity) to inform the space of its curve.

I wish you success in pursuing a convincing physical model for your mathematics. As it stands, I do not find it physical for the reasons cited. I leave open the possibility that I could be convinced; however, I find the foundational premise demonstrably false.

All best,

Tom

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Hi Tom, Larry,

Tom, I really appreciate your thoughtful and considered comments. However, I think you may have inadvertently set up a straw man argument to contend with. When I assert that motion can only be defined by changing space and time, you resist by pointing to an interpretation of what Einstein called Mach’s principle, which you say is defined in terms of the changing positions...

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Hi Tom, Larry,

Tom, I really appreciate your thoughtful and considered comments. However, I think you may have inadvertently set up a straw man argument to contend with. When I assert that motion can only be defined by changing space and time, you resist by pointing to an interpretation of what Einstein called Mach’s principle, which you say is defined in terms of the changing positions of mass points. But then, an object’s change of location necessarily involves a change of distance, which is one-dimensional space. The changing position of the object relative to other positions merely identifies the spatial change defining the motion.

If you say “space counts for nothing in Mach’s mechanics, and then say that time is measured by “changes of position,” it seems contradictory to me. What are these positions, if not positions in space? It’s sort of like Dr. E trying to define dimension autonomously. It makes no sense to me.

So, it cannot be that space counts for nothing in Mach’s mechanics, since stars occupy locations in space. For Mach, it was that these “stationary” stellar locations constitute the reference for measuring change, and without their marking of these reference locations, the change in distance, entering into the definition of the motion of an object, cannot be discerned.

But, then, Einstein understood his concept of Mach’s principle in the sense that “…inertia originates in a kind of interaction between bodies,” which reflects Mach’s concept that “matter there influences inertia here.”

However, if this influence is to exist as a consequence of a continuous, unified, field, the system must be a closed system, after all. But how then does Einstein escape the conclusion that not only all motion is relative, but all mass too? The answer is that he does it via the introduction of dynamic spacetime, which in his theory is “independent in its physical properties, having a physical effect but not itself influenced by physical conditions.” That is to say, dynamic spacetime is fundamental, in Einstein’s theory.

As a result, we reject Newton’s notion of a static, absolute, reference of space and time, with which to measure the change of motion, and we replace it with a dynamic “fabric” of spacetime in general relativity’s concept of inertial interactions, but we cannot adapt it to quantum mechanic’s concept of force interactions, where neither position nor momentum can be measured to arbitrary precision.

But then you write:

“…yet I do know that the assumption of motion as a primary property of space and time is a false premise. You can't derive inertia from it, because when mass is defined in terms of geometry alone, not even an "oscillating pseudoscalar" (nor any geometric object) can impart energy to what is essentially a static--not kinetic--model…”

It’s hard to know where to begin. First of all, no one is assuming that motion is “a primary property of space and time.” In physics, motion, by definition, is a reciprocal relation between changing space and changing time. The challenge we face is how to define the changing units of space and time consistently. Of course we can choose arbitrary units to describe the space of 1D distance, if we are not too careful about the philosophical contradictions this entails. But, as Einstein pointed out, this is not a wise course:

“The reciprocal relationship of epistemology and science is of noteworthy kind. They are dependent on each other. Epistemology without contact with science becomes an empty scheme. Science without epistemology is — insofar as it is thinkable at all — primitive and muddled.”

So, we can say we “know” something in a scientific way, but the question of how we “know” what we “know” cannot be disregarded with impunity. We “know” that E=mc^2, but we don’t “know” why this is so. In terms of space and time, this equation simply tells us that there is a reciprocal relation between space and time; that is, t/s = t^3/s^3 * s^2/t^2, and this means that we “know” that the dimensions of space and time are significant, and if we “knew” what the units of space and time were, we could calculate the unit energy of unit mass from unit velocity.

Nevertheless, we don’t “know” what those fundamental units of space and time are, or even how to define them consistently. So, we have to resort to the arbitrary unit of the gram and the meter and the second, and go on from there to determine a consistent relationship between them that works to some degree of approximation.

Einstein has done the same sort of thing only in terms of mass and spacetime geometry. What he did works to some degree of approximation, but we don’t “know” why it works, and that is the problem. If we are to understand how nature combines the continuous with the discrete seamlessly, we need to know something about how we “know” what we “know,” and this leads us to the philosophical realm and smack into Lynds’ essay.

My answer to Lynds’ assertion that nothing exists but change is that change has two, reciprocal, aspects, space and time. His retort is that intervals of space, or time, in which there is no change, cannot co-exist with continuous change, because the definition of intervals necessitates instants of no change.

My answer to this challenge points out that there are two aspects of the dimensions of change. These two aspects are magnitude and direction, and, while his argument holds for changes in the magnitude aspect of change, in a given dimension, it does not hold for changes of direction in that dimension, which cannot be intervals of change, but must be instants of change, in a given dimension.

But we “know” that instants of directional change, in a given dimension, cannot include the 1D motion of mass, because of inertia. But, then, since we also “know” that we can change the direction of the 1D motion of mass over an interval of changing space and time, this implies a contradiction, unless an instant of directional change exists somewhere within that interval of changing space and time in which the direction of the object changes. How can this be? The answer is that the instant the inertia of the 1D motion of mass is overcome, the 1D path of the object moves into a second dimension.

But what is the magnitude of the point of demarcation between the first and second dimension of the object’s motion? Can an interval exist between dimensions of change? Obviously not, therefore this transition into the second dimension must be instantaneous, at some point, because an object cannot move simultaneously in two directions and remain intact. It’s a matter of one or the other.

These considerations have deep philosophical implications for physics, Tom, and theoretical physicists must care about them. My contention is that describing changing space and time in three dimensions, where each dimension of change has two “directions,” and instantaneous changes in these “directions” make it possible to define discrete units of magnitude of change, without contradiction, which are manifest in the quantified properties of matter and energy, leads to new theoretical possibilities.

However, a correct understanding of the foundational premise is the first step. I hope we can reach that understanding eventually, and I am confident that we can, Tom.

Larry, meantime I will try to address your question, perhaps in the next post.

Regards,

Doug

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Hi Doug,

You wrote,

"Tom, I really appreciate your thoughtful and considered comments. However, I think you may have inadvertently set up a straw man argument to contend with. When I assert that motion can only be defined by changing space and time, you resist by pointing to an interpretation of what Einstein called Mach’s principle, which you say is defined in terms of the...

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Hi Doug,

You wrote,

"Tom, I really appreciate your thoughtful and considered comments. However, I think you may have inadvertently set up a straw man argument to contend with. When I assert that motion can only be defined by changing space and time, you resist by pointing to an interpretation of what Einstein called Mach’s principle, which you say is defined in terms of the changing positions of mass points. But then, an object’s change of location necessarily involves a change of distance, which is one-dimensional space. The changing position of the object relative to other positions merely identifies the spatial change defining the motion.

"If you say “space counts for nothing in Mach’s mechanics, and then say that time is measured by “changes of position,” it seems contradictory to me. What are these positions, if not positions in space? It’s sort of like Dr. E trying to define dimension autonomously. It makes no sense to me."

I'm not making this stuff up, whether it makes sense to you or not. I am merely repeating what Mach and Einstein found--and it's no straw man. The references are readily available in Einstein's The Meaning of Relativity and Mach's The Science of Mechanics.

Mach was a true relativist. Even though Einstein is known for "relativity," special relativity is actually a theory of the absolute. I.e., the absolute measurement standard of the speed of light, by which one can analyze motion dynamically, so as to demarcate the Newtonian limit from Einstein's universe. In Mach, all motion is measured (in principle) relative to the motion of all other bodies in the universe, and assumes by consequence a closed universe; space is a topological property empty of distance considerations. In Einstein, motion is measured relative to observers in different inertial frames (general relativity) who reconcile the differences in their observations by a mathematical operation called Lorentz Transformation; in other words, there is no preferred inertial frame and no necessary assumption of a closed universe. Again, this is fundamental classical physics, not my personal opinion.

So when you say "...no one is assuming that motion is 'a primary property of space and time.' In physics, motion, by definition, is a reciprocal relation between changing space and changing time ..." whose "physics" are you talking about? Certainly, not known physics, where motion is not defined independently of changes in position of points from a point of observer-dependent fixed reference. Quite clearly, you (as Lynds) assign a preferred inertial frame to observers that is independent of the physical motion of the universe. That is why I keep stressing the lack of physics in that view; it doesn't lack physics merely because I say so, but because it is demonstrably so. You don't have to take my word for it.

You say, "...a correct understanding of the foundational premise is the first step. I hope we can reach that understanding eventually, and I am confident that we can, Tom."

Maybe, but I doubt it. When your foundational premise contradicts known physics, and redefines motion with a preferred inertial frame outside the universe, there will have to be considerable revision of that premise for me to consider it.

Tom

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Larry,

As promised, I want to try to answer your question, based on Peter Rowland’s assertion that “If physics is to prove itself the most fundamental possible way of understanding the ‘natural world’, then it must explain space, time and matter, as well as use them, and it must generate the mathematical structures it uses.”

Your question was, “Does the progression of...

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Larry,

As promised, I want to try to answer your question, based on Peter Rowland’s assertion that “If physics is to prove itself the most fundamental possible way of understanding the ‘natural world’, then it must explain space, time and matter, as well as use them, and it must generate the mathematical structures it uses.”

Your question was, “Does the progression of space and time [in the RST] generate the mathematical structure it uses?” The answer is yes it does, and the key to understanding this is to understand that the definition of motion does not require the changing location of an object to describe the change of space that is the reciprocal of the change of time in its equation.

While it’s true, as Tom keeps pointing out, that physics as we know it has always defined motion in terms of an object’s changing position, whether that position is defined relative to some imaginary reference frame of space points, as in Newton’s case, or relative to the fixed stars, as in Mach’s case, the fact remains, an object’s position is not part of the actual equation of motion.

Since we must measure both space and time with the motion of an object, for scientific purposes, the view that motion consists of something moving, and thus that it’s possible to define a state of no motion, a state of rest, seems to be a natural conclusion, but we observe that the affects of the progression, or the increase, of time, and the associated increase of entropy, occur independent of our existence.



Sean Carroll put it best in his essay, when he observed:

“For something so basic, time is remarkably elusive, and there is a strong temptation to throw up one’s hands and proclaim the whole thing is an illusion. In this essay I will take the opposite tack, doubling down on the contrarian impulse: time is real, it needs to be dealt with, and by taking the implications of time seriously we are led to important insights concerning the nature of reality.”

To take time seriously, we must acknowledge its independent progression, and when we realize that time is simply the reciprocal of space, in the equation of motion, we are obliged to acknowledge that space is real as well, and needs to be dealt with, by taking its implications seriously.

But to say that space, as a frame of reference for the motion of objects, is the inverse of time is just absurd, and this is where Tom, and many others, gets tripped up. How can the set of positions that satisfy the postulates of geometry be the inverse of time? The answer is found in the more precise definition of space, as the reciprocal of time, in the equation of motion.

While we call the set of positions that satisfy the postulates of geometry “space,” which Newton regarded as an absolute reference frame, for his purposes, and which Leibniz insisted didn’t exist, the truth is that neither conclusion was correct. One of them no doubt would have realized this had they known, as we know, that space, like time, is eternally, inexorably, expanding.

The fact is, Larry, observation tells us that BOTH time and space are continually increasing, defining a universal motion, independent of anything else. Lynds calls this universal motion, a universal change, but he is unable to see how it can be possible to consistently quantify it. Yet, it is possible to quantify it consistently, and, as it turns out, this leads to an explanation of space, time and matter, and the mathematical structure that enables us to use them in physics.

The key to understanding how this can be is to understand that the concept of dimension has magnitude and direction, and that while a change in locations that enters into the magnitude of a given dimension of motion cannot be instantaneous, a change in the “direction” of the magnitude must be. The only way we can manage this requirement with inertia is to change from one dimension to another instantaneously, which effectively changes the “direction” in the original dimension of the motion over an interval, as I’ve been attempting to explain here, via the concepts of rotation.

With this much understood, a whole new approach to physics becomes possible, which is not based on Newton’s force equation, or on Schrödinger’s wave equation, or on Einstein’s covariance equation, as its fundamental point of departure, but simply the equation of motion, the reciprocal relation of changing space and time.

What this does is eliminate the need for a reference frame of absolute space, like the covariance of general relativity does, but then, unlike general relativity, it generates a fixed reference frame for special relativity, from the unit datum of the universal motion.

This is why all motion of objects is relative to other objects, but at the same time inertial mass is not, even though its interaction makes it seem that way. In an RST-based theory, inertial mass is motion relative to the constant speed of light, which speed quantifies the universal motion that is the natural datum of the system.

Since this datum is a unit ratio, not zero, it is displacement from this unit ratio that is measurable, not displacement from zero. Hence, displacement, in the two “directions” of the unit ratio, is possible: The first “direction” is displacement from unity that is less than unity, and the second is displacement from unity that is greater than unity.

This simple relationship generates all the mathematics of the system, which is then used to construct the combinations of the space/time displacements that constitute the entities that are identified as physical entities in the system and to describe the necessary relationships between them.

Once the origin of these entities is thus explained, and the mathematics to use them is thus generated, the equations of Newton, Schrödinger and Einstein become quite useful, as we all know. Clearly, however, the implication is that, with the benefit of the new system’s remarkable insight into the fundamental nature of space and time, exciting new ways of doing physics are ahead, which are not so philosophically vexing.

Well, that’s it in a nutshell. Now, that the contest is closed, and we are awaiting the announcement of the winners, I wish everyone good luck, and I hope you all have a happy and prosperous new year.

Warm regards,

Doug Bundy

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Happy New Year Tom,

It’s great to start the New Year off talking theoretical physics. Hopefully, I can convince you that the foundational premise of an RST-based physical theory does not contradict known physics and certainly does not redefine motion with a preferred inertial frame outside the universe.

True, to accept the premise of the RST, one has to think outside the box, but...

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Happy New Year Tom,

It’s great to start the New Year off talking theoretical physics. Hopefully, I can convince you that the foundational premise of an RST-based physical theory does not contradict known physics and certainly does not redefine motion with a preferred inertial frame outside the universe.

True, to accept the premise of the RST, one has to think outside the box, but this does not mean outside the physical universe, only outside the established cultural and scientific universe. If we go back and revisit the foundations of our modern thinking and consider things like the Pythagorean theorem and squaring the circle, we can see that there is actually a lot of room for thinking outside the box, and, if we do it at that fundamental point, the ramifications it might have downstream, for currently accepted scientific thought, is potentially very serious, even iconoclastic.

For example, the resolution of the crisis that the ancient Greeks faced, vis-à-vis the square root of two, is central to our modern way of thinking, for both quantum physics (QP) and covariant physics (CP). In the case of QP, this takes the form of rotation in the complex plane, and, in the case of CP, it takes the form of the fourth coordinate in the spacetime metric, which is equivalent to the radius of the unit circle in the complex plane, x4 = ict..

However, the basis of all this thinking is the relation of the right triangle’s hypotenuse to its sides, when the sides are length 1. While it’s true that the length of this hypotenuse is the square root of 2, it’s also true that the ratio of the perpendicular sides is 1:1. What I’m saying is that the RST is a system of physical theory that has, as its foundation, the latter truth, rather than the former truth.

I’m thinking that, if the representations of the symmetry groups of the two systems can be equated, this might go a long way in getting your attention, as far as the new system’s potential application to theoretical physics goes, so let me explore that a bit.

Based on the square root of 2 (SR2), QP quantizes the infinite positions on the circumference of the unit circle into a rotation group (U(1)), with its identity element of 1 implied by the complex number of size one, which then is used to work out the physics of the wave equation. Similarly, for the higher-dimensional group SU(2), and, with some difficulty, SU(3).

On the other hand, based on the unit ratio of the sides (URS), the RST quantizes the infinite sizes of the unit expansion into an equivalent, but unnamed, set of groups, with the identity element of 1, derived from the URS. The important thing to understand in both cases is that SR2 squared is equal to 2/1 and the inverse of this is equal to 1/2, which provides the fundamental symmetry of both systems, since 1/2 * 2/1 = 2/2 = 1/1 = 1, satisfying one of the most important requirements of a group.

However, the devil is in the details, as they say. Referring to figure 5 in my essay, it’s easy to see that this squaring operation, in real numbers, expands the SR2 radius, r’ = SR2, to the larger radius, r’’ = 2, and the inverse of this is the smaller radius, r = 1, requiring us to deal with three circles, not one.

Nevertheless, thanks to the ad hoc invention of imaginary numbers, we can combine them with real numbers, to form the almost magical complex numbers, which we can then use in our operations and still remain on the circumference of the unit circle, which suits our purposes in QP quite well.

Notice, though, that the (x, y) rectangular coordinates of r, r’ and r’’ are equal to the square root of (.5, .5), (1, 1) and (2, 2) respectively. These coordinate values are not indicated in the figure, but you can quickly calculate the ratios of the radii, r : r’ = 1/SR2 = SR.5, r’: r’ = SR2/SR2 = 1 and r’’: r’ = 2/SR2 = SR2, which are equivalent to the coordinate values.

Consequently, while we know that we can’t square the circle, we see from this that we can square the coordinates of the three circle radii, and on this basis get the ratio of the three squares, which corresponds to the ratio of the radii of the three circles, 1/2, 1/1, 2/2.

But now the question, “So what?” arises. Well, the crux of the answer is that, while the mathematics of vector rotation in the complex plane can clearly be used to form representations of the three groups, U(1), SU(2) and SU(3), it should also be possible to use the mathematics of scalar expansion/contraction in the pseudoscalar sphere to form them.

If this is a valid conclusion, then all we need to get from the geometry and algebra of the new system, to its physics, is something like the wave equation of QP, or the covariant equation of CP; that is, the concept of energy. My assertion is that energy, with dimensions t/s, is the inverse of motion, with dimensions s/t, and since the inverse of the spatial pseudoscalar is the temporal pseudoscalar, I figure that we are in good shape, both mathematically and physically, from a fundamental point of view.

However, you protest my assertion that you have set up a straw man, in which the importance of the fundamentals just described are not fully appreciated, by characterizing the new concept as a geometric model that, while “static,” nevertheless attempts to derive inertia from this geometry and thus impart energy to the model, something that can’t be done from geometry alone.

But, while I need to correct the misconception that we are only dealing here with geometry, the science of space, and not with time, the science of algebra, and not with space/time, the science of physics, I first have to point out that your protest illustrates exactly our dissatisfaction with QP and CP, doesn’t it?

The fact that we have to introduce free parameters, such as mass and charge, into our current theories is what drives Hawking to characterize the standard model as “ugly and ad hoc,” from the point of view of a unified theory of physics. And, on this basis, the same judgment that indicts QP theory also indicts CP theory, in my mind.

The fact is that we want to move beyond QP and CP, and, as Peter Woit maintains, this may require more than a unification of the theories of physics; it may require unification of physics with mathematics.

Can you see a little of what I mean, Tom? If the observed expansion of space and the observed flow of time constitute motion, by definition, then all the energy of the universe is there as well, and, given the mathematics of right lines and circles, we need only seek to understand how it is quantized and manifest as mass aggregates, magnetic fields, point charges, and radiation that have the relationships and interactions that we observe, when and where we observe them.

LOL. Sounds so easy!

Doug

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And happy new year to you, Doug!

First, I have to say that the idea of a self-interacting geometry that generates energy lacks a necessary quality of a physical theory--dynamic exchange of information.

At least one reason that Einstein's general relativity is so brilliant is that by making the geometry of spacetime physically real, he created the means for mass points to interact...

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And happy new year to you, Doug!

First, I have to say that the idea of a self-interacting geometry that generates energy lacks a necessary quality of a physical theory--dynamic exchange of information.

At least one reason that Einstein's general relativity is so brilliant is that by making the geometry of spacetime physically real, he created the means for mass points to interact over distance without begging the question of whether space possesses energy inherent to the form of the space. Points of space are discrete and static; spacetime points are dynamic and continuous, because the metric tensor changes continuously as energy transfers from point to point, i.e., the geometry of spacetime changes continuously as point particles exchange energy (information) by differentiation between energy states (diffeomorphisms). Special relativity disallows preference for any observer's inertial frame to describe an objective physics (otherwise, there would be no objective physics in GR), and so we use Lorentz transformations to reconcile the geometry between observers with the actual energy content and metric state.

When one proposes a geometry without a continuous transform, one risks assigning a privileged inertial frame--because the metric correspondence between one point and another is assumed externally, i.e., not as a continuous function. See how Fotini Markopoulou ("Space does not exist, so time can") solves the problem:

"The problem of the emergence of geometric time

is the same as the problem of the emergence of space, of geometry. "Time does not exist" refers to geometric time. By making the geometry not fundamental, we are able to make a distinction between the geometric and the fundamental time, which opens up the possibility that, while the

geometric time is a symmetry, the fundamental time is real.

By distinguishing the two notions of time we may be able to have our cake and eat it: emerging geometric time from fundamental time is not remotely as intractable as dealing with a fully timeless world.

"It is important to note that the relation between geometric and fundamental time is non-trivial and that the existence of a fundamental time does not necessarily imply a preferred geometric time."

I agree with Markopoulou as far as she goes--(my theory adds dimensions in order to derive her "funadamental time")--but the point is this:

I think Markopoulou would say, and I would certainly say, that a theory that depends on "geometric time" is fatally flawed. It takes the observer out of the universe of non-geometric events and therefore obviates a continuous function model of dynamic interaction. Markopoulou recognizes that "geometric time" can never bridge the gap between points, as long as we are inside the universe. "Diffeomorphisms are not about timelessness but about being inside a dynamical universe, affecting and being affected by it, constituting it."

When you say that in RST, space and time are reciprocal (vice general relativity in which spacetime is continuous), you not only risk assuming an observer-independent universe, you risk breaking a fundamental rule of arithmetic--division by zero. That is, if you don't let one of your terms go to zero, your theory is not mathematically complete, and if you do, division by zero is unavoidable. So if "energy" is expressed as a "dimension" t/s and "motion" as s/t(though I confess that I don't know what you mean by this, since energy and motion are the same thing)--even without knowing further content, I know that it doesn't work mathematically, becaue it doesn't allow zero time or zero space. General relativity, we know, breaks down at zero time and quantum mechanics assumes a spacetime background where time drops out of the equations. I can't see that your theory makes these problems go away.

That you invoke the Pythagorean Theorem and squaring the circle, I see as red herrings. The Riemannian geometry that supports general relativity _is_ the Pythagorean theorem--in 4 dimensions. And we certainly can square the circle--map points of a circle to points of a square with arbitrary accuracy--if we are not restricted to construction by compass and straightedge.

Forgive me, but your "squaring the coordinates of the three circle radii" kind of reminds me of the saying, "Two wrongs don't make a right, but three rights do make a left." We're moving, but are we really getting anywhere?

All best,

Tom

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Hi Larry,

I agree with you. Tom is no doubt thinking in terms of speed defined as a moving mass, since in Newton’s system of theory there is no velocity without the changing location of mass to define it. So, in this sense, one might be led to conclude that energy and motion are identical, but, in order to avoid confusion, we have to be much more precise than that.

Tom wrote...

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Hi Larry,

I agree with you. Tom is no doubt thinking in terms of speed defined as a moving mass, since in Newton’s system of theory there is no velocity without the changing location of mass to define it. So, in this sense, one might be led to conclude that energy and motion are identical, but, in order to avoid confusion, we have to be much more precise than that.

Tom wrote earlier:

“When you say that in RST, space and time are reciprocal (vice general relativity in which spacetime is continuous), you not only risk assuming an observer-independent universe, you risk breaking a fundamental rule of arithmetic--division by zero. That is, if you don't let one of your terms go to zero, your theory is not mathematically complete, and if you do, division by zero is unavoidable. So if "energy" is expressed as a "dimension" t/s and "motion" as s/t(though I confess that I don't know what you mean by this, since energy and motion are the same thing)--even without knowing further content, I know that it doesn't work mathematically, becaue it doesn't allow zero time or zero space. General relativity, we know, breaks down at zero time and quantum mechanics assumes a spacetime background where time drops out of the equations. I can't see that your theory makes these problems go away.”

I think the same sort of confusion is evident here. To say that space is the reciprocal of time in the equation of motion is indisputable, but Tom argues against it, because Einstein’s spacetime is continuous. Huh? At first glance, the continuous nature of spacetime has nothing to do with the reciprocity of space and time in the equation of motion, but then one can see what he means from a different perspective: Mathematically, we can’t have zero time in the denominator, in the case of the dimensions of motion, or zero space in the denominator, in the case of the dimensions of energy. Consequently, he dismisses the fundamental postulate of the RST out of hand.

But what we assume in the fundamental postulate of RST-based theory is that everything in the universe is comprised of motion, i.e. changing space and time, so it is impossible to define a state of rest in the system. The only way the changing denominator in the equation of motion (energy) can reach zero is if the change that is assumed in the fundamental postulate of the system stops.

But Tom says that this implies then that the mathematics of “your theory is incomplete.” I’m not sure what he means by mathematics or incomplete here, but the fact is that the new system is based on the pure mathematics of scalars, which is the only number system that is complete!

As we know, the properties of scalar algebra (the algebra of real numbers) are lost as the dimensions of the numbers are increased: The complex numbers lose the first property of scalar algebra (its order property), quaternions lose the second property of scalar algebra (its commutative property), while the octonions lose the third property of scalar algebra (its associative property).

The only way to maintain a complete algebra, without defining scalars in terms of operations on vectors, is to stick with the scalars, and this is what an RST-based theory is constrained to do, by its fundamental postulate. The result is that instead of having to define scalars in terms of the inner product of vectors, as done in vector algebra, an RST-based theory can use its n-dimensional scalars, defined as the relation between two changing, n-dimensional, scalars, an n-dimensional ratio. To most engineers and scientists, speaking of “n-dimensional scalars” seems like a contradiction in terms. Nevertheless, it’s possible to define them in terms of pseudoscalars, as discussed in this forum.

The contrast between the approaches of the two systems is clearly illustrated in the case of energy. In the Newtonian system, energy, while a scalar by definition, as you point out, is defined in terms of force and work, which not only confuses you, but probably Tom and many others as well.

The best way to understand the difference, is to imagine the real number line of scalars divided by a perpendicular force vector at the zero point; that is, a vertical line, representing force, standing straight up at zero, between positive and negative one. If the force vector is displaced at all, either to the left or to the right, the projection of its point on the real number line below it will have a positive or negative value on the scalar line, depending on the direction of the displacement.

A 1D displacement of the force vector in either direction is caused when force does work, defined on the scalar line as energy; that is, work is the amount of energy transferred by a force acting through a distance, in this view. The trouble is, rest mass, and its equivalent energy, cannot be defined in this way, their values must be assumed as free parameters in the equations.

In contrast, in an RST-based theory, the work theory is not incorporated into the definition of energy in this way, because the theory does not assume mass and F=ma, in its fundamental assumptions. To the contrary, the energy of rest mass must be defined in terms of an assumed universal motion, which is the initial state of the new system.

It is in this sense that we seek to understand E = mc^2 and E = hv purely in terms of the space/time dimensions of these equations, without resort to the free parameters of mass, m, and action, h. These physical entities must be understood only in terms of changing space and changing time, existing in discrete units, as explained above. Clearly, an endeavor such as this would seem impossible to those unfamiliar with the basic assumptions of the new system, but a little reflection will convince you that it has to be possible to do such a thing, given what we know.

I hope this helps.

Doug

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Hi Dr. E,

I am a little conflicted here, for while I feel somewhat compelled to reply in order to clear up misconceptions, I have no desire to impose on Doug's good natured tolerance for dissent from his views, in his own forum.

Nevertheless, I think I will make just this one post to clarify why I invoke Einstein's definition of "physically real." He was very specific, with no room...

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Hi Dr. E,

I am a little conflicted here, for while I feel somewhat compelled to reply in order to clear up misconceptions, I have no desire to impose on Doug's good natured tolerance for dissent from his views, in his own forum.

Nevertheless, I think I will make just this one post to clarify why I invoke Einstein's definition of "physically real." He was very specific, with no room for doubt about his meaning: "... independent in its physical properties, having a physical effect but not itself influenced by physical conditions." Einstein used this definition to explain how the spacetime continuum of general relativity influences the motion of matter.

I entered this forum in this first place, to point out Peter Lynds's error--that there is no physics in Lynds' claim that motion is primary; his physics is identical to metaphysical philosophy. Doug allows that Lynds's questions are valid, however, and that is how Doug and I became engaged in dialog.

It still holds to reason that no primarily geometric theory can withstand the test of "physically real" in Einstein's context (note, e.g., the arguments for "pre-geometry" emanating from the Perimeter Institute). Even though geometric tools are prominent in their construction, both special and general relativity are kinetic theories. They are theories of the behavior of matter; special relativity in a uniform rest frame of motion, general relativity in an accelerated inertial frame. Key to the consistency of relativity is that no observer's inertial frame is to be preferred over another--one cannot stand outside the universe and prescribe physical properties; those properties are self-consistently described within the system by their effects on physical conditions as measured from the observer's point of view.

The key geometric concept of special relativity is a rigid transformation (Lorentz Transformation) made possible by the finite vacuum speed of light limit, c. The geometry of general relativity is a Riemann surface, a four dimensional Pythagorean theorem in which a "finite but unbounded" universe allows continuous functions consistent with the rigid transformations of special relativity. The geometries let us describe the limits of motion, but they have no primary causal effect. Motion is not independent in its physical properties, as are mass and spacetime. Even quantum field based theories must rely on an independent field of vacuum energy, and not on the field geometry, to supply inertia.

Now to your special postulate, Dr. E. Does it pass the test of "physically real?" Well, yes, of course, the fourth dimension is expanding relative to the three spatial dimensions. This is not, however, a unique physical property. All coordinate systems of a particular dimension d, have an added coordinate d+1 expanding relative to the system. A line expands relative to a point, a line expands relative to a plane (projectively, points and lines are dual), a plane expands relative to a cube. The geometric rules don't change with hyperspatial expansion--when time is treated, in general relativity, as a fourth dimension, it is naturally expanding relative to the three spatial dimensions. In fact, one can even add a fourth spatial dimension (as in Kaluza-Klein theory) and have time expanding as a fifth dimension of the Riemann metric tensor field, to show Einstein's gravity unified with the electromagnetic field in five dimensions. How to show that such extradimensional theories meet the test of "physically real" is a primary challenge to fundamental physics today.

Your "prime mover" as a geometric object, though, can't really move anything, any more than Kaluza's adding an extra dimension to Einstein's theory caused any physical motion. Motion, and the geometry of motion, do not possess independent physical properties--it's a one-way street: physics prescribes motion; motion does not prescribe physics. A physicist's life would be simpler if it did, because then there would be no need to worry about initial conditions--there wouldn't be any. We could not--just as Lynds avers--identify any particular point where motion is not continuous. In that case, though, we also could not do any physics. Lynds's philosophy contradicts the facts of quantum measurement and relativity. Motion is relative (observer dependent) and not primary. Our deep physical question is not the origin of motion, it is the origin of inertia. At the crux of this question may be the role of time in physics. Or not.

All best,

Tom

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Hi Tom,

An interesting FQXI article came out yesterday, entitled “Through a Glass Darkly,” evidently alluding to the apostle Paul’s characterization of the faith of the Saints in the New Testament, illustrating the faith of a mathematician and a physicist, seeking to work out a non-schizo physical theory.

I was very interested in it for several reasons. Number one, it’s all...

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Hi Tom,

An interesting FQXI article came out yesterday, entitled “Through a Glass Darkly,” evidently alluding to the apostle Paul’s characterization of the faith of the Saints in the New Testament, illustrating the faith of a mathematician and a physicist, seeking to work out a non-schizo physical theory.

I was very interested in it for several reasons. Number one, it’s all about theoretical work with the octonions, which are our pseudoscalar/scalar numbers, but described with the use of ad hoc imaginary numbers, instead of magnitudes of space/time displacement. Number two, the theorists engaged in the work, Tevian Dray and Corinne Manogue, who are married, work out of the University of Oregon, at Corvallis, Dewey Larson’s alma matter. And, finally, reason number three, the success that they have achieved in describing the properties of the standard model entities is remarkable. “These properties seem to be inherent in the language of the octonions,” observes the author of the article, which is what the proponents of an RST-based theory would expect.

The major obstacle they face now is identifying quarks and the origin of charge, while wrestling with the strange mathematical properties of the octonions. It’s ironic to me that this work is being conducted at the University of Oregon, yet, I’d be willing to bet that, while probably well-acquainted with the work of Linus Pauling, neither Dray or Corinne have ever even heard of Pauling’s classmate, Larson.

But it was Larson who first pointed out that the nature of space and time is best understood as a reciprocal relation in the equation of motion, and that this relationship does not depend upon the changing location of an object for its existence. I’m sure he would also agree that it doesn’t depend upon the tension of a string either.

Yet, without this insight, our hands are tied, because we must insist on “something moving” in order to do our physics, as you have made clear. Funny, though, how, like bees buzzing around the hive, we are repeatedly drawn to the octonions. That’s where string theorists ponder the structure of the physical universe, vexed by the bewildering array of possibilities that they have found there, and that’s where Hestenes has constructed his entire career, no doubt disappointed by the slow recognition of the power of his unfamiliar mix of scalars and vectors in the geometric product.

Mathematicians like John Baez, while not convinced that string theory, or Hestenes’ work, points us in the right direction, nevertheless can’t resist the lure of the mystery of the tetraktys in general and the octonions in particular. Baez writes a lot about the octonions in his protoblog, “This Week’s Finds in Mathematical Physics,” explaining their mysterious connection with triality for SO(8), the exceptional Lie group G2, the SU(3) group, and lattices like E8, Lambda_(16), and the Leech lattice.

But it’s the connection of the octonions to the Bott periodicity theorem that almost teases Baez out of thought. It’s one of those “spooky facts in mathematics,” he writes. This, and the fact that the octonions are non-associative, but still the fourth and last “normed division algebra,” confining these algebras to the four of the tetraktys, “bugs me,” writes Baez.

He goes on to write about how Monague explained to him the tantalizing relation of the four division algebras to the Lorentz transformations in 10 dimensions, and how Robert Helling sees the relation of the four algebras to Supersymmetry, but, like Christians, seeing the realization of their hope afar off, through a glass darkly as it were, they pursue these hints of something very fundamental in the numbers of the tetraktys over a life-long career, filled with hope, with a firm conviction that it will be worthwhile in the end.

Baez sums it up nicely: “Cool, no? There are obviously a lot of major issues involved in turning this into a full-fledged theory, and they might not work out. The whole idea could be completely misguided! But it takes guts to do physics, so it's good that Tevian Dray and Corinne Manogue are bravely pursuing this idea.”

That was written almost twelve years ago. In the new FQXI article, Dray laments, “What we cannot do in our language at all is have them do anything other than sit there. If I stand up in front of a physics audience and say, ‘here’s my electron, and by the way, I don’t yet even know how it interacts with electric fields,’ I’ll get laughed at.”

So it is, but now here, at FQXI, I don’t think there is any danger of them being laughed at. I hope the success of FQXI’s work to encourage foundational thinking like this continues to grow. It’s the “out of the box” thinking, like Dray’s and Monague’s, and maybe even that outlined in the “Mystic Dream of Four,” where the one of time, of space the three, might, in the chain of symbol, girdled be,” which could eventually lead us out of the darkness of faint reflections, into the brilliant light of empirical discovery.

For this reason, I’m grateful that you don’t laugh and scorn at these ideas, even though you yet remain to be convinced. It’s gentlemen like you that are setting the example for what should become a refreshing new forum for discussing thoughts and ideas about foundational issues, without fear of ridicule.

More on your latest comment later.

Regards,

Doug

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Peter,

You wrote:

"If you've read my essay, you'll know why I think motion is fundamental, not time. I can't see how this negates the existence of energy or makes motion independent of physics. Why you think this is one of the things I wanted you to explain."

First, that you imply that this conclusion is merely my personal opinion makes it necessary that you read and digest...

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Peter,

You wrote:

"If you've read my essay, you'll know why I think motion is fundamental, not time. I can't see how this negates the existence of energy or makes motion independent of physics. Why you think this is one of the things I wanted you to explain."

First, that you imply that this conclusion is merely my personal opinion makes it necessary that you read and digest the sources I gave.

Physics is not the study of motion as an essential property. If it were, physics would be metaphysics, just as Aristotle proposed it—"The name 'circle,' for example, designates a certain 'whole' without further determination; definition of the circle analyzes it into its various features or meanings." (Aristotle, Physics) Contrast this to Euclid's axiomatic method of geometry, in which the existence of such an object can be deduced from more primitive notions. It is clear why Aristotle—as you—rejects mathematics to describe the universe, e.g., Plato's geometry and Pythagoras's numbers, in favor of essential causes (of which he named four: formal, material, efficient and final).

Also like you, Aristotle recognized the arguments of his contemporaries that motion is not primary: "Melissus, by the way, argues that All is independent of movement; if it were subject to movement then according to him there would have to be a void which, however, is not to be found among beings. This, then, is one way in which the thinkers under discussion seek to prove that there is a definite 'void.'" (op. cit.)

Fast forward a couple of thousand years to Ernst Mach. Holding to classical philosophy, Mach defined the void out of existence by doing away with space altogether. Only the relative and moving positions of bodies could be measured. No space, no void, no problem.

Enter Einstein. If there is no void, how does one explain the propagation of light at a constant speed? That is, if nothing is interfering with the path of light except the vacuum of space, then the vacuum (void) has to be real, or else we should observe light particles accelerate infinitely; that we do not, supports the unity of space with time (Minkowski space-time) in which one reciprocally limits the other. The rigid transformations of uniform speed (special relativity) are traded for continuous functions in an accelerated frame (general relativity). “Motion” is not, however, the cause of this limitation—it is the result (speed of light particles are immortal, experiencing no time lapse and therefore no temporal motion). “If … we are going to do away with the vexing question as to the objective reason for the preference of certain systems of co-ordinates, then we must allow the use of arbitrarily moving systems of co-ordinates. As soon as we make this attempt seriously we come into conflict with that physical interpretation of space and time to which we were led by the special theory of relativity.” (Einstein, The Meaning of Relativity, p. 59) Einstein then goes on to explain rest frames, observer dependence, clock differences between observers, and then, “We therefore arrive at the result: the gravitational field influences and even determines the metrical laws of the space-time continuum.” (ibid., p. 61) As John Archibald Wheeler summed it up, "Space tells matter how to move; matter tells space how to curve."

Your paper therefore makes the glaring error of declaring that Einstein did not consider spacetime physically real. On the contrary, both his philosophical basis (Mach’s Principle) and his mathematics support the physical reality of “the void.” This is not controversial; it is standard, known physics. (That the void itself contains energy in the form of virtual particles is the jumping off place for quantum field theory.)

If you can’t appeal to Einstein, then—and you demonstrably cannot—to whom can you appeal if not Aristotle?

Unfortunately for any physical theory in which one wants motion to be primary—Aristotelian physics is long falsified.

Best,

Tom

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Hi Tom, Peter,

Thanks for the link to your papers, Tom. I’ve started reading the first conference (2006) paper and find it fascinating, but I will have to find more time to read it entirely. You make some statements in section 1 that are very provocative to me.

For instance, you write

“One is compelled to ask, therefore, whether – or in what sense – phenomenological...

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Hi Tom, Peter,

Thanks for the link to your papers, Tom. I’ve started reading the first conference (2006) paper and find it fascinating, but I will have to find more time to read it entirely. You make some statements in section 1 that are very provocative to me.

For instance, you write

“One is compelled to ask, therefore, whether – or in what sense – phenomenological order becomes mathematical order. Is the fundamental notion of counting something that one is born with the knowledge of, as Leopold Kronecker assumed (“God created the natural numbers, all else is the work of man”) or even deeper, what nature itself is born with, an order programmed into our brains (as Kant believed) that we translate into abstract language.”

We may not be able to answer that question definitively, but we can use it as the basis of a fundamental postulate, as Hamilton did, when he translated it into an abstract language, an algebra that he called ”The Science of Pure Time.”

What Larson did (and Einstein and Lynds in a different way) was to recognize that time is only one aspect of change, that one cannot properly speak of changing space without the notion of changing time. Of course, one can fashion continuous notions of other changing quantities, such as stock market values, which change over time and do not involve any notion of space, but when we speak of changing space and changing time, we are speaking of one fundamental entity, motion, with two, reciprocal, aspects, neither of which can be said to enjoy an independent existence.

My point is that the assumption that this relationship defines a number that can be counted can be justified by recognizing that, as Grassmann, Clifford and Hestenes pointed out, two interpretations of number are possible, the quantitative and the operational. As Hestenes writes, “On the first interpretation, number is a measure of ‘how much’ or ‘how many’ of something. On the second, number describes a relation between different quantities…either a quantitative or an operational interpretation can be given to any number….”

Thus, in measuring motion, we are actually interpreting a number operationally, as a relation between two numbers, a function, and while Peter’s argument is directed at the limits of this function, which can only be infinite, without contradiction, your argument is that the function itself cannot exist without the changing location of an object, which requires the identification of a preferred frame of reference.

My answer to your argument is that we can assume, very rationally, based on observations, that the function does indeed exist independently of the existence of objects and preferred frames of reference, and when we do, the consequences deduced so far are startling in their fidelity to the observed properties of matter, energy and radiation, in addition to explaining the origin of these and their observed relation to one another.

The key to meeting Lynds’ requirement is found in recognizing that change in “direction,” when inertia is not involved, must be instantaneous, as can be easily demonstrated. It is this change in “direction,” as understood in n-dimensions, which becomes the basis for understanding how ”phenomenological order becomes mathematical order.”

The mathematics of the function are continuous, even though the “direction” of the function changes instantaneously, defining its discrete boundaries. That this fact can be demonstrated geometrically, and successfully translated into the abstract language of algebra, in four dimensions, opens up the possibility that we can derive physics from it, as Dray and Monague have shown, even though it requires a drastic change in our thinking of the fundamentals.

More after I’ve finished reading your papers.

Regards,

Doug

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Hi Everybody,

I want to give more complete answers to Tom's many assertions, but I find it difficult, because they tend to cover so much ground. It's not easy to succinctly address the philosophical and scientific issues of motion, space and time inherent in a span of ideas from Pythagoras and Aristotle to Mach and Einstein!

But let me try to take just one of his blanket statements...

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Hi Everybody,

I want to give more complete answers to Tom's many assertions, but I find it difficult, because they tend to cover so much ground. It's not easy to succinctly address the philosophical and scientific issues of motion, space and time inherent in a span of ideas from Pythagoras and Aristotle to Mach and Einstein!

But let me try to take just one of his blanket statements and focus on it for just a moment. He wrote, “Physics is not the study of motion, as an essential property. If it were physics would be metaphysics, just as Aristotle proposed it...”

The definition of metaphysics in one dictionary is: “The branch of philosophy that examines the nature of reality, including the relationship between mind and matter, substance and attribute, fact and value.” In other words, Tom is saying that, if physics were the study of motion, as an essential attribute of nature, it would not be science, but a branch of philosophy. Tom then contrasts Aristotle's philosophical musings with Euclid's science of geometry, to make the point, before asserting that Peter, like Aristotle, “rejects mathematics to describe the universe.”

Next, he uses Aristotle's words to change the subject from science without mathematics to philosophy without a void, which Mach embraced, but Einstein argued against, on grounds of observed Lorentz transformations, leading to the idea that spacetime is physically real, something deformable by matter, per general relativity, because the mathematics makes it so.

Thus, Tom argues that it's the mathematics of general relativity that makes the void real, and since Peter rejects mathematics, as a way to describe the universe, he cannot appeal to anyone but Aristotle, whose “physics is long falsified.”

Like I said, it's hard to know how to answer something like this. Peter is forced into the argument over the reality of the “fabric” of spacetime, which is really irrelevant to the point of his essay, which is simply that our notion of motion is incomplete, reflecting the fact that there is something philosophically inconsistent with our notion of the discrete and continuous, when it comes to change.

I have made the point that, by definition, motion is the reciprocal relation between changing space and changing time in the science of physics, i.e., v = ds/dt. There is no mass term in this equation and this is a crucial point: The definition of motion does not require the changing location of an object, but only the reciprocal change of two quantities, space and time.

In our universe, these two quantities are observed to be eternally changing. They are ever increasing. The mathematical and geometrical consideration of this fact leads us to the conclusion that motion may be primary, under this definition, because all our physics equations can be expressed in terms of these two quantities, including the relation between mass, radiation and energy.

However, in order to define motion in terms of two, reciprocal, changes, mathematically, one must resolve the philosophical inconsistency between the discrete and the continuous, which Peter's essay addresses. In the case of engineering, it's enough to eliminate the practical concern by approximation, but not so in the case of developing physical theory. We need a non-perturbative theory of the structure of the physical universe that resolves the continuous – discrete duality in the way nature does – seamlessly.

I believe that the recognition that scalar “direction” changes must be instantaneous does just that, and, as Newton observed, the science of geometry has nothing to say about how its right lines and circles are drawn. These must come through principles outside those of geometry, but once given its right lines and circles, the glory of geometry is manifest.

So, in the end, physics is all about motion, as an essential property. Space is nothing but a measure of motion, either past or contemplated, while time too is nothing but a measure of motion. Changing space is not something than can exist independently of changing time, and changing time is not something than can exist independently of changing space. In my opinion, those are the physical facts we have to deal with philosophically and mathematically. There is no other way out of the mess we are in.

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Hi Tom,

The links work fine for me. I don't know what the problem might be, but oh well. You wrote,

“Let me turn this around. Why should we be interested in a theory that claims motion as a property of the geometry, with no mechanism or experimental evidence? Why should we be interested in Lynd's claim that motion is fundamental, which is demonstrably false?”

Ok, first...

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Hi Tom,

The links work fine for me. I don't know what the problem might be, but oh well. You wrote,

“Let me turn this around. Why should we be interested in a theory that claims motion as a property of the geometry, with no mechanism or experimental evidence? Why should we be interested in Lynd's claim that motion is fundamental, which is demonstrably false?”

Ok, first of all, I know of no theory that claims motion as a property of the geometry, with no mechanism or experimental evidence. In the case of an RST-based theory, like mine, motion is defined as a change in space per change in time. The experimental evidence upon which this theory is based is the observation of the progression of time and the progression of space. We know that time is progressing, or increasing, because we can measure the increase of entropy associated with it. We know that space is progressing, or increasing, because we can measure the increase of wavelength in the light emitted from the hot elements of distant stars.

I have never heard of anyone insisting on the identification of a mechanism responsible for the observed increase of time, and I don't think that a reasonable demand can be made for identifying a mechanism responsible for the observed increase of space either. These two expansions are our fundamental observations of nature, the characteristics and properties of which we seek to explain in our physical theory.

As far as disproving the validity of Lynds' claim that motion is fundamental, you have your work cut out for you, because you can't escape the fact that space and time are the reciprocal aspects of motion. By appealing to Einstein's arguments for the fundamental role of spacetime, you establish the need for the space/time progression, which by definition is motion.

The problem here is clear: By insisting that motion can only be defined by something that is changing locations, we limit ourselves unnecessarily to 1D motion, driving us to search for order in the higher dimensions of complex analysis, for the greater degrees of freedom we need in our physical theories.

However, the natural order, commutativity and associativity of algebra based on the reals can be maintained in higher dimensions, if we recognize the proper dimensions of space and time and the reciprocal relationship they have in the equation of motion. The extra degrees of freedom we need are obtainable without resorting to the ad hoc invention of imaginary numbers, and this is why it's important to understand the n-dimensional geometry involved in the motion equation, not because we are trying to make motion out of the properties of geometry.

You wrote,

“The only really valid "why" question in physics, is why there is something rather than nothing. Any other "why" is philosophical, not physical.”

That's right, and the RST-based system of theory addresses this question directly: Nothing is perfect, so something is not perfect. It is broken perfection. When we realize the key role that symmetry plays in both physics and mathematics, we see how that assuming motion is fundamental opens up the floodgates to understanding.

This is because a unit ratio is perfect, but a non-unit ratio can be non-unit in two “directions,” which we can call “positive” and “negative.” In this way, the unit ratio is also zero, because, like a pan balance, when there is no difference of magnitude between the two, reciprocal, aspects, of the ratio, unity is equivalent to zero. The question is, then, how is the perfection of the unit ratio broken? Is there a mechanism to do this? Is a mechanism required to do it?

Well, this is another philosophical question, but we can now see how related it is to the physical question. In theoretical physics, we invoke the idea of spontaneous symmetry breaking, and leave it at that. This spontaneous symmetry breaking is invoked philosophically, because the state of perfection is highly unstable, like a pencil balanced on its sharpened point.

However, as we discovered with gauge theory, local symmetry breaking is more powerful than global symmetry breaking, and it behooves us to explore that possibility. When we do, low and behold we find that we obtain a finite system of finite energy that should be completely describable by a set of finite real numbers, without the necessity of resorting to complex numbers and rotations in the complex plane.

This is a tremendous breakthrough, Tom, because, as you point out, we seek an algebraic description of reality, one which Einstein sought in vain. As he lamented to one of his former students:

“...the continuum of the present theory contains too great a manifold of possibilities...The problem seems to me [to be] how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction, not justified by the essence of the problem, [a construction] which corresponds to nothing “real.” But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way.” (see Stachel, 'Einstein from B to Z', pg 414)

I believe that the mathematical structure that we need is to be found in the discrete ratios of space/time, or motion, that we find in the tetraktys. We are accustomed to characterizing the mathematical structure of the tetraktys in terms of the reals, the complexes, the quaternions and the octonions, but these definitions depend upon the functionality of imaginary numbers, which in turn invoke the concept of rotation.

Hestenes has shed great light on the confusion involved in this structure, showing us how unnecessarily complex it has become, but his reduction of its complexity does not remove from it the concept of an imaginary number implying rotation, but rather only transforms it into an explicit operation.

However, when we see the mathematical structure of the tetraktys in the light of an expanding/contracting pseudoscalar, and we interpret its magnitudes in terms of space/time ratios, its algebraic structure is truly transformed into a suitable basis of physical theory.

Regards,

Doug

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Hi Doug,

Sorry, the links don't open for me either at work or at home.

Anyway, you wrote: "Ok, first of all, I know of no theory that claims motion as a property of the geometry, with no mechanism or experimental evidence. In the case of an RST-based theory, like mine, motion is defined as a change in space per change in time."



A lot of fallacies here. First, your...

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Hi Doug,

Sorry, the links don't open for me either at work or at home.

Anyway, you wrote: "Ok, first of all, I know of no theory that claims motion as a property of the geometry, with no mechanism or experimental evidence. In the case of an RST-based theory, like mine, motion is defined as a change in space per change in time."



A lot of fallacies here. First, your definition of motion does not imply change. "...change in space per change in time ..." is empty of physical content. It's not Einsteinian at all--one does not measure change in a space that is isomorphic for all observers (as special relativity informs us); one only measures change by the differences in relations among mass points. Second, your model separates space and time into inversely proportional components, which is entirely different from Einstein's Minkowski spacetime in which space and time are unified. Again, I point out thzt Einstein's definition of "physically real" spacetime is crucially important, and your geometry does not fit that definition. You also contradict yourself from an earlier posting in which you wrote, "...when we speak of changing space and changing time, we are speaking of one fundamental entity, motion, with two, reciprocal, aspects, neither of which can be said to enjoy an independent existence." Obviously, you are giving them an independent existence--to have an inversely proportional relation, they have to be independent. What's it going to be?--inversely proportional space and time or Minkowski spacetime? Nert fallacy:

"The experimental evidence upon which this theory is based is the observation of the progression of time and the progression of space. We know that time is progressing, or increasing, because we can measure the increase of entropy associated with it."

Entropy implies a thermodynamic arrow of time in one direction; however, that does not imply that time increases. Even if we say that time increases in the direction of entropy, we mean only that we can measure an increase in entropy in one direction and that the measurement process also increases entropy. In any case, we cannot say that time increases _because_ entropy increases; there's no warrant for that. Correlation is not causation. Next fallacy:

"We know that space is progressing, or increasing, because we can measure the increase of wavelength in the light emitted from the hot elements of distant stars."

Not a fact. We can say that the redshifted stars are moving away from us, but this does not necessarily mean that space itself is running ahead of the stars. It's a assumption made from the necessity of theoretical self consistency in big bang cosmology.

You write, "As far as disproving the validity of Lynds' claim that motion is fundamental, you have your work cut out for you, because you can't escape the fact that space and time are the reciprocal aspects of motion. By appealing to Einstein's arguments for the fundamental role of spacetime, you establish the need for the space/time progression, which by definition is motion."

I don't need to disprove the validity of Lynds's claim, because it has no physical content, unless or until Lynds comes up with the math to show that "fundamental" motion causes inertia. Good luck. Aristotle couldn't. And since I have already shown that yyour definition of motion is flawed ("...space and time are the reciprocal aspects ..."), this is as far as we can go. I can't debate things that I know are wrong in the context of current knowledge, especially when Einstein is cited as the source.

Best,

Tom

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Tom,

You wrote,

“A lot of fallacies here. First, your definition of motion does not imply change. "...change in space per change in time ..." is empty of physical content. It's not Einsteinian at all--one does not measure change in a space that is isomorphic for all observers (as special relativity informs us); one only measures change by the differences in relations among mass...

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Tom,

You wrote,

“A lot of fallacies here. First, your definition of motion does not imply change. "...change in space per change in time ..." is empty of physical content. It's not Einsteinian at all--one does not measure change in a space that is isomorphic for all observers (as special relativity informs us); one only measures change by the differences in relations among mass points.”

You see it as “empty of physical content,” only because you insist on defining the change of space in the equation of motion, as the change in the location of a mass point. If something isn't moving, if an object is at rest in an observer's rest frame, as time passes, you see no motion present.

However, we have no fundamental definition of a mass point. If we assume it is an electron, and try to describe it, we find an inherent contradiction. This mass point is charged, a point with no extent, yet it possesses angular momentum in the form of something called quantum spin that science has no clue how to describe. We have to hold it together with something, but not knowing what it could be, we just call the energy “Poincare stresses,” and leave it at that, even though we know the thing should blow itself apart.

That sounds a lot more fallacious to me than the claim that the only known relation between space and time is reciprocal. The problems I see in these discussions always comes down to definitions, or the lack thereof. When I say “changing space,” I don't necessarily mean “changing distance.” The definition of motion includes changing distance, but it's not limited to it. When I say “changing time,” I mean a succession of moments, of some duration. There is no way to measure space without a succession of moments, and no way to measure time, without a changing interval of space. That is, space and time don't have an independent existence, but are two, reciprocal, aspects of one component, motion, just as the numerator and denominator of a ratio are two, reciprocal, aspects of a rational number.

Given the numerator of a rational number, there's got to be a denominator and vice versa. We don't speak of numerators and denominators as if they were independent entities. They are simply part of the unified whole, different aspects of a rational number, like two sides of a coin.

While I will concede the point that there is no causal relation between time and entropy, one cannot measure entropy without a passage of time. In the same way, we wouldn't be able to measure the increased wavelength of light, without the notion of an increase of time. As far as the cosmic redshift is concerned, it seems as though you are at odds with established fact there.

But regardless, we must define motion in terms of units of accumulated space and units of accumulated time. If it were not so, there would be no spacetime to measure. The only way to measure spacetime points is to choose a point of reference in some observer's frame of space and time and start counting a change of space over a change in time in some direction. The 1D trajectory of some physical entity, such as a set of photons, to mark the change in a given direction is useful, but it doesn't characterize the motion completely, since the actual motion may be outward from the observer in all directions simultaneously, as observed in the case of receding galaxies.

In this case, if there are three galaxies, moving away from each other, this doesn't mean that there is only motion in three directions. No matter how many galaxies there are, they will all move away from each other. If they all explode and evaporate, the motion separating their locations doesn't cease, just because they did. In fact, if galaxies A, B and C are in a line, the direction of the motion separating them is indeterminate. An observer on B will observe A and C moving in opposite directions, while an observer on A will observe B and C moving away in the same direction, and an observer on C will observe B and A moving in the same, but opposite, direction reported by the observer on A.

Which observer is right? The truth is that they are all right, because the direction of expansion is in all directions simultaneously. Such motion is motion of the locations themselves, not the objects occupying the locations, and exists regardless of whether or not mass points occupy the locations.

Regards,

Doug

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Hi Steven,

Thanks for writing. You are right. Larson's concept of the photon stems from his idea of simple harmonic motion (SHM). He realized that this type of motion would be a stable condition that we would expect to find in a universe of motion, simply because a constant change of “direction” is one of the different kinds of motion one can think of.

In classifying scalar...

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Hi Steven,

Thanks for writing. You are right. Larson's concept of the photon stems from his idea of simple harmonic motion (SHM). He realized that this type of motion would be a stable condition that we would expect to find in a universe of motion, simply because a constant change of “direction” is one of the different kinds of motion one can think of.

In classifying scalar motion in general, Larson identifies translation, rotation, linear vibration, and rotational vibration as the basic types of scalar motion. Linear vibration is the SHM that provides the departure from the perfect symmetry of the unit progression, and so he begins his development with this type. He writes in “An Outline of the Deductive Development of the Theory of the Universe of Motion,”

“16. The continuity of the progression within the units enables the existence of another type of scalar motion of physical locations. This is a motion in which there is a continuous and uniform change from outward to inward and vice versa; that is, a simple harmonic motion. At this stage of the development only continuous processes are possible, but a continuous change from outward to inward and the inverse is just as permanent as a continuous outward or inward motion.”

This SHM “kills” the progression so-to-speak, but in only one of the three dimensions. He explains:

“17. In the two-unit complete cycle of the simple harmonic motion the net change of the spatial position of the physical location is zero. As represented in the spatial reference system, the two-unit combination remains stationary in the dimension of motion.”

That is, there is no net increase, or progression, of space in this case, because each half of each two-unit cycle is a decrease, off-setting the increase in the other half of the cycle. However, Larson concludes that each dimension of the three-dimensional progression is independent, therefore he assumes that the continuous change from outward to inward and the inverse,” may occur in each dimension independently, leaving the progression in one of the remaining dimensions to carry the vibrating unit outward, relative to a fixed reference system. He writes,

“19. The path of the combined progressions then takes the form of a sine curve.

20. We identify such scalar motion combinations as photons. A system of photons is electromagnetic radiation.

(This derivation shows why radiation has the properties of a wave as well as those of particles. It is composed of particles (discrete units), but the motion (progression) of these particles is wave-like.)”

Hence, he begins his development of the consequences of the RST. In effect, he is saying, “Let there be light.” With this discrete entity of light, identified as a photon, constituting the fundamental building block of his development, Larson builds more complex entities, by rotating the photon in various ways.

However, many students of his development (I refer to the development of the consequences of the system, as the RSt, to distinguish it from the system of theory itself, the RST) have found this line of development problematic, since it can't account for all the quantum properties of the photon, including the property of quantum spin, Heisenberg's uncertainty principle, etc.

In considering this problem, I realized that it is inconsistent to treat the dimensions of the space/time progression separately, that a reversal in the progression of the space, or time, aspect of the progression, at a given location, would necessarily be in all three dimensions simultaneously, not just one dimension.

The new approach solves many problems of Larson's original development in that it provides for the observed properties of the photon, as well as supplying the basis for more complex units of discrete motion, as shown in figure 1 of my essay.

The most striking feature of this new approach to the deductive development of the RST, however, is its correspondence with the mathematics of the tetraktys. In Larson's mathematical development of the system, displacement from the unit progression is, again, one-dimensional, enabling him to introduce his concepts of one and two-dimensional scalar rotation, where the degrees of freedom inherent in these concepts, together with rotational vibration, lend themselves quite well to his subsequent theoretical development, but, at the same time, this approach introduces problems related to scalar versus vectorial magnitudes: Rotation is simply not a scalar phenomenon, because something must rotate, and for Larson, the rotating object is the initial, 1D vibration.

Nehru and others took the position, based on concepts of projective geometry, that rotation is just as fundamental a motion as vibration, that across the time region boundary, the two types of motion are actually two sides of the same coin, so nothing needs to rotate. However, while this approach has much to recommend it, it follows Larson's thinking in treating the space/time dimensions independently.



Nevertheless, when we follow the mathematics of the tetraktys, we find that rotation is not necessary to obtain the degrees of freedom needed in the development of n-dimensional magnitudes of scalar motion, that the 3D vibration of the pseudoscalar opens up a startling array of new possibilities, and that the description of these in terms of the time region's rotational analog of pseudoscalar vibration can then be incorporated into the development, once this is understood.

In short, the S|T unit of the new development is a combination of two pseudoscalar vibrations, one spatial and one temporal, accounting for the quantum properties of the photon, and its propagation at unit speed relative to a fixed reference system. In the new development, SHM is found in the expansion/contraction of the two, inverse, pseudoscalars, not in the 1D vibration of Larson's photon.

Regards,

Doug

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Hi Steven,

You are right about the impact in Larson's early development, but I was just following my nose. I couldn't escape the fact that space is three dimensional, and time is zero dimensional. Since scalar magnitudes have no direction, and pseudoscalar magnitudes have all directions, scalar expansion/contraction, or spatial/temporal magnitudes, have to be 3D/0D, in the absence of any...

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