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CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: Time for a Change - The Instantaneous, Present and the Existence of Time by Peter Lynds [refresh]
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Peter Lynds wrote on Aug. 25, 2008 @ 18:38 GMT
Essay Abstract

Beginning with an explanation of the historically accepted solutions to Zeno's paradoxes by calculus, the implications for physics, time, and space, of the conclusion that instants in time and instantaneous magnitudes do not actually exist and that calculus has its "limits" when applied to the physical universe are explained. This includes discussion of the solution to Zeno's paradoxes, why time, space, and space-time do not exist, and why time and space cannot be quantized. The article concludes with some general comments about the work.

Author Bio

Peter Lynds is a 33 year-old independent who lives in Wellington, New Zealand. His research interests largely revolve around the subject of time and physics and cosmology. Links to his papers are available at his website http://www.peterlynds.net.nz, while an FQXi discussion of a recent paper about time and cosmology may be found at http://www.fqxi.org/community/forum/topic/111

Download Essay PDF File




Anonymous wrote on Sep. 6, 2008 @ 13:53 GMT
Very intriguing essay!

report post as inappropriate


Peter Lynds wrote on Sep. 8, 2008 @ 20:42 GMT
As the pdf file doesn't seem to be enabling the link, I think it could be a good idea to include it and the following note (from the essay) here:

In order to meet the essay word limit, I was unable to include some material that I would have really preferred to. This included discussion of (1) the problem of time in quantum gravity, (2) the non-existence of instants, (3) the solution to William James' version of the dichotomy paradox, (4) others who have been on the right track with Zeno's paradoxes, (5) the non-existence of interval, and (6) why time and space cannot be quantized. The omitted material, along with references, may be found here

PS: Thanks Anon




Giannis wrote on Oct. 1, 2008 @ 10:01 GMT
Dear Peter,

Totally interesting essay.

In regard to non-existence of space, I remember a thought experiment that points to this direction. If our eyes had a mirror and we perceived the world as looking it in that mirror, (i.e. things that are now left would be at the right position and vice versa) then there would be no difference. Our brains would evolve in the way to work normally as it is now.

From this, one realizes that it is the relative order of the things that matters not the space itself. This sounds analogous to your solution of Zeno's paradoxes

Nice work, keep on

Best wishes,

Giannis




Clinton "Kyle" Miller wrote on Oct. 14, 2008 @ 15:09 GMT
Dear Peter,

This essay was a great exposition of your work, which conveys an extremely important solution to Zeno's paradox. It crucially reminds us of the assumptions underlying the calculus. I can only hope that the time will come when people begin to see (and espouse) the importance of it and the breadth of the implications!

I also would like to add that in my own essay entry (see "The Here-and-Now") I referenced both your paper on time etc. and your paper on consciousness. I utilized these concepts to begin the construction of a new type of world-view: one that dispenses with the existence of the assumed "objective reality". Unfortunately the essay does not elaborate on all the information contained in the references (e.g., Paul Davies' paper on the implications of a cosmological information bound for the laws of physics) due to length constraints; however, the references are included for the interested reader.

Thank you again for your intrepid ideas!

I look forward to your response (and possible comments on my own work).

CKM




matthew kolasinski wrote on Oct. 16, 2008 @ 06:25 GMT
Hello Mr Lynds,

a very fun paper. love the quotes. a very interesting argument. it reminds me a bit of Heisenberg's indeterminacy principle... can determine location or velocity, but not both at any given moment. 'cept you appear to have taken it further - can't determine either - no "moment".

i'll have to hang onto a copy, in case i should ever get a speeding ticket, present it in my defense - 'the citation states that this occurred at such and such a time. that would appear to be a physical impossibility to determine' ;-)

you might have fun reading some of the notes on the development of the cultural concept of time and the nature of perception in "some thoughts on time" elsewhere here.

it's an interesting experience reading the papers that have been presented. i'm reminded of the story of the group of blind men encountering an elephant, trying to describe it....

thank you :-)

matt k.




Peter Lynds wrote on Oct. 21, 2008 @ 03:09 GMT
Thanks Giannis. Good to see you on this thread too.

Thanks Kyle. That's really nice of you. I'll have to read your paper, but I must admit that I don't have much time for arguments against the existence of objective reality. An assertion that a rock (or the universe) exists independently of a person may be subjective, but the rock is still there. All manner of philosophical objections can be made to this, but the bottom line is that, if someone gets fed up with a person talking about things such as brains in a vat, and throws a rock at him, it still hurts. Moreover, trying to assert (and decide between ourselves) what physically is and isn't, is what science is all about. Without this (in other words, a belief in objective reality), science is pointless.

Thanks Matthew. I hadn't thought of the speeding ticket defence. I should give it a go one day.

In relation to the uncertainty principle, it is often assumed that if it weren't for quantum uncertainty, all physical magnitudes would be exactly determined. However, the non-existence of instantaneous magnitudes means that, even if there were no such thing as quantum uncertainty, physical values would not be precisely determined anyway.

Best wishes

Peter




Clinton "Kyle" Miller wrote on Oct. 21, 2008 @ 05:37 GMT
Peter,

Thank you for you response!

I probably should have been more explicit in my account of "objective reality". I regard this as more of a 'material objective reality'.

"An assertion that a rock (or the universe) exists independently of a person may be subjective, but the rock is still there."

I agree that the 'universe' exists independently of us, however, What is the universe? Does it need to be a material universe? Could it be a information-based universe? Could it be a 'universe of possibilities'? Could physics *really* be a part of statistics? (Please see the attached high-lighted article.)

"All manner of philosophical objections can be made to this, but the bottom line is that, if someone gets fed up with a person talking about things such as brains in a vat, and throws a rock at him, it still hurts."

I like this one, good point. But, in my essay, this example would be only possible in the here-and-now.

"Moreover, trying to assert (and decide between ourselves) what physically is and isn't, is what science is all about. Without this (in other words, a belief in objective reality), science is pointless."

Might we be trying to decide what physically is and isn't *possible*. Do we need to extend our theories as an ontology? Could there be a more parsimonious theory of 'what is'?

I look forward to seeing your response!

CKM

attachments: Theories_of_almost_everything.pdf




Clinton "Kyle" Miller wrote on Oct. 22, 2008 @ 01:50 GMT
I also wanted to add: that I feel although this "belief in an [material] objective reality" without which "science is pointless" is indeed common among many in our society. Yet it may be so common, in our belief structures, that it is almost taken for granted. (Think about the first time you consciously realized that you can die.) I think it should be every scientists job to make sure that they articulate this state of epistemology—that, in fact, all of reality is perception—which is a profound fact we have discovered. Just as the church goer believes in a 'God' we, scientists, believe in an 'objective reality'. Without this faith—life would be meaningless—as death would be but an idea, and not a conscious-realization.

So it is, in a funny way, that death makes us human.

“Reason dreams of an empire of knowledge, a mansion of the mind. Yet sometimes we end up living in a hovel by its side. Reason has shown us our capacity for power, both to create and to destroy. Yet how we use that power rests on our deeper capacities which lie beyond the reach of reason, beyond our traditions and culture, stretching far back into the depths of the evolutionary process that created our species, a process that ultimately asserts the power of life over death. And, ironically, even death, as part of the process of life, asserts that power. That is how we have come into being and now find ourselves committed to the unrelenting moral struggle of ordinary human existence.” - Heinz R. Pagels

CKM




Narendra Nath wrote on Oct. 31, 2008 @ 04:23 GMT
Dear Peter and commentator Kyle,

This is my first posting on the essay. Whenever, one breaks a new background, only he understands it fully. The rest need time to comprehend in silence! Science started as philosophy but soon got tempered with more and more precise measurements. However, all measurements are subject to limitations of instruments used and basically no measuremental accuracy has reached the limits set by the Uncertainty relations. Thus there is full scope for precepts and concepts based on critical observations and analysis both external and internal. The latter is confined to our most important laboratory, the human brain. If i am allowed to add, the human brain as also the cosmos is covered by the non-physical entity called 'consciousness'. We are thus subjected to the interaction with the cosmos. The 'wider' is one's conception the better one interacts with the cosmic consciousness and higher the chance to reach closer to the truth or 'relative truth' being sought in science.

Space & time are concepts that may get replaced with suitable others in a new explanation for gravity. However, gravity will remain a fact. There is a problem in modern physics as one attempts to unify the four known physical interactions,viz., strong and weak nuclear, electromagnetic and gravity. The last one continues to defy this conceptualization. Perhaps it was the first to emerge as soon as the Universe was created. What the nature desired for the Universe to evolve in the early stages of the 'volatile' Universe is somehow unobservable in the cosmological experiments conducted thus far. i have made some speculations in this regard in my essay posted in the competition and have also provided two other manuscripts in my own first two posts that led me to the main essay i posted. i will greatly appreciate comments of all authors/ interested public on the aspects discussed therein. NN




Brian Beverly wrote on Nov. 8, 2008 @ 03:43 GMT
I like your essay and use of classical philosophy, but I think Heisenberg disagrees with you:

Your essay is a classical Newtonian argument, but taking ever smaller intervals of time and space makes the fundamentally a quantum mechanics argument. Heisenberg disagrees because Zeno's Paradox assumes you know both the position and velocity of the arrow with certainty. A counter paradox is for an arrow with a velocity near the speed of light. The relativistic Lorentz contraction would make the arrow appear shorter. Would the arrow look like a quantum object to an observer? Is it possible for a Lorentz contraction to be smaller than the Planck length?




Peter Lynds wrote on Nov. 8, 2008 @ 20:19 GMT
Dear Brian,

Zeno's paradoxes assume exact position, but not necessarily exact velocity. For the paradoxes to result, all that is required is that the respective body be in motion. I don't really understand your comment, as, in addition to the above, the main point of the essay is that instantaneous magnitudes do not actually exist. Trying to deny the applicability of Zeno's paradoxes is something different. Moreover, quantum uncertainty is unrelated to a moving body not having a determined or instantaneous position. Even without qm, instantaneous position would not exist.

Best wishes

Peter




Narendra wrote on Nov. 9, 2008 @ 01:05 GMT
Dear Peter,

your response to my post of Oct 31 still awaited! hopefully you don't find my comments ae irrelevant so as not to deserve your enlightened comments. Nature of my essay on this website follows such perspectives about the mysteries of the Universe!

NN




Clinton "Kyle" Miller wrote on Nov. 9, 2008 @ 08:52 GMT
Peter,

I have found my faith in a sort of cosmic religion, based on a hypothesis:

Sometimes I feel like we are funny looking black holes existing on a whole different scale, and that somewhere and somehow our brains are connected to that “deeper level,” so just as each black hole has its singularity we have our “I’s” whose even horizon—coupling with electromagnetic force—exists in our eyes: because the connection of light goes at the speed of light, so objectivity there is no time between “you” and “me,” our intersubjective beings, with subjective memories that lay beyond “your” even horizon, forever missing from “it” by that funny information paradox that just won’t quit... as we live in this combination of interconnection and introspection delivered by light for our perception.

The objective reality is gravity.

The only certainty is death.

CKM




Brian Beverly wrote on Nov. 18, 2008 @ 09:07 GMT
Let me give a more straight forward example of quantum mechanics being violated. The arrow has momentum which must be conserved. The bow and arrow must be considered. The bow and string are composed of atoms and when Zeno draws the string potential energy is stored in the bow. When he releases the string the potential energy is converted to kinetic energy and the arrow takes flight.

Planck solved the ultraviolet catastrophe with the revelation that energy is absorbed and emitted in discrete, whole, amounts. If the kinetic energy is:

E = 1/2 mV^2

then how can there be discrete energy but not discrete velocity? In fact, accelaration, velocity, position, force, momentum and energy are all related; how could some be continuous and others discrete?




Peter Lynds wrote on Nov. 19, 2008 @ 16:21 GMT
Dear Brian,

I think your point/question this time is a good one. Time and space cannot be quantized (see my comment and/or Carlo Rovelli's response on his essay thread). If time and space cannot be quantized, velocity and acceleration cannot be either. I don't think that the idea of velocity or acceleration being quantized even actually makes sense as a concept. This, however, does not stop magnitudes such as momentum, mass and energy from being quantized. I don't really understand what the equation for kinetic energy is supposed to illustrate, as if mass is quantized, so will the energy, but velocity needn't be.

Also, because magnitudes such as mass and energy are quantized, does not mean that motion is. It just means that a moving body is made up of discrete parts. If the body in question is one of those discrete parts, it moves along just as continuously as anything else. That is, although Planck time and length represent operational roadblocks for rulers and clocks, and the constitutes of clocks and rulers are also quantized, intervals of time and space are not. They do not exist.

Best wishes

Peter




Narendra Nath wrote on Nov. 22, 2008 @ 13:41 GMT
Dear Peter,

The quantization limits for energy are beyond the capability of our present day instruments to measure directly. Indirect measurements indicate the truth about the same and that is fine. What i wish to say is that we are so much worried about getting close to the truth. But what we achieve is just a broad limit. This limit can be lowered but will it help us better in real science to progress. For example, The large Ion Beam Collider at Geneva is already a money guzzler and more of the higher energy accelerators will not be able to carry us to the end , as the end has its way of receding from us further!! What we need to do is to think out alternate strategy for the growth of science through Expanding its present Paradigms, e.g., we may think of modifying our 'Methodology of Science'

by including extensive research on the levels of 'consciousness'. i have hinted at the state of meditation in my essay, as a state that is beyond the three awareness states of wakeful, dream and deep sleep. It is the state of human mind ( we call ingeneous levels)that has resulted in bright ideas of science developed thus far. Now we need to much higher levels of consciousness for our mind to come with something called path-breaking development!




Brian Beverly wrote on Nov. 23, 2008 @ 03:30 GMT
Peter, this will be my final comment for your essay. I believe you are wrong but don't fret, everyone else who has submitted an essay is probably wrong too. I may give you a restricted vote because your essay is easy to understand and forced me to think deep about the fundamental nature of the universe.

Carlo's response to your comment agrees with me:

[The "atoms of space" and the "atoms of time" of LQG are only figures of language, to indicate that certain physical

observables aspects of the gravitational field have a discrete spectrum.]

An example of an observable is energy and he believes such observables are discrete as I do. Carlo is discussing LQG in his post; I am discussing Planck's century old observation that energy is discrete. My first comment on the uncertainty principle still holds, but it requires esoteric physics. I felt there should be a counter example that matched the elegance of Zeno's paradox.

E = 1/2mV^2 is the kinetic energy equation it is one half of the mass multiplied by the velocity squared. The mass is not changing because the relativistic effects for a classical arrow in flight are negligible. However, just in case you want to push the relativistic energy/mass issue please read this:

http://www.physorg.com/news146415074.html

As Zeno releases the bow string the kinetic energy of the arrow increases as the potential energy in the bow decreases. The increase and decrease in energy is discrete on a fundamental level. The mass in the kinetic energy equation is a constant as is the 1/2 coefficient. The only variable in the equation is the velocity. If the kinetic energy of the arrow is increasing by discrete amounts then the velocity MUST increase by whole amounts too.

I dislike using psychology in physics, but I think it is needed in this case. We have two different frames or mental pictures of how to think about the universe. Last week I came across a TED lecture that shows the different frames we are using.

http://www.ted.com/index.php/talks/lee_smolin_on_scien
ce_and_democracy.html

Your frame is four minutes into the video.

Thank you for the essay,

B^2




Peter Lynds wrote on Nov. 24, 2008 @ 14:51 GMT
Thanks Narendra.

Thanks Brian. In relation to your comment about Carlo's, all right-minded physicists believe that observables such as energy are quantized. My point was obviously that time and space cannot be. In respect to your argument about kinetic energy and velocity, however, I unthinkingly made a mistake. Two actually. I was thinking of constant velocity rather than an acceleration, and secondly, I said/agreed that energy is quantized. Of course, in many cases it is, but translational kinetic energy - the relevant one here - isn't. As such, again, it doesn't follow that velocity is.

I'm a little bit baffled by your comment about the video. I can only assume that you're missing the point about quantum mechanics being unrelated to there being no so such as thing as instantaneous magnitudes in Nature.

Best wishes

Peter




Paul Halpern wrote on Nov. 25, 2008 @ 05:13 GMT
Peter,

Your essay is well-written and innovative. I enjoyed your examination of the classical notions of time, as expressed by Heraclitus and Zeno, and found it interesting how you have developed an alternative formulation of time as a way of resolving age-old paradoxes as well as modern issues.




Narendra wrote on Nov. 25, 2008 @ 07:05 GMT
Dear Peter,

Thanks for thanking me, no re-comments.My suggestion may be taken as an emphasis for broadening our educational system all over the world. May be work is needed to see that the curriculum lays emphasis on whatever knowledge exists from any corner of the world to get incorporated adequately/properly in the couse work all over the world. The world has come closer today due to means of communication, but we are still very much isolated in education to our neighborhood community, instead of the world community. This anomaly may not prove to be good for our world full of beauty and love of scenario and humanity,

respectively!!




Peter Lynds wrote on Nov. 25, 2008 @ 22:17 GMT
Thanks Paul. That's really nice of you. It's great to see you here. Great too that you've submitted an essay. I'll be sure to read it and leave a comment.

Best wishes

Peter

PS: Thanks once more Narenda.




Peter Lynds wrote on Dec. 3, 2008 @ 01:58 GMT
In a discussion on Douglas Bundy's essay thread, I said that I would post some comments here about Einstein's possible view on instants and instantaneous magnitudes. Although he must have been aware of them, as far as I know, Einstein is not on record as having ever talked about Zeno's paradoxes, so we are unable to look there for clues. His theories of special and general relativity are heavily...

view entire post





Armin Nikkhah Shirazi wrote on Dec. 3, 2008 @ 05:26 GMT
Dear Peter,

I found your essay well-written and interesting.

I do have some comments:

If I understand your thesis correctly, you argue that there are no such things as instants of time and points in space. From this you conclude, among other things, that there is no such thing as a velocity.

A velocity dx/dt by your argument is really 0/0, and if a point is the exact spatial analog of an instant, then our (by your argument incorrect) conceptions of time and space approach their respective zeros in the exact same way. But from this it would seem to follow that it is possible to define velocity: It becomes a constant.

Put slightly more formally, let f be a continuous function which models time. By your argument f is an incorrect representation of reality because there is no time (t=0).

Let g be a continuous function which models length. By your argument g is an incorrect representation of reality in exactly the same way that f is incorrect because there is no length (L=0).

Velocity becomes v=dg/df which describes the change in g with respect to f. But because the error in the numerator changes in exactly the same way as the error in the denominator, as g and f tend to zero, v tends to a constant. At the limit at which both actually are zero, which by your argument is the correct physical model of time and length, we can thereby still define v to be the constant that corresponds to the rate of the change of the error in modeling length with respect to the rate of change of the error in modeling time.

So it appears to me that your argument does not rule out the existence of velocities in reality.

If my argument is correct, then this creates a difficulty for your idea because then there should only exist infinite accelerations. In other, words, the existence of inertial charge i.e. mass falsifies your hypothesis.

To see this, let a=d(dg/df)/df. The numerator is even in reality definable as a constant, but the denominator is by your argument in reality exactly zero.

Thank you for raising some interesting questions, I enjoyed thinking about them.

Armin




Armin Nikkhah Shirazi wrote on Dec. 3, 2008 @ 05:46 GMT
Hello,

Immediately after submitting my post, I realized that I erred in the last step: I overlooked the "d" in front of the numerator, including which of course means that a=0/0.



Therefore, my conclusion that accelerations should be infinite by your argument is invalid.

However, it does raise another question, namely how it is, by your argument, possible that we can distinguish accelerations from velocities in an isolated environment in reality (We certainly cannot distinguish constant velocities from rest in an isolated environment.)

Again, thanks for provoking my thoughts.

Armin




Peter Lynds wrote on Dec. 5, 2008 @ 02:30 GMT
Dear Armin,

Thanks for your kind words. It just rules out instantaneous velocity (and any other instantaneous magnitude). As always, we can still measure (more, correctly, represent) a velocity if a moving body is within some distance and time interval (as represented by a clock and meter). These intervals can naturally potentially be taken up to the limits of possible measurement.

I do not really understand your other point, as I do not see any reason why my conclusions would make a constant velocity and acceleration indistinguishable.

Best wishes

Peter




Doug wrote on Dec. 5, 2008 @ 15:48 GMT
Hi Peter,

I think Armin’s point can be understood in terms of Newton’s thought experiment of the isolated water bucket. There is no way to define motion of the bucket (if the observer is on the bucket), by reference to outside objects, since it is isolated, but if it is rotated with water in it, the water in it will rise up the sides, showing an acceleration due to the constant change of direction.

I think Armin’s question is, “Why is the change of motion detectable (i.e. acceleration), while motion itself is not?” The answer is that the change in motion that is detectable, in the case of rotation, is the change in its “directional” property, which is distinct from its magnitude property.

If the motion of the bucket were translational motion, a change in the magnitude property of the motion would also be detectable, by the water rising up the side opposite the direction of the applied acceleration.

However, the question of why only the change in these quantities, and not the quantities themselves, is detectable, goes to the heart of your essay: Only change really exists, because intervals of no change are impossible, and given that change must be measured in terms of some indivisible unit, to be quantifiable, a paradox is created that is at the heart of the crisis in fundamental physics.

Thus, the question arises, “While an instant of change is impossible to define, is it possible to define an instant of change in the magnitude, or direction, of change?




Peter Lynds wrote on Dec. 5, 2008 @ 20:40 GMT
Dear Doug,

"...Only change really exists, because intervals of no change are impossible, and given that change must be measured in terms of some indivisible unit, to be quantifiable, a paradox is created that is at the heart of the crisis in fundamental physics."

Well put. The thing is, as clocks and meters are just as useful as they have always been (a theoretical paper isn't going to change that!), it needn't actually be a problem. It just requires one to realise that instants, instantaneous magnitudes etc, are non-physical, and based on this, to not let oneself fall into faulty assumption or paradox. A problem also obviously arises when these faulty assumptions are not recognized and are used as building blocks in the construction of other theories, e.g. the idea of time and space being quantized, Chronons, any theory that assumes or posits the existence of time, space-time etc.

"Thus, the question arises, "While an instant of change is impossible to define, is it possible to define an instant of change in the magnitude, or direction, of change?"

No, I don't think so. Again, though, as long as one is careful not to fall into faulty assumption, there needn't be a problem. With the majority of people not being aware of these things, however (including some who do not think that time exists), there is a problem.

Best wishes

Peter

PS: I just realised that I should have probably mentioned about a paper I wrote in 2003 about time, the present, and consciousness. Although I'm not very proud of the way it is written, and I unfortunately haven't had a chance to publish anything further on it yet, I still very much believe in the conclusions it reaches. Namely, that conscious awareness and our seemingly innate conception of a preset moment or a now, are actually two sides of the same coin, and that figuring out how the brain creates this conception (of a present moment), also holds the key to understanding how conscious awareness is possible. This is the paper




Eckard Blumschein wrote on Dec. 7, 2008 @ 01:27 GMT
Hi Peter,

You did not consider your essay valuable. It will perhaps not hurt anybody. I largely agree with your point of view, and I am trying to reveal some rather unbelievable consequences that can be derived for mathematics as well as for physics. To what extent can you support me?

Regards,

Eckard




amrit wrote on Dec. 7, 2008 @ 16:15 GMT
yes, universe is atemporal, time is an observer effect

attachments: The_Concept_of_Atemporality_into_The_Theory_of_Relativity__amrit_2008.pdf




Peter Lynds wrote on Dec. 7, 2008 @ 22:59 GMT
Dear Eckard,

I take it that you are referring to my comment that, in relation to physics, I consider the work's value to be limited. I think this is true, and explain why in the essay, but as the work has direct relevance to a number of very fundamental questions and problems in physics (the question of whether or not time and space are quantized, the question of the existence of time, space, and space-time, the problem of how, despite a number of theoretical roadblocks, change is possible, etc), I do consider it valuable. In relation to the non-existence of instants and instantaneous magnitudes, I also think that it could potentially play a part in the solution of some outstanding puzzles in quantum mechanics and quantum gravity. While I'm being a little bit bold, I should also probably note that the argument contained in the essay doesn't represent another solution to Zeno's paradoxes. As it is the assumption of instantaneous relative position that causes the paradoxes to result, it is the solution.

Dear Armit,

Thanks. I enjoyed your essay. I naturally agree with it too. Best of luck.

Best wishes

Peter




amrit wrote on Dec. 8, 2008 @ 17:19 GMT
Dear Peter

We are living into ATEMPORAL UNIVERSE, into ethernal NOW.

How to bring that into science is a big work.

I see that we are close to the success.

In a few years time will accepted by the main stream as a scientific tool to describe irreversible stream of material change that run into atemporal space in a linear way past-presdent-future.

This will be a great jump into human consciousness from "I" to the consciousness itself that is a basic frequency of guanta of space that build up atemporal space.

yours amrit




Peter Lynds wrote on Dec. 8, 2008 @ 19:11 GMT
Dear Armit,

Thanks. I should note that I do not think that "atemporal space" or an "Eternal now" exist either.

Best wishes

Peter




Dr. E (The Real McCoy) wrote on Dec. 9, 2008 @ 17:15 GMT
Hello Peter,

I enjoyed your essay--more than once! Thanks!

It seems you are searching for something--for a "deeper" mechanism--a more fundamental *physical* invariant powering time and all its arrows and assymetries.

Well, Moving Dimensions Theory provides such a mechanism! The fourth dimension is expanidng at the rate of c, or dx4/dt=ic.

In the attached paper, you...

view entire post


attachments: 14_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf




Eckard Blumschein wrote on Dec. 11, 2008 @ 14:35 GMT
Dear Peter,

Thank you very much for your reply. I largely agree wholeheartedly. I only object you might not be too bold but perhaps rather not consequent enough. Maybe you did not yet carefully read my essay, most likely you did not read what I wrote when commenting on Christinel Stoica concerning the notion real vs. what I coined irreal number. Irreal numbers include the irrational but not the imaginary ones and are uncountable, i.e., they do not exist.

Irreal numbers belong to instantaneous values. Every mathematician declares me wrong if I argue |sign(x)|= 1 does not require an exception for x=0 if the x are the continuous irreal numbers. However, no mathematician so far had a convincing answer how to deal with the zero between IR+ and IR- if one splits IR. It does not exist if considered an irreal number.

Don't you agree that Zeno's paradox is closely related to Buridan's donkey, and the latter is almost identical with Schroedinger's cat and Wigner's friend?

While our founded criticism has little or no chance yet to overcome funded speculations, I agree with someone who argued: Physics needs serious criticism rather than endless futile speculations.

Those who did not yet take the opportunity to choose three votes are kindly requested to draw attention to essays like that of you, of Dr. E, and of mine. Maybe you can suggest better votes?

I feel, Prof. Ellis, Le Rouge, and several others also reject pure speculations like the block universe.

Those who perform funded research will perhaps not hesitate voting for Carlo Rovelli, Christinel Stoica or the like.

Regards,

Eckard Blumschein

eckard.blumschein@arcor.de




Peter Lynds wrote on Dec. 12, 2008 @ 01:03 GMT
Dear Dr. E,

Thanks.

"It seems you are searching for something--for a "deeper" mechanism--a more fundamental *physical* invariant powering time and all its arrows and asymmetries.

I'm simply after motion (and I have that). Thanks for mentioning your essay.

Dear Eckard,

Thanks. I haven't read your essay yet, but I will. Thanks for mentioning it.

In relation to the block universe, as it is an outflow of the lack of absolute simultaneity in Nature, I think it is the correct view. As I just explained on George Ellis' and Cristie Stocia’s essay threads (and mentioned in my essay), however, I think it is just in the interpretation where the problem is.

"While our founded criticism has little or no chance yet to overcome funded speculations..."

I disagree. Although I may be a bit naive, and I must admit that I sometimes find pursuing my work frustrating (more so in the past before I properly learnt that some things are really just to be expected as being par for the course), I wouldn't bother pursing my work if I didn't feel that I was in the hunt with it.

There a large number of essays that I think deserve votes. Carlo's is certainly one of them.

Best wishes

Peter




Eckard Blumschein wrote on Dec. 12, 2008 @ 08:51 GMT
Dear Peter,

I look forward getting your detailed comments on at least my essay. Having learned a lot from the current discussion, I do not expect any physicist voting for my accusation that the obvious mess in physics most likely simply relates to improper interpretation of complex calculus.

I agree that the philosophical point of view is crucial. My university is named after Otto von Guericke who was one of the first who gave priority to experiment rather than to Platon's attitude in physics. Later more.

Kind regards,

Eckard




S. Baron wrote on Dec. 12, 2008 @ 18:45 GMT
Thank you for this essay. I agree that the present can't exist, as its duration can not be determined. However, does this really prove that time can not flow from the past to the future (sidestepping the present)? For example, the duration of the past can be known. If the duration of the future can be known, both can be said to exist. The recent future affects ITS past (the so-called present). An example of this is how a musical note changes the sound and feeling of the note that preceded it. So, what about a flow from past to future without the construct we call the present?

Thank you,

Sandy




Dr. E (The Real McCoy) wrote on Dec. 13, 2008 @ 15:36 GMT
Thanks Peter,

You write, "I'm simply after motion (and I have that)."

How do you weave change and motion into the fundamental fabric of spacetime? I'm not sure I caught that in your paper.

Moving Dimensions Theory weaves change into the fundamental fabric of spacetime by noting that dx4/dt=ic--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. For the first time in the history of relativity, change has been woven into the fundamental fabric of spacetime with a new universal invariant: dx4/dt=ic.

And, the great thing about MDT is that in addition to providing a mechanism for motion, it also provides a physical model for entropy, time and all its arrows and assymetries across all realms, quantum nonlocality and entanglement, Huygens' and Heisenberg's principles; and all of relativity can be derived from MDT.

Assume a 4D universe x1, x2, x3, x4 where the foruth dimension is expanding at c: dx4/dt=ic. Ergo relativity and E=mc^2. Ergo quantum nonlocality and entanglement. Ergo time and all its arrows and assymetries. Ergo entropy and Huygens' and Heisenberg's principles. Ergo the constancy of c and all motion.

But how do you acocunt for motion in a *physical* manner?

All the best!

Dr. E (The Real McCoy)




Peter Lynds wrote on Dec. 13, 2008 @ 18:06 GMT
Dear Eckard,

Although I haven't read your paper yet, if it stands up, I hope you're wrong about that.

Dear Sandy,

Thanks. I don't think so, as without its building blocks (instants) being there, there is no sense in which time (whether a flow, interval, past, present and future), could be said to exist. Without the water, there can be no river. With relativity, Einstein also showed us that the differentiation between the past, present and future is just an illusion; all times (those shown by a clock) share equal footing. In relation to cosmology, I think it can also be argued that what we normally term as being the future can equally be termed the past, and vice versa. If correct, this would again mean that the past and future do not exist. Finally, in relation to your comment, "the duration of the past can be known. If the duration of the future can be known, both can be said to exist," duration or interval do not exist either, while, without the present/an instant, there could be no transition point/time from past to future.

I think it is interesting to ask, if the future and past did exist, how would they exist? To exist, they would presumably have to be something physical. I think the ridiculousness of their actually existing then becomes more apparent.

Dear Dr. E,

In relation to block time vs. motion, and as I explained in my essay, as long as one recognizes that instants, instantaneous magnitudes, space-time points etc, do not exist, motion and change become possible and can be seen to be completely compatible with general relativity and the block view, with all times (those shown by a clock) sharing equal footing. That is, the problem of block time not allowing for motion and change is precisely due to the assumption that instants, space-time points etc, exist.

Best wishes

Peter




EB wrote on Dec. 14, 2008 @ 00:00 GMT
My last reply to Elliot McGucken at 238 was mutilated when I begun to explain what essential details he was not aware of. Then he quoted Born in order to lecture me. I consider the following details important for all who are using complex physical quantities.

One safely arrives at the complex frequency domain and correctly returns only via several steps while it is common practice to skip...

view entire post





Dr. E (The Real McCoy) wrote on Dec. 14, 2008 @ 00:06 GMT
Thanks Peter,

You write, "as I explained in my essay, as long as one recognizes that instants, instantaneous magnitudes, space-time points etc, do not exist. . ."

Yes--but why do points not exist in spacetime?

I propose that the anwser to this is "because the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic." ...

view entire post


attachments: 15_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf




Eckard Blumschein wrote on Dec. 14, 2008 @ 00:20 GMT
If this continuation will be truncated again, I would see this an indication of lacking arguments against my essay.

As well known, Oliver Heaviside, continued the function f(x>0) into the negative half-plane x




Robert Sadykov wrote on Dec. 16, 2008 @ 10:36 GMT
Dear Peter Lynds,

If something has any physical properties then it exists. Both the motion and time have physical properties. Therefore, we accept their existence. The time is created by the motion and depends on the motion. Therefore, in case of the discontinuance of any motion the time disappears. The problem arises, if we unreasonably expand number of physical properties of time. For example, in case of the gravitational radiation the time exists irrespective of a source of the gravitational field and has substantial character, in particular, contains energy. It is a mistake of the general theory of relativity and by the way not single.

Regards,

Robert Sadykov

The Theory of Time, Space and Gravitation




Peter Lynds wrote on Dec. 17, 2008 @ 20:22 GMT
Dear Robert,

Thanks. Yes, I agree, although time has no physical properties. A clock naturally does, but as with all other natural process, the movement of its hands are just the result of the capability for motion in Nature. Time plays no role.

Best wishes

Peter




Eckard Blumschein wrote on Dec. 18, 2008 @ 01:30 GMT
Dear Peter,

In order to avoid problems that may be due to use of certain symbols, I wrote the attached pdf file. I did not yet post at M286.

Regards,

Eckard

attachments: 1_Microsoft_Word__How_do_negative_and_imaginary.pdf




Dr. E (The Real McCoy) wrote on Dec. 18, 2008 @ 23:50 GMT
Hello Peter,

You write, "Yes, I agree, although time has no physical properties. A clock naturally does, but as with all other natural process, the movement of its hands are just the result of the capability for motion in Nature. Time plays no role."

The movement of a clock's hands depends on the emission and propagation of photons. Whether in an unwinding copper clock spring or in an oscillating quartz crystal or osciallating computer circuit, a clock's rate relies on the emission and propagation of photons. All such clocks are fundamentally light clocks, which are streated in the attached paper in the context of MDT.

Photons are but matter that surfs the fourth expanding dimension. And as the expansion of the fourth dimension is an invariant that is independent of the velocity of the source or clock, the faster an object/clock moves, the slower the period of any clock. Simple algebra and geometry demonstrates this for photons in moving frames of reference--time is slowed equally in light clocks that depend on both transverse and/or lateral motion of photons relative to the inertial frame. And as all clocks are fundamentally light clocks, moving clocks run slow, due to the fact that the light is carried by a fourth dimension expanding relative to the three spatial dimensions.

So it is that nature is "capabale of motion" and time because motion and change are fundamentally woven into the fabric of spacetime with dx4/dt=ic--the fourth dimension is epxanidng relative to the three spatial dimensions at the rate of c.

All of relativity is derived from MDT, which also liberates us from the block universe while providing a common *physical* model for time and all its arrows and assymetries across all realms, as well as nonlocality and entanglement and Huygens' and Heisenbergs' principles.

dx4/dt=ic (underlying relativity) means the fourth dimension is expanding at the rate of c.

xp-px = ih (underlying quantum mechanics) means the fourth dimension is expanding in units of the Planck Length.

Best,

Dr. E (The Real McCoy)

attachments: 18_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf




amrit wrote on Dec. 22, 2008 @ 15:16 GMT
Dear Peter

your definition

»Time enters mechanics as a measure of interval, relative to the clock completing the measurement”

I find extraordinary good.

yours amrit

attachments: Time_is_what_is_measured_with_clocks_sorli.pdf




Peter Lynds wrote on Dec. 22, 2008 @ 20:31 GMT
Dear Armit,

Thanks. In relation to that 2003 quote, I should note that it was before I properly realised that clocks only refer to themselves, hence the word "measurement".

Best wishes

Peter

PS: For if anyone is interested (and wasn't aware of it), there has been an interesting and forthright discussion about the existence of time, and then the block universe, on George Ellis' essay thread.




Eckard Blumschein wrote on Dec. 23, 2008 @ 07:28 GMT
Dear Peter,

Yes, in contrast to Rovelli and many others, Ellis does not feel obliged to "explain" problems that arise from presumably flawed theory.

Would you agree that a clock can never measure future time but it always measures a timespan between a moment in the past and the actual moment when one reads it?

Please find attached part 2.

Best wishes,

Eckard

attachments: 7_Microsoft_Word__How_do_part_2.pdf




Peter Lynds wrote on Dec. 29, 2008 @ 21:57 GMT
Dear Eckard,

I wouldn't say that about George Ellis. I think it is petty clear that he is open to discussing any aspect of his theory.

In relation to your question, I don't think that the past, future, or moments exist.

Best wishes

Peter




Peter Lynds wrote on Jan. 6, 2009 @ 02:46 GMT
For if it seems like I'm talking to ghosts in some of my replies above, it's because a number of comments by people seem to have just been removed by the moderator. The moderation seems a little bit hit and miss.




Cristi Stoica wrote on Jan. 10, 2009 @ 07:58 GMT
Dear Peter,

You say “it seems that Nature has wisely traded certainty for continuity”.

In order to understand better your essay, can you please tell me:

1. What do you mean by “continuity”? Is it the same as in Topology (http://en.wikipedia.org/wiki/Continuity_(topology))? If not, can you provide a definition?

2. What do you mean by “uncertainty”? It is a real but unknown value? Can we know an interval containing the value, or a fuzzy set, or a probability distribution?

Best regards,

Cristi Stoica




Peter Lynds wrote on Jan. 12, 2009 @ 00:59 GMT
Dear Cristi,

Thanks. In relation to continuity, just the regular meaning .i.e. continuous, the capability for motion and change etc.

"What do you mean by "uncertainty"?"

Certainty rather than uncertainty. If instants and instantaneous magnitudes existed, such magnitudes would be exactly determined and certain. If they did exist, however, one could also forget about any continuity; everything would be frozen. Moreover, and taking the case of motion as an example, because for something to be motion, its relative position has to be constantly changing and undetermined, a moving body cannot have a determined/instantaneous relative position. As such, and although relative position can naturally be measured/determined up to the limits of measurement, as far as Nature is concerned, one can say that that there is a trade off of exact or instantaneous relative position [certainty, but static and discontinuous], for movement [continuity/indeterminacy]. In relation to this trade off, the same can be said for all physical magnitudes. Note that this in unrelated to quantum uncertainty, except in relation to the general assumption that if it weren't for quantum considerations, physical magnitudes would be exactly determined. The non-existence of instantaneous magnitudes means that, even without quantum uncertainty, they wouldn't be exactly determined. Also note that this doesn't mean that instantaneous vales cease to be very useful. The point is that they are non-physical, so one must be careful about what infers about them. There are a number of problems, paradoxes and additional assumptions that can be shown to be the direct result of assuming that instants and instantaneous magnitudes actually exist.

Best wishes

Peter




Cristi Stoica wrote on Jan. 12, 2009 @ 06:35 GMT
Dear Peter,

Thank you for your answer. If you agree, I will ask for some clarifications.

1. Continuity.

A. According to your theory, is time continuous? If it is, by the regular meaning of continuity, time is a connected topological space. The same holds for space. Are space and time topological spaces?

B. Is “continuous motion” described by a continuous function f : Time - > Space, where Time and Space are topological spaces?

If the answer is “no”, can you provide the correct definition of continuity in your theory?

2. Uncertainty.

You say: “The non-existence of instantaneous magnitudes means that, even without quantum uncertainty, they wouldn't be exactly determined.” I understand that you infer “uncertainty” from non-existence.

A. But what is “certainty”, according to you?

By saying that the physical quantities do not exist, without defining or postulating something else that looks like those quantities but satisfy also your own exigencies, you cut any chance for making Physics.

B. What can we put instead of the non-existent instantaneous magnitudes?

Intervals? Probabilities? Can we replace the instantaneous magnitudes with something well defined, but which is not instantaneous?

Please do not consider that I am too exigent with your ideas. I considered the two terms important, because your statement “it seems that Nature has wisely traded certainty for continuity” seems to contain the main implication of your ideas to the physical reality. This is why I asked you to define them.

If you don’t define the concepts you use, nobody can contradict you.

Warm regards,

Cristi




Peter Lynds wrote on Jan. 13, 2009 @ 08:53 GMT
Dear Cristi,

Thanks. While I'm happy to answer your questions, I do think that the answers to some of them should already be evident from reading my essay and this thread.

"According to your theory, is time continuous?"

According to my theory, time doesn't exist. Continuous motion does.

"Is "continuous motion" described by a continuous function f : Time - > Space, where Time and Space are topological spaces?"

Yes, that's one way of looking at it. In relation to gr, however, this is conditional on one recognizing that a point on the manifold (an "event") is non-instantaneous, as the t, x, y and z coordinates cannot be either.

"You say: "The non-existence of instantaneous magnitudes means that, even without quantum uncertainty, they wouldn't be exactly determined." I understand that you infer "uncertainty" from non-existence."

I prefer the word "indeterminacy", which, yes, I infer from the non-existence of instantaneous magnitudes, and as such, the existence of continuity and change.

"But what is "certainty", according to you?"

In this context, an exactly determined (objectively) or instantaneous magnitude.

"By saying that the physical quantities do not exist, without defining or postulating something else that looks like those quantities but satisfy also your own exigencies, you cut any chance for making Physics."

I'm saying that instantaneous quantities don't exist, not that physical quantities in general do not exist or that they cannot be determined by measurement.

"Can we replace the instantaneous magnitudes with something well defined, but which is not instantaneous?"

No, I don't think so, but again, I'm not saying that instantaneous values are not valuable in physics. The point is that they are non-physical, so must be careful about what infers about them. Zeno's paradoxes, the problem of motion and change not being seen to be compatible with gr, the idea of time and space being quantized, and even, it can be argued, the assumption of the existence of time, space, and space-time, can all be shown to result from assuming that instants (and spatial points) and instantaneous magnitudes actually exist.

In relation to finding fault with my work, its possible validity is completely reducible to and hinges upon the simple question of whether a body in relative motion has a determined or instantaneous relative position. If someone wants to negate my conclusions, I think this is where to try to chop.

Best wishes

Peter




Cristi Stoica wrote on Jan. 13, 2009 @ 20:18 GMT
Dear Peter,

1. How is it possible that continuous motion exists and is described by “a continuous function f : Time - > Space, where Time and Space are topological spaces”, but in the same time, Time does not exist? Isn’t this a contradiction?

2. You said: “If a moving object could be said to have a determined position relative to something else at an instant, as is the very nature of this ethereal notion – a static “snap-shot” of a physical process – the object would necessarily be frozen still at that instant and could not be in motion at all.”

Does the “frozenness” really follow logically from the assumption of a determined position at an instant? If so, why did you need to postulate your main claim: “We begin by considering the simple and innocuous postulate: “there is not a precise static instant in time underlying a dynamical physical process.””?

What is the reference frame in which the object would be frozen? What is frozen in one reference frame, in another appears to move.

3. You say: “I'm saying that instantaneous quantities don't exist, not that physical quantities in general do not exist or that they cannot be determined by measurement.”. What is the difference between “physical quantities” and “instantaneous quantities”? I cannot think at a physical quantity which is not instantaneous. Even the physical constants arise as instantaneous quantities which don’t change in time.

Best regards,

Cristi




Peter Lynds wrote on Jan. 14, 2009 @ 11:21 GMT
Dear Cristi,

Thanks. To answer your first question, again, as far as Nature is concerned, I don't think that topological spaces, the manifold's points, "instantaneous" events etc, exist either.

"Does the "frozenness" really follow logically from the assumption of a determined position at an instant?"

Through the derivation of the rest of physics through motion (changing relative position), it can be seen to, and I think this is the most fundamental, but it can also be seen by considering the impossibility of math to represent something that is constantly changing (without freezing it), or by thinking about what the existence of instants and instantaneous magnitudes would actually entail and mean for Nature and continuity. Then we have problems and paradoxes such as Zeno's which directly result from assuming the existence of the instantaneous, while, intuitively, I think one can also just look around, and note that the idea of Nature being frozen/determined at an instant, or at an instantaneous "now", seems to be faulty, as Nature seems to be dynamic.

"What is the reference frame in which the object would be frozen? What is frozen in one reference frame, in another appears to move."

Any reference frame in which a moving body is assumed to have a determined relative position (this also naturally applies to the other reference frame you mentioned). Of course, this statement is contradictory, as, if it is assumed to have a determined relative position, the body could not actually be in relative motion.

"What is the difference between "physical quantities" and "instantaneous quantities"? I cannot think at a physical quantity which is not instantaneous.”

All empirically based values actually represent intervals, not instantaneous ones. For example, a distance value of 1m, represents the distance interval of 1 and 1.9999...m, and not an instantaneous value. Moreover, and taking motion as an example, one can naturally (potentially) measure the position of a moving body up to the limits of possible measurement as defined by the uncertainty principle. In relation to position, we can then say the body is somewhere within some time and space interval (as represented by a clock and meter). A similar thing can naturally be said for all physical magnitudes, such as momenta, energy etc.

"Even the physical constants arise as instantaneous quantities which don't change in time."

That's not the case, as the existence of constants such as the speed of light is completely indifferent to the instantaneous. That is, while constants are unchanging, this has nothing to do with instants/the instantaneous.

Best wishes

Peter




Cristi Stoica wrote on Jan. 16, 2009 @ 06:14 GMT
Dear Peter,

Thank you for your time.

You say: “I don't think that topological spaces, the manifold's points, "instantaneous" events etc, exist either.”

This contradicts the usual notion of continuity, which is based on topological spaces. You accept continuity: “time doesn't exist. Continuous motion does.”. In order to use another type of continuity, which is not based on topological spaces, you have to define it. When I asked you to define this notion of, let’s say, “continuity without continuum”, you said:

“In relation to continuity, just the regular meaning .i.e. continuous, the capability for motion and change etc.”

Here is a contradiction: the regular meaning of continuity is based on topological spaces, whose existence you deny.

You start from an undefined notion of continuity, and then infer from it the “indeterminacy”, non-existence of “instantaneous”, and non-existence of “instantaneous quantities”. You can’t infer from something which is not defined.

Good luck,

Cristi




Peter Lynds wrote on Jan. 16, 2009 @ 09:34 GMT
Dear Cristi,

Thanks. I don't think there is anything undefined about my use of the word continuity (the regular meaning), as the definition in my essay, to you just above, and a dictionary would attest! Moreover, if correctly interpreted, I very much do think that continuous motion is described by gr. This is actually the main thing that places our views at odds, as your interpretation of gr and the block universe explicitly denies that motion and continuity is possible! Lastly, my work starts from considering the nature of instants, limits, relative position etc.

Best wishes

Peter




Cristi Stoica wrote on Jan. 16, 2009 @ 10:53 GMT
Dear Peter,

Thank you for answering. You say:

“I don't think there is anything undefined about my use of the word continuity (the regular meaning), as the definition in my essay, to you just above, and a dictionary would attest! “

If you are right, then everything will be clear if you will just:

1. Provide your formal definition of continuity of motion which is compatible with the nonexistence of time, space and spacetime as topological spaces.

2. Provide your formal proof, based on formal definitions and logic, that continuous motion forbids the existence of instants and instantaneous positions.

If you have it, you can write or paste it below. If you don’t have it, you can just say that you don’t have it. It is simple.

Best regards,

Cristi




Peter Lynds wrote on Jan. 17, 2009 @ 01:36 GMT
Dear Cristi,

I can only assume that you've decided that the contents of my essay don't count for your 1 and 2 because of my use of the word continuity (despite it having nothing to do with my arguments).

In relation to perhaps providing a mathematical model, if you have read my essay or some of the comments above, you will already know that I don't think such a model exists, as using calculus itself to try to show why calculus has its limits when applied to the physical universe would be impossible. As such, I don't think that this can really be used as a criticism of the work.

Best wishes



Peter




Cristi Stoica wrote on Jan. 17, 2009 @ 07:28 GMT
Dear Peter,

Thank you for answering.

Since from “continuous motion” you conclude the “nonexistence of time and positions”, “continuity” has everything to do with your theory.

1. Can you write below a definition of continuity, even a “non-mathematical” one?

2. Can you then write how you infer from “continuous motion” the nonexistence of “instantaneous”?

Even if you wish to start your proof from another place than continuity, you will need to provide clear definitions of the terms, and then to express your arguments in a logical form, based on these terms.

Best wishes,

Cristi




Eckard Blumschein wrote on Jan. 20, 2009 @ 17:28 GMT
Dear Cristi Stoica,

Because Peter did not reply yet, I will try and answer your questions. Hopefully someone will answer my question to Brian concerning Ritz if he needs too long for a reply.

1. Peirce followed Leibniz when he called a continuum something every part of which has parts.

2. Already Aristoteles (384-322) followed Anaxagoras (500-426) in that the continuum is endlessly divisible as later described by Peirce. Aristoteles was aware of the contradiction between rest and beginning motion at the starting point of motion.

Anaxagoras was just ten years elder than Zeno (490-430) who lived in Italy.

Zeno was strictly speaking correct when he said: "The true being evades reception by measurement."

Exhaustion by Eudoxos (408-355) is a method that just provides an approximation as good as you like.

Pythagoreans called irrational numbers alogos.

Best,

Eckard




Cristi Stoica wrote on Jan. 20, 2009 @ 20:21 GMT
Dear Dr.-Ing. Blumschein,

Thank you for the explanations. You provide interesting historical information. You refer to alternative definitions of continuity, much older than topology. Yet, I do not see how they apply to our problem.

You say: “Aristoteles was aware of the contradiction between rest and beginning motion at the starting point of motion.”

This contradiction is solved by topology. Let’s assume that the position x(t) is constant = c before t=0, then x increases continuously. x^{-1}(c) is a closed set: the instants of rest time form a closed set, and the instants for motion form an open one. At t=0, the position is still c. If we want to know whether at t=0 the object is moving, we need calculus: we can calculate the first derivative (which at t=0 is 0, when it is defined).

Some may be disturbed by the asymmetry between open sets and closed sets, but this is the key feature of topology. Anyway, the contradiction seems to be due to the definition of continuity employed by Aristoteles, but the topological definition of continuity solves it. Fortunately, we advanced a bit since the great Greek philosophers.

Best regards,

Cristi




Eckard Blumschein wrote on Jan. 21, 2009 @ 16:07 GMT
Dear Cristi,

Don't EPR illustrate that the brutal "solution" by Dedekind and Cantor a is an ambitious mathematical twist but not really justified? The reason for me to deal with the matter was my question to mathematicians how to deal with the very nil when separating IR into IR+ and IR-? I got so many arbitrary suggestions as there are possibilities.

So I looked for and found myself solution that I consider free of arbitrariness:

Continuum and discrete points are two mutually excluding and complementing worlds inside a broader understood mathematics. Something that is fully continuous cannot at the same time be fully discrete. Accordingly it is impossible to have a complete list of all numbers which would correspond to all points of any piece of a line. Sets of points merely approximate continua because infinity is no quantum but the property to have no end at all.

I do not deny that the fictitious entity of all numbers with a also fictitious infinite resolution can be thought to constitute a continuum. I prefer to avoid the notion real numbers because the property to not allow a full numerical representation demands that "embedded" rational numbers have to have lost their numerical approachability. On could say it somewhat smugly: (Un)real numbers must be solutions to a not immediately resolvable, with numbers of finite accuracy, problem.

Mathematicians will immediately object: Every number is absolutely accurate. I disagree: The difference between two non-(un)real numbers must be tangible. Any given number including zero is not tangible if considered as a unreal number. Therefore stupid people could call zero non-existent at all. Anyway, it makes no sense to deal with a singular zero between IR+ and IR-, and for (un)real numbers there is no reason to distinguish between open and closed intervals.

I even consider it reasonable to make no exception for x=0 in |sign(x)|=1 except for rational numbers.

Topology pretends to deal with uncountable numbers too. Actually it merely deals with the countable rationals. I see the definition of reals a self-deceptive maneuver. While in numerical practice, there is anyway no room for (un)reals, I consider the subtle distinction a must for correct physical interpretation. Additionally I found cases where mathematics itself, in particular integral tables, suffers from intentional subordination of continuum under the realm of numbers.

Is the fundamental crisis of mathematics really settled?

I refer to Weyl and argue: Confusion in physics has proven the putative solution not fertile but futile.

Do not belittle the ancient mathematicians as philosophers. Do not belittle Galilei who reasoned: For infinite quantities, >, = , and < are not valid. Do not tell me the gospel of set theory. Meanwhile I delved into this shallow water.

I apologize for hurting feelings.

Eckard Blumschein




Cristi Stoica wrote on Jan. 21, 2009 @ 21:30 GMT
Dear Dr.-Ing. Blumschein,

Your posts are interesting and obviously they reflect long years of thinking at the very foundations of Mathematics, perhaps with the purpose of attacking them. I welcome the periodical shaking of the fundamentals. Although I disagree with your arguments, I have reserves of engaging myself in this “battle”, because I think that your points represent rather a philosophical preference, and I see neither reason, nor possibility, to contradict someone’s personal preference. Although I don’t share your viewpoint, I can read your ideas and find them interesting.

This discussion started when you offered to answer my questions instead of Peter. Maybe I don’t understand your point. Do you want instead to prove something about the validity of Math? What kind of reaction do you expect from me? Please do not consider the answers obvious, for me they are not.

To paraphrase you:

Do not belittle Galilei who reasoned: “The great book of nature is written in mathematical symbols.”.

Best wishes,

Cristi




Eckard Blumschein wrote on Jan. 21, 2009 @ 23:28 GMT
Dear Cristi,

Thank you for your readiness to respect my suggestions. I consider myself a bit slowly in revealing and understanding some notorious flaws of signal processing by means of complex calculus based on time between minus infinity and plus infinity. I am arguing that spectral analysis of recorded data does not need future time. Is this a philosophical preference or just a successful attempt to get rid of arbitrary redundancy?

Of course I got angry when my flawless alternative approach was rejected for "mathematical reasons". I found some of my arguments against naive set theory already uttered in literature, others arose from own reasoning. My final conviction that modern mathematics needs fundamental correction is the result of a rather comprehensive study of original work. This was easy to me because I am a German, I have a lot experience in revealing misconceptions in religious or political agitation as well as in scientific papers. The ignored mathematical symbol is ||. What I found were understandable intentions, naive ideas, flawed evidence, and the brutally enforced attempt to substitute lacking basics by arbitrarily chosen axioms. I reiterate: Dedekind still admitted to have no basic evidence. Cantor misinterpreted his DA2. Fraenkel confessed that Cantor's definition of a set is untenable and cannot be corrected.

Hilbert called his axiomatic method something that allows to maintain the formerly naive belief in certain relationships.

After more than one hundred years, we also may judge the result: While aleph_0 and aleph_1 roughly correspond to the reasonable notions infinite and uncountable, already aleph_2 is obviously futile. The whole tempest with CH and AC was in vain. Even Ebbinghaus let Lessing denote Cantor's theory an obvious error. Fraenkel warned of a possible breakdown of mathematics into a huge heap or rubble without set theory.

Actually, mathematics does not need what is claimed to be its fundamentals.

I do not expect those who have to fear loosing their job to swim against the "piper" Hilbert and his space. However, a back to understandable basics might resolve some notorious enigma of physics. Again: Why did v. Neumann no longer believe in Hilbert space?

You asked for a definition of continuity. The good old genuine one is definitely the original and basic one. Hausdorff dealt with the surroundings of points. There is no distance between the fictitious points of a genuine continuum. Example 0.999... = 1.000... = (1.000... - 0.999...). In this sense, Peter is correct: There is no separable incident exactly at 1.000... . For those who are thinking in terms of probability: The likelihood for x exactly equating 1.000... is zero.

Best wishes,

Eckard




Cristi Stoica wrote on Jan. 22, 2009 @ 08:54 GMT
Dear Dr.-Ing Blumschein,

You say: “I am arguing that spectral analysis of recorded data does not need future time. Is this a philosophical preference or just a successful attempt to get rid of arbitrary redundancy?”

I never said something about this subject.

“Again: Why did v. Neumann no longer believe in Hilbert space?”

My guess is that von Neumann did not question the Hilbert space as a mathematical structure, but the way it is used in Quantum Mechanics. I propose a smooth approach to QM, and I advocate the use of a rigged Hilbert space, maybe for similar reasons.

“Do not tell me the gospel of set theory.”

Is this what I am doing? These three points make me believe that you are not talking with me, but with a projection. I have the feeling that you expect me to play the role of the establishment in your fight against the very foundations of Mathematics. Why do you think I deserve this honor?

---

To make our discussion easier to follow by myself, I propose a sequential approach. The first step would be to ask you kindly to write below your final answer to the question that started our discussion: “2. Can you then how you infer from continuous motion the nonexistence of instantaneous?”, if you have it. Assuming that you succeed in demolishing the basics of Mathematics, this will not prove Peter’s viewpoint.

After we resolve the first step in one way or another, if you want to discuss a specific problem of Math’s foundations, you can address it. If I can answer, I will be willing to provide my viewpoint. Shaking the foundations can lead to interesting discoveries. But my request is to advance in a step by step manner. Otherwise, I will not be able to follow you.

Warm regards,

Cristi




Eckard Blumschein wrote on Jan. 23, 2009 @ 16:28 GMT
Dear Cristi Stioca,

Yes, I do not feel bound to what the mainstream considers the very foundations of mathematics if there are serious reasons to doubt in their correctness. You are perhaps correct in that v. Neumann did not doubt in HS as a mathematical structure but in the HS as appropriate basis for physics. What about RHS, I just looked into http://philsci-archive.pitt.edu/archive/00000814/00/QSA2001.
pdf

and did not get the impression that it will resolve the problem. Already choices of riggings are problem dependent. If I am correct, then reality does not overlap with future, and an unlimited positive elapsed time would be sufficient in principle for a single unrelated function of time.

Now to your question 2: "Can you infer from continuous motion the non-existence of instantaneous?"

I have to clarify that I prefer the notion of a continuum as something every part of which has parts. Accordingly, a continuous motion is not a stepwise one but a smoothly gliding one.

Aristoteles argued that rest and simultaneously beginning motion at the same first instant contradict to each other.

The notion existence might be inappropriate because there is no trichotomy with continuous gliding. In principle, it is impossible to take a snapshot without non-vanishing duration. When I made records of physical quantities I was happy with sample width as small as a few picoseconds. I do not consider band-limitation a technical problem but a question of appropriate mathematics. Do we really need each single natural number? There are certainly huge natural numbers that are extremely unlikely to be used ever. Likewise, virtually nobody needs rational numbers with huge denominator. So they exist as a mathematical potentiality without any physical relevance. If we try and formalize the very moment, it gets as nonsensical as Buridan's donkey, Schroedinger's cat, Wigner's friend, and G. Cantor's transfinite numbers.

Uncertainty affects for instance the pairs elapsed time/frequency and position/momentum. The products of these quantities is equal to one or to a constant, respectively.

If time goes to zero, frequency goes to infinity and vice versa. Frequency and momentum have to be expressed as quanta, i.e. as natural numbers. This is obvious for instance for transversal em waves. Transversal waves of too large wavelength do not fit in a waveguide. A time-frequency representation becomes questionable for short time-spans that correspond to split frequencies, cf.

http://home.arcor.de/eckard.blumschein.M284.html and M285

I do not intend shaking genuine fundamentals. However, I picked up hints which indicate that some putative fundamentals might be elusive.

Best regards,

Eckard




Dr. E (The Real McCoy) wrote on Mar. 7, 2009 @ 16:34 GMT
Hello Peter,

Hope all is well down under in Australia!

“In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.” –Galileo Galilei

I think it's cool how MDT solves all the philosophical problems you perceive (misperceive in some cases) with a simple *physical* model, postulate, and equation: The fourth dimension is...

view entire post


attachments: j.a._wheeler_recommendation_mcgucken_medium2.jpg, MDT_EINSTEINS_RELATIVTY_SCHRODENGERS_CHARACTERISTIC_TRAIT.pdf




pierre sabatier wrote on Mar. 8, 2009 @ 16:47 GMT
Dear Peter,

I think I agree almost entirely with what you wrote in your paper “Time for a change”. I came to the same conclusions regarding the inexistence of time and space in observer-independent reality – but by a different path.

Just some comments about your paper.

“The paradoxes of Achilles and the Tortoise and the Dichotomy, on the other hand, have generally been...

view entire post





Peter Lynds wrote on Mar. 14, 2009 @ 11:34 GMT
Dear Pierre,

Thanks for your very sharp thoughts. I appreciated them. Naturally enough, I agree with everything you said too. In relation to your point about instants and the flow of time, I agree too. I was trying to show how, given the discontinuous nature of instants, the idea of time flowing and progressing by way of them (the only way it potentially could do), is entirely contradictory. For if you might like to have a look, section 4 in my essay notes goes into this a little further. http://www.peterlynds.net.nz/fqxiessaynotes.pdf

Dear Dr E,

I have to agree with you about it not being correct that Einstein seems to often have been careful to note that space-time does not have exitance in itself. Not because I don't think it is evident that he believed this – at least later in his life - but because I think I was too generous to him in this respest and that he could have maybe done a bit more.

Of course, it is also evident that he didn't think that time, space, or indeed, instants, existed either. As with his initial reluctance to fully embrace general covariance, "by which time and space are robbed of the last trace of objective reality", unsurprisingly, it just seems that his views on things time, space and space-time sometimes changed developed with time.

Dear Cristi,

C x Mi = E(ssay)2

Best wishes

Peter




Giannis wrote on Mar. 25, 2009 @ 15:12 GMT
Dear Peter,

I thought it would be interesting to give a connection of your two papers, i.e. how one can conclude from the first paper to the second.

Giannis




Peter Lynds wrote on Mar. 29, 2009 @ 13:10 GMT
Dear Giannis,

The only real connection between the two papers I can think of is that my cosmology theory/model is consistent with a timeless, block view of the universe. If all events, past, present and future, are all mapped out together, and there is no present moment gradually "unfolding", there is no issue with Nature seemingly being able to anticipate (what we would regularly term) future or past events (i.e. so that the order of events that Nature employed would always be an order in which entropy increased), as all events in the universe, so-called future and past, are already just "there" and given. They don't happen all at once, as motion and continuity (including the continuous workings of a clock) is indifferent to the past, present, future, time etc. They are things that we ascribe to Nature, rather than the other way around.

There is naturally a strong connection between my 2003 time paper and my paper about the present and consciousness.

Best wishes

Peter




Avalons Child wrote on Apr. 24, 2009 @ 23:30 GMT
simultaneous synchronicity




Susan Quist wrote on Jul. 18, 2009 @ 05:08 GMT
TIMEPIECE

The day before yesterday,

yesterday was the future.

Today yesterday is history.

Yesterday the day before yesterday

was history and today was the future.

Today tomorrow is the future. Today

will be history tomorrow and

the day after tomorrow, tomorrow

will be history and so on.

We are making history all the time.

The future comes and goes.

The future is over --

over and over.

But you can't prove it. No one can

prove the future exists

until it's here -- and then it's gone,

but who knows where? And where

does that leave us? In the present?

Take a moment to think about that.

We live in the present, we live in

the moment – moment to moment.

We live in the moment that soon

will be history. Sooner than you

think. This moment will be history in

the time it takes to cross your mind.

The present is gone in no time at all.

There is no time like the present.

But that’s all the time we've got.

Whatever it is. The present --

the gift.

© Susan Quist 2009

Dear Peter –

Kurt Vonnegut liked my poetry. I hope you will too. I love your work, thanks -- and your outsiderness. I found you through Google – you can Google me too.

Best wishes –

Susan Quist




Giannis wrote on Jul. 24, 2009 @ 09:44 GMT
Dear Peter,

I had this thought and I wanted to share it,

It can be proven that an object cannot disappear and appear suddenly in a different position, such as the effect of a "magician". This would mean that in a time instant the object would be in a precise position and then appear in another precise position of a given time instant. This cannot be done according to your theory.

I had this thought when I was watching magic tricks and I thought that if I was born yesterday without experiences and only with logic I could prove that this is just a trick and not something that really happens.

Sincerely,

Giannis




Tom wrote on Aug. 30, 2009 @ 14:43 GMT
Hi Peter, I'm late to the game (just found out about FQXI), am just now reading

the essays, and so far, I find yours comes closest to what I believe is essential about understanding the nature of time. In an hourglass analogy, reality truly does appear to manifest in this rarefied instant we call the present - the 'aperture' of the hourglass - that 'place' where the omni-present sands of past and future are seemingly processed. The paradoxes we find, when trying to grasp instantaneous quantities in the present, appear because time is the defining example of a true continuum: unlike the sands of an hourglass, between any two instants, another actually does exist, ad infinitum. Should you find the time,

my thoughts can be found at singularityshuttle.com.




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