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**Odessa Sabah**: *on* 1/5/17 at 13:19pm UTC, wrote Pretty remarkable post. I simply came across your blog and desired to say...

**Joe Fisher**: *on* 4/6/15 at 15:00pm UTC, wrote Dear Ken, I think Newton was wrong about abstract gravity; Einstein was...

**Janko Kokosar**: *on* 4/5/15 at 13:04pm UTC, wrote Dear Ken, AS I understand, your (B(n),iB(n)) really means 45° on the...

**Ken Matusow**: *on* 4/4/15 at 14:39pm UTC, wrote Janko, I'm not sure I understand your question. The order paired...

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**Armin Nikkhah Shirazi**: *on* 3/25/15 at 7:43am UTC, wrote Dear Ken, A few comments: "All metric spaces, are by definition,...

**Ken Matusow**: *on* 3/23/15 at 8:21am UTC, wrote Adel, Thanks for you comments. It turns out there are number of essays...

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October 22, 2019

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[back]

TOPIC: A Systems Theoretic Approach to Physics by Ken Matusow [refresh]

TOPIC: A Systems Theoretic Approach to Physics by Ken Matusow [refresh]

It can be argued that the Holy Grail of physics is to develop a model of physical processes based on first principles. That is, a simple set of rules, or axioms, is presented from which a complete description of physics is unavoidably emergent. It is in the spirit of this quest that an axiomatic system is presented in this paper. The paper will derive from first principles three specific equations/relations that map to physics; analogs of the Lorentz transform, the uncertainty principle, and the Einstein field equations. It is argued that the common threads that exist between the theorems of the abstract general system and the equations, relations, and constants that define most of modern physics provide a strong foundation upon which to explore the deeper relationship between mathematics and physics.

Ken Matusow has an MS in General Systems Theory from the State University of New York at Binghamton. In addition to his unaffiliated research in foundational physics and systems theory Ken is a Silicon Valley entrepreneur and writer.

Dear Ken Matusow,

You have stated that the symbols in your equation are general, but “a semantic interpretation of each of these symbols maps very closely, if not exactly, to the meanings of these systems as used in traditional physics”. The symbols in the equations of 'traditional physics' are similar to that of your equations, the only difference is that these are meant to represent the physical variables. As these symbols map to the empirical behaviors, their general nature is just ignored.

The actual problem is not with the equations, but with the interpretation of the symbols. A symbol can have multiple interpretations, and all of these interpretations will be valid for the given equation. Selecting the appropriate one is the problem. QM and GR become incompatible because their proponents cling on to their favorite interpretations regarding the symbols. These interpretations are not only incompatible, but also have no physical meanings.

Assuming that your mathematics is correct and believing that you have not gone wrong anywhere in the derivations, your claim,“A mathematical bridge has been developed …. between quantum mechanics and general relativity” should be correct, provided by QM and GR you mean just the equations.

report post as inappropriate

You have stated that the symbols in your equation are general, but “a semantic interpretation of each of these symbols maps very closely, if not exactly, to the meanings of these systems as used in traditional physics”. The symbols in the equations of 'traditional physics' are similar to that of your equations, the only difference is that these are meant to represent the physical variables. As these symbols map to the empirical behaviors, their general nature is just ignored.

The actual problem is not with the equations, but with the interpretation of the symbols. A symbol can have multiple interpretations, and all of these interpretations will be valid for the given equation. Selecting the appropriate one is the problem. QM and GR become incompatible because their proponents cling on to their favorite interpretations regarding the symbols. These interpretations are not only incompatible, but also have no physical meanings.

Assuming that your mathematics is correct and believing that you have not gone wrong anywhere in the derivations, your claim,“A mathematical bridge has been developed …. between quantum mechanics and general relativity” should be correct, provided by QM and GR you mean just the equations.

report post as inappropriate

Jose,

Your interpretation is accurate. I am not claiming that the mathematics in the article describe physics, merely that they are correct within the general system. If the mathematics is shown to be accurate (which must still be established), then others can argue whether or not the general system can be applied to physical systems. I am trying to argue that a formal system, in general, could be applied to the study of physics. The point of the article is to explore the relationship between a formal (mathematical) system and physics.

Ken

Your interpretation is accurate. I am not claiming that the mathematics in the article describe physics, merely that they are correct within the general system. If the mathematics is shown to be accurate (which must still be established), then others can argue whether or not the general system can be applied to physical systems. I am trying to argue that a formal system, in general, could be applied to the study of physics. The point of the article is to explore the relationship between a formal (mathematical) system and physics.

Ken

Dear Ken Matusow,

Your essay is well written, and you make some pretty big claims. Obviously these cannot all be "proved" in nine pages. One of the nice features of FQXi is that it's perfectly legitimate to use comments on your thread to expand upon your arguments and the details of your essay, and I suggest that you might wish to do so here.

I also agree with the essence of Jose Koshy's remarks above.

Your key point seems to be that the distance of any point in the system must be an integer multiple of your dimensionless constant c. This seems to imply a lattice, with walks propagating only outward from the origin. Is it truly a random walk if steps are taken in only one direction? If you can walk 'backwards' this would seem to conflict with the requirement that the distance from the origin is proportional to the number of steps taken, given a constant of proportionality. Am I missing something?

If it is the case that the system walks in only one direction (after the first step is taken) then need it be discrete? The discreteness is then equivalent to picking integer points on an outgoing ray with constant velocity. Perhaps I'm confused by how you got from the origin to the point (0, 2) by going out the x-axis then stepping in the y-direction. Is one confined to a ray or can you walk in two dimensions? Since most of your paper deals with implications of this basic system, you might wish to expand on the most basic details of the system here.

Best regards,

Edwin Eugene Klingman

report post as inappropriate

Your essay is well written, and you make some pretty big claims. Obviously these cannot all be "proved" in nine pages. One of the nice features of FQXi is that it's perfectly legitimate to use comments on your thread to expand upon your arguments and the details of your essay, and I suggest that you might wish to do so here.

I also agree with the essence of Jose Koshy's remarks above.

Your key point seems to be that the distance of any point in the system must be an integer multiple of your dimensionless constant c. This seems to imply a lattice, with walks propagating only outward from the origin. Is it truly a random walk if steps are taken in only one direction? If you can walk 'backwards' this would seem to conflict with the requirement that the distance from the origin is proportional to the number of steps taken, given a constant of proportionality. Am I missing something?

If it is the case that the system walks in only one direction (after the first step is taken) then need it be discrete? The discreteness is then equivalent to picking integer points on an outgoing ray with constant velocity. Perhaps I'm confused by how you got from the origin to the point (0, 2) by going out the x-axis then stepping in the y-direction. Is one confined to a ray or can you walk in two dimensions? Since most of your paper deals with implications of this basic system, you might wish to expand on the most basic details of the system here.

Best regards,

Edwin Eugene Klingman

report post as inappropriate

Ed,

Good points all. You bring up what is perhaps the core idea of the paper, that the axioms force the coordinate system to expand from the reals to the complex numbers (one dimensional to two dimensional).

First, the system is axiomatic, meaning by definition is stochastic and priori cannot be deterministic. (This in itself could disqualify the system as a viable model for physics, but this is another discussion). A random walk is a Markov process which has the property of being memoryless. That is, the next state of the system is dependent on the current state and not any other previous states. A random walk is a Markov process with an attached metric. If the system is currently in state k, then after the next state transition the system must be either in state k-1 or k+1. This is in fact the case in the system described in the paper. What is called the 'imaginary state' is more or less a bookkeeping mechanism. Admittedly, it is an odd example of a random walk, but it still qualifies as a random walk. If the state of the system is a real number, then your supposition that the next state cannot be k-1 (going backwards) is indeed correct. The question is that can a system be cobbled together that is both Markovian (state can go backwards) and still satisfy the metric axiom (distance to the n-th event is proportional to n. The answer is no if the system is constrained to the real numbers. But the answer is yes if a new degree of freedom is extended. The system can be both stochastic and the distance is proportional to n, IF AND ONLY IF, the domain of the system is extended the reals to the complex plane. This is perhaps the central idea of the paper.

Ken

Good points all. You bring up what is perhaps the core idea of the paper, that the axioms force the coordinate system to expand from the reals to the complex numbers (one dimensional to two dimensional).

First, the system is axiomatic, meaning by definition is stochastic and priori cannot be deterministic. (This in itself could disqualify the system as a viable model for physics, but this is another discussion). A random walk is a Markov process which has the property of being memoryless. That is, the next state of the system is dependent on the current state and not any other previous states. A random walk is a Markov process with an attached metric. If the system is currently in state k, then after the next state transition the system must be either in state k-1 or k+1. This is in fact the case in the system described in the paper. What is called the 'imaginary state' is more or less a bookkeeping mechanism. Admittedly, it is an odd example of a random walk, but it still qualifies as a random walk. If the state of the system is a real number, then your supposition that the next state cannot be k-1 (going backwards) is indeed correct. The question is that can a system be cobbled together that is both Markovian (state can go backwards) and still satisfy the metric axiom (distance to the n-th event is proportional to n. The answer is no if the system is constrained to the real numbers. But the answer is yes if a new degree of freedom is extended. The system can be both stochastic and the distance is proportional to n, IF AND ONLY IF, the domain of the system is extended the reals to the complex plane. This is perhaps the central idea of the paper.

Ken

Dear Ken,

I find your axiomatic approach interesting (it reminded me a bit of the approach presented in Richard Shoup's paper).

I did not follow your entire derivation but there are two issues I would like to point out in the spirit of constructive criticism. First, it seems that you would like to derive the introduction of additional coordinate degrees from your original axioms,...

view entire post

I find your axiomatic approach interesting (it reminded me a bit of the approach presented in Richard Shoup's paper).

I did not follow your entire derivation but there are two issues I would like to point out in the spirit of constructive criticism. First, it seems that you would like to derive the introduction of additional coordinate degrees from your original axioms,...

view entire post

report post as inappropriate

Armin,

Thanks so much for your constructive criticism. You bring up a raft of issues, all of which need to be explored in more detail. First of all, you appear correct in that there are similarities between my paper and the one submitted by Richard Shoup. Thanks for the pointer.

Your primary issue lies in the ability to resolve an apparent inconsistency by simply creating an...

view entire post

Thanks so much for your constructive criticism. You bring up a raft of issues, all of which need to be explored in more detail. First of all, you appear correct in that there are similarities between my paper and the one submitted by Richard Shoup. Thanks for the pointer.

Your primary issue lies in the ability to resolve an apparent inconsistency by simply creating an...

view entire post

Dear Ken,

Thank you for your nice answer (not everybody responds nicely to constructive criticism). Let me just comment on the following:

1. Regarding the expansion of coordinate degrees of freedom, my understanding is that if the real line is extended to the complex space, then this has to be accompanied by the definitions of operations involving complex numbers, and I don't know...

view entire post

Thank you for your nice answer (not everybody responds nicely to constructive criticism). Let me just comment on the following:

1. Regarding the expansion of coordinate degrees of freedom, my understanding is that if the real line is extended to the complex space, then this has to be accompanied by the definitions of operations involving complex numbers, and I don't know...

view entire post

report post as inappropriate

Armin,

Let me focus on issues 2,3, and 4.

You bring up an excellent point regarding assigning a probability to a point in a continuous system. The key issue revolves around the notion of discrete versus continuous. The underlying geometry is a Riemann manifold, an example of a metric space. General relativity describes the geometry of space-time as a Minkowski space, another...

view entire post

Let me focus on issues 2,3, and 4.

You bring up an excellent point regarding assigning a probability to a point in a continuous system. The key issue revolves around the notion of discrete versus continuous. The underlying geometry is a Riemann manifold, an example of a metric space. General relativity describes the geometry of space-time as a Minkowski space, another...

view entire post

report post as inappropriate

Dear Ken,

A few comments:

"All metric spaces, are by definition, continuous."

No, a space with a discrete metric is a counterexample. In fact, originally, I thought that that something like that was what you had in mind in your initial steps of building your theory.

"And on top of the reals let define a traditional random walk, where the metric (the distance measure) is described by stating the distance between any two states is a constant, in this case 1"

Yes, after you pointed out to me that the underlying space is continuous, I understood that this is what you meant, and my question 3 still stands: What is it that gets you to a particular step size and not some other in your random walk? If you don't provide any argument for that, then I have to take that to be another hidden assumption.

"However, this apparent contradiction can be resolved if a displacement in a new dimension is assumed. As an example think of a chord connecting to points on the surface of the earth. It is a provable statement that if the earth is not flat, then the length of the geodesic connecting the two point on the earth must be greater than and not equal to the length of the chord."

Ah, I think I am beginning to get a better idea of where the curvature is coming from. Apart from the same issue as before regarding to whether this amounts to a hidden assumption, I am not clear how it connects to the explanation of curvature in GR. Note that in GR, the curvature can manifests itself in modifications of both time and space coordinates (relative to those associated with a flat space), whereas your explanation (as best as I can tell) of curvature only gives potentially an explanation for modifications of spatial coordinates relative to those of flat space.

Again, hope you find my critique useful.

Best,

Armin

report post as inappropriate

A few comments:

"All metric spaces, are by definition, continuous."

No, a space with a discrete metric is a counterexample. In fact, originally, I thought that that something like that was what you had in mind in your initial steps of building your theory.

"And on top of the reals let define a traditional random walk, where the metric (the distance measure) is described by stating the distance between any two states is a constant, in this case 1"

Yes, after you pointed out to me that the underlying space is continuous, I understood that this is what you meant, and my question 3 still stands: What is it that gets you to a particular step size and not some other in your random walk? If you don't provide any argument for that, then I have to take that to be another hidden assumption.

"However, this apparent contradiction can be resolved if a displacement in a new dimension is assumed. As an example think of a chord connecting to points on the surface of the earth. It is a provable statement that if the earth is not flat, then the length of the geodesic connecting the two point on the earth must be greater than and not equal to the length of the chord."

Ah, I think I am beginning to get a better idea of where the curvature is coming from. Apart from the same issue as before regarding to whether this amounts to a hidden assumption, I am not clear how it connects to the explanation of curvature in GR. Note that in GR, the curvature can manifests itself in modifications of both time and space coordinates (relative to those associated with a flat space), whereas your explanation (as best as I can tell) of curvature only gives potentially an explanation for modifications of spatial coordinates relative to those of flat space.

Again, hope you find my critique useful.

Best,

Armin

report post as inappropriate

Dear Ken,

I think your system is very interesting and it SEEM to have some flavor similar to my system( and ironically to Armin's, but that is another story).

Now, I have not really delved into the details, but from some reading and the comments I can see that the main issue again surround discrete vs continuous. My system sheds a strong light on the subject, because I use both integer and the reals. However, the real number that I am using is based on a computer system and also I throw a UNIFORM random numbers. I get very nearly the same results, However, the simulation for spin seem to work for only integers. But we also know that quantum mechanics is based on the continuum and we get spin also, hence the strange connection.

I think we can discuss more once you have gotten maybe just a bit familiar with my system.

It is unfortunate that your idea and mine has not been discussed more because it seems that most of the essays have concentrated more on wordy philosophy which are easier reads.

Essay

Thanks and good luck.

report post as inappropriate

I think your system is very interesting and it SEEM to have some flavor similar to my system( and ironically to Armin's, but that is another story).

Now, I have not really delved into the details, but from some reading and the comments I can see that the main issue again surround discrete vs continuous. My system sheds a strong light on the subject, because I use both integer and the reals. However, the real number that I am using is based on a computer system and also I throw a UNIFORM random numbers. I get very nearly the same results, However, the simulation for spin seem to work for only integers. But we also know that quantum mechanics is based on the continuum and we get spin also, hence the strange connection.

I think we can discuss more once you have gotten maybe just a bit familiar with my system.

It is unfortunate that your idea and mine has not been discussed more because it seems that most of the essays have concentrated more on wordy philosophy which are easier reads.

Essay

Thanks and good luck.

report post as inappropriate

Adel,

Thanks for you comments. It turns out there are number of essays that roughly lay out a similar idea, namely that an abstract, axiomatic foundation of physics is indeed possible to formulate. As you note, the notion of discrete versus continuous is a common thread connecting your essay as well as mine. But I think an even deeper thread is the notion of deterministic versus stochastic. If I understand your essay correctly you have developed a probabilistic model where the state of the system is essentially the expectation value generated by your simulations.

The idea of a fundamentally stochastic/probabilistic model of physics is a radical concept, one that most physicists would reject out of hand (although I strongly adhere to a stochastic approach). I would be interested in your ideas regarding a non-deterministic model of physics. Although quantum mechanics operates on probabilities, the math itself is decidedly and unambiguously deterministic.

Ken

Thanks for you comments. It turns out there are number of essays that roughly lay out a similar idea, namely that an abstract, axiomatic foundation of physics is indeed possible to formulate. As you note, the notion of discrete versus continuous is a common thread connecting your essay as well as mine. But I think an even deeper thread is the notion of deterministic versus stochastic. If I understand your essay correctly you have developed a probabilistic model where the state of the system is essentially the expectation value generated by your simulations.

The idea of a fundamentally stochastic/probabilistic model of physics is a radical concept, one that most physicists would reject out of hand (although I strongly adhere to a stochastic approach). I would be interested in your ideas regarding a non-deterministic model of physics. Although quantum mechanics operates on probabilities, the math itself is decidedly and unambiguously deterministic.

Ken

Dear Ken Matusow

Your approach seem promising, at least for pedagogical visualization of quantum mechanics, for instance something as Bohr's model of an atom. But, alhough you wish to show, that your formulae are independent from real space and time, you can draw them with figures in real space. They can be easier to comprehend.

I do not understand some your expressions, for instance because this means always the same angle, 45° in complex space. Is this correctly written?

My essay

Best regards,

Janko Kokosar

report post as inappropriate

Your approach seem promising, at least for pedagogical visualization of quantum mechanics, for instance something as Bohr's model of an atom. But, alhough you wish to show, that your formulae are independent from real space and time, you can draw them with figures in real space. They can be easier to comprehend.

I do not understand some your expressions, for instance because this means always the same angle, 45° in complex space. Is this correctly written?

My essay

Best regards,

Janko Kokosar

report post as inappropriate

Janko,

I'm not sure I understand your question. The order paired (B(n),iB(n)) represent displacements in both the X and Y dimensions. The displacements represent an angle on the unit circle and may be explained as follows:

A priori we know the distance to the ordered pair from the origin must be n*c(bar). This distance is imposed directly by the metric axiom. From some of the early theorems developed we know that the distance in the X dimension is proportional to B(n). Given these two pieces of information we can now use the Pythagorian equation to compute the displacement in the Y dimension, namely:

d(y)=SQRT((n*c(bar))**2 + (B(n)*c(bar))**2)

Again, a priori, the order pair (B(n),iB(n)) is a point of a circle with a radius of n*c(bar) that has a displacement in the X dimension of c*B(n) and a displacement in the T-dimension of SQRT((n*c(bar))**2 + (B(n)*c(bar))**2). This displacement angle from the Y axis to the point (B(n),iB(n)), corresponds to a velocity since it represents a spatial displacement divided by a temporal displacement. In this scenario a value of 45° represents a velocity of exactly c/SQRT(2).

Admittedly, these ideas are quite difficult to get across with lots of diagrams and pictures, but I hope this helps.

Ken

I'm not sure I understand your question. The order paired (B(n),iB(n)) represent displacements in both the X and Y dimensions. The displacements represent an angle on the unit circle and may be explained as follows:

A priori we know the distance to the ordered pair from the origin must be n*c(bar). This distance is imposed directly by the metric axiom. From some of the early theorems developed we know that the distance in the X dimension is proportional to B(n). Given these two pieces of information we can now use the Pythagorian equation to compute the displacement in the Y dimension, namely:

d(y)=SQRT((n*c(bar))**2 + (B(n)*c(bar))**2)

Again, a priori, the order pair (B(n),iB(n)) is a point of a circle with a radius of n*c(bar) that has a displacement in the X dimension of c*B(n) and a displacement in the T-dimension of SQRT((n*c(bar))**2 + (B(n)*c(bar))**2). This displacement angle from the Y axis to the point (B(n),iB(n)), corresponds to a velocity since it represents a spatial displacement divided by a temporal displacement. In this scenario a value of 45° represents a velocity of exactly c/SQRT(2).

Admittedly, these ideas are quite difficult to get across with lots of diagrams and pictures, but I hope this helps.

Ken

Dear Ken,

AS I understand, your (B(n),iB(n)) really means 45° on the unit circle in (x,iy)? Thus, the first and the second B(n) are the same?

But, once you wrote above a formula for d(y) = ..., and another time you said ''displacement in the T-dimension of'' and you gave the same formula. So, d(y)=''displacement in the T-dimension of'' ??

I suggest that once in a future you draw your derivation, it will be easier to understand.

Regards

Janko Kokosar

report post as inappropriate

AS I understand, your (B(n),iB(n)) really means 45° on the unit circle in (x,iy)? Thus, the first and the second B(n) are the same?

But, once you wrote above a formula for d(y) = ..., and another time you said ''displacement in the T-dimension of'' and you gave the same formula. So, d(y)=''displacement in the T-dimension of'' ??

I suggest that once in a future you draw your derivation, it will be easier to understand.

Regards

Janko Kokosar

report post as inappropriate

Dear Ken,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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