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RECENT POSTS IN THIS TOPIC

**Milen Velev**: *on* 5/27/15 at 22:31pm UTC, wrote Dear Vesselin, I very much enjoyed your essay! You offer convincing...

**Peter Jackson**: *on* 4/22/15 at 20:02pm UTC, wrote Vesselin, Great essay. Tom flagged it up for me. It was on my list but...

**Alma Ionescu**: *on* 4/21/15 at 10:13am UTC, wrote Dear Vesselin, Thank you very much for explaining, now it makes perfect...

**Vesselin Petkov**: *on* 4/20/15 at 17:44pm UTC, wrote Thank you all for your comments. Due to some urgent issues in the last ten...

**Sujatha Jagannathan**: *on* 4/19/15 at 13:52pm UTC, wrote You are very much gelled with the concepts. Great. - Sincerely Miss....

**Alma Ionescu**: *on* 4/19/15 at 11:40am UTC, wrote Dear Vesselin, You make a compelling case as to how equivalent theories...

**Vladimir Rogozhin**: *on* 4/16/15 at 13:51pm UTC, wrote Dear Vesselin, I read with great interest your depth analytical essays in...

**Joe Fisher**: *on* 4/9/15 at 15:51pm UTC, wrote Dear Vesselin, I think Newton was wrong about abstract gravity; Einstein...

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FQXi FORUM

April 21, 2021

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: A mathematical formalism in physics is not "just a matter of description" by Vesselin Petkov [refresh]

TOPIC: A mathematical formalism in physics is not "just a matter of description" by Vesselin Petkov [refresh]

Can metatheoretical misconceptions be ultimately responsible for the lack of breakthroughs in fundamental physics in recent decades? The answer outlined in the essay is yes. First I discuss such a misconception - that mathematics in physics is merely a description and therefore even fundamental mathematical entities (such as a manifold) do not represent counterparts in the physical world. Then I examine an instance of this misconception - that the four-dimensional manifold in relativity is only “an abstract four-dimensional mathematical continuum” - and summarize Minkowski's arguments that this four-dimensional manifold does represent a real four-dimensional world (spacetime). Finally, I discuss several negative implications of this misconception for the advancement of fundamental physics, including one which makes it impossible even to identify a radical (but not inconceivable) reason for the unsuccessful attempts to create a theory of quantum gravity.

I am a physicist with some background in philosophy (for selected publications see spacetimecentre.org/vpetkov/).

I am traveling until the end of March and have very limitted access to the Internet. After I return I will be able to check any comments left here.

"this four-dimensional manifold does represent a real four-dimensional world (spacetime)."

Rather, a four-dimensional absurdity, a consequence of the false principle of constancy of the speed of light. Both the frequency and the speed of light (relative to the observer) VARY with the speed of the observer, as the following videos clearly show:

"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

"Doppler effect - when an observer moves away from a stationary source. ...the velocity of the wave relative to the observer is slower than that when it is still."

Pentcho Valev

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Rather, a four-dimensional absurdity, a consequence of the false principle of constancy of the speed of light. Both the frequency and the speed of light (relative to the observer) VARY with the speed of the observer, as the following videos clearly show:

"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

"Doppler effect - when an observer moves away from a stationary source. ...the velocity of the wave relative to the observer is slower than that when it is still."

Pentcho Valev

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Dear Vesselin Petkov,

Very interesting essay that was a pleasure to read.

Regarding the comment "As quantum objects are not worldlines in spacetime, it could have been examined whether they might be more complex structures in spacetime (for a conceivable example see [4, Chap. 10] and the references therein).", is it possible to post additional comments to elaborate on this or perhaps an online reference for those who do not have easy access to your references?

Thanks for the essay and good luck,

Ed Unverricht

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Very interesting essay that was a pleasure to read.

Regarding the comment "As quantum objects are not worldlines in spacetime, it could have been examined whether they might be more complex structures in spacetime (for a conceivable example see [4, Chap. 10] and the references therein).", is it possible to post additional comments to elaborate on this or perhaps an online reference for those who do not have easy access to your references?

Thanks for the essay and good luck,

Ed Unverricht

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Dear Ed,

Chapter 10 of my book “Relativity and the Nature of Spacetime” [2ed 2009] is available at:

spacetimecentre.org/vpetkov/docs/

If you have additional questions I will be glad to answer.

Best,

Vesselin

Chapter 10 of my book “Relativity and the Nature of Spacetime” [2ed 2009] is available at:

spacetimecentre.org/vpetkov/docs/

If you have additional questions I will be glad to answer.

Best,

Vesselin

Vesselin, you already know that I am a huge fan of you and the other distinguished members of the Minkowski Institute! I am never disappointed in your exposition and defense of the physically real Minkowski space.

I will make no further comment for now than that my own essay also deals with pairwise simultaneity. A productive dialog is sure to follow.

All best,

Tom

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I will make no further comment for now than that my own essay also deals with pairwise simultaneity. A productive dialog is sure to follow.

All best,

Tom

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Thanks, Tom. I have almost dealt with the most urgent issues that have accumulated during my absence and will soon start reading essays.

Best,

Vesselin

Best,

Vesselin

Vesselin,

Besides the essay itself, I hope you will read my defense of the physical reality of Minkowski space in a series of posts & attachments beginning 2 April. Thanks.

All best,

Tom

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Besides the essay itself, I hope you will read my defense of the physical reality of Minkowski space in a series of posts & attachments beginning 2 April. Thanks.

All best,

Tom

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Dear Vesselin Petkov

I agree with you that math in more than only physical model and I agree that gravitational force is not a force. (''no gravitational force'' means that no force is felt in homogenic gravitational field of differential volume.)

But, I think that theory of quantum gravity still ever exists. Maybe even so, that virtual graviton does not exist, I guess. (This is more conservative estimation than your conclusion.) Intuitively I think that spacetime is Machian on some way, this means that (1) we live like in virtual reality, like Carroll claims. (2) Machian principle means that spacetime does not exist without matter. At this it is unclear, how to combine Machian principle with ''that gravitational force does not exist''.

I claim that spacetime does not exist without matter, gravitational waves also not exist, thus this can be the main distinction between you and me.

Let us say, that we have a rocket on a photonic propulsion. Thus its acceleration is not a smooth curve, but changes happens in random steps. According to the principle of equivalence (elevator versus gravitational field) it is not necessary to demand that gravitational acceleration is uniform, but it can also be in steps. This can be called quantum principle of equivalence (QPE). What is your opinion how QPE can affect on properties of a spacetime.

What do you think about this?

My essay

Best Regards

Janko Kokosar

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I agree with you that math in more than only physical model and I agree that gravitational force is not a force. (''no gravitational force'' means that no force is felt in homogenic gravitational field of differential volume.)

But, I think that theory of quantum gravity still ever exists. Maybe even so, that virtual graviton does not exist, I guess. (This is more conservative estimation than your conclusion.) Intuitively I think that spacetime is Machian on some way, this means that (1) we live like in virtual reality, like Carroll claims. (2) Machian principle means that spacetime does not exist without matter. At this it is unclear, how to combine Machian principle with ''that gravitational force does not exist''.

I claim that spacetime does not exist without matter, gravitational waves also not exist, thus this can be the main distinction between you and me.

Let us say, that we have a rocket on a photonic propulsion. Thus its acceleration is not a smooth curve, but changes happens in random steps. According to the principle of equivalence (elevator versus gravitational field) it is not necessary to demand that gravitational acceleration is uniform, but it can also be in steps. This can be called quantum principle of equivalence (QPE). What is your opinion how QPE can affect on properties of a spacetime.

What do you think about this?

My essay

Best Regards

Janko Kokosar

report post as inappropriate

Dear Janko,

I am afraid I cannot answer what you ask since I share the views expressed by:

J.L. Synge in his excellent General relativity book: “The Principle of Equivalence performed the essential office of midwife at the birth of general relativity… I suggest that the midwife be now buried with appropriate honours and the facts of absolute space-time faced.”

Einstein himself, later in his life, changed his opinion of Mach's principle and wrote: “Actually, one should no longer speak of Mach's principle at all.”

And here is why I think Mach’s ideas contradict spacetime physics (properly understood in terms of Minkowski’s four-dimensional formulation of Einstein’s special relativity). Only two examples:

1. According to Mach, if there existed a single particle in the universe, one could not say anything about its motion (e.g., whether it is moving with constant velocity or is accelerating). That is true in Einstein’s original special relativity, but clearly wrong in its accepted Minkowski’s formulation: if there existed a single particle in the universe, its worldline would be either straight (which, in three-dimensional language, means that the particle is moving with constant velocity) or curved (representing accelerated motion).

2. According to Mach, one cannot distinguish between the Copernican and the Ptolemaic systems because, on Mach’s view, it is not clear what orbits what. This is plain wrong in spacetime physics because the worldlines (rather worldtubes) of the planets are helixes around the worldtube of the Sun (which, in three-dimensional language, means that it is the planet that orbit the Sun).

Best,

Vesselin

I am afraid I cannot answer what you ask since I share the views expressed by:

J.L. Synge in his excellent General relativity book: “The Principle of Equivalence performed the essential office of midwife at the birth of general relativity… I suggest that the midwife be now buried with appropriate honours and the facts of absolute space-time faced.”

Einstein himself, later in his life, changed his opinion of Mach's principle and wrote: “Actually, one should no longer speak of Mach's principle at all.”

And here is why I think Mach’s ideas contradict spacetime physics (properly understood in terms of Minkowski’s four-dimensional formulation of Einstein’s special relativity). Only two examples:

1. According to Mach, if there existed a single particle in the universe, one could not say anything about its motion (e.g., whether it is moving with constant velocity or is accelerating). That is true in Einstein’s original special relativity, but clearly wrong in its accepted Minkowski’s formulation: if there existed a single particle in the universe, its worldline would be either straight (which, in three-dimensional language, means that the particle is moving with constant velocity) or curved (representing accelerated motion).

2. According to Mach, one cannot distinguish between the Copernican and the Ptolemaic systems because, on Mach’s view, it is not clear what orbits what. This is plain wrong in spacetime physics because the worldlines (rather worldtubes) of the planets are helixes around the worldtube of the Sun (which, in three-dimensional language, means that it is the planet that orbit the Sun).

Best,

Vesselin

Dear Vesselin,

I very much enjoyed reading your essay, which is right on topic and warns against grave metatheoretical misconceptions. Indeed, many research directions are plagued with the misconception that "mathematics in physics is merely a description and therefore even fundamental mathematical entities (such as a manifold) do not represent counterparts in the physical world." And I...

view entire post

I very much enjoyed reading your essay, which is right on topic and warns against grave metatheoretical misconceptions. Indeed, many research directions are plagued with the misconception that "mathematics in physics is merely a description and therefore even fundamental mathematical entities (such as a manifold) do not represent counterparts in the physical world." And I...

view entire post

report post as inappropriate

Thanks a lot, Cristi. I see we agree on a lot of issues related to the interpretation of general relativity and to quantum gravity. Thank you also for the link to your paper in Annals of Physics.

In fact, regarding your PhD thesis, if you are planning to publish it, would you also consider the new academic publisher - the Minkowski Institute Press; we have a special Doctoral Theses Series. You can always contact me at the email address given at my webpage.

In fact, regarding your PhD thesis, if you are planning to publish it, would you also consider the new academic publisher - the Minkowski Institute Press; we have a special Doctoral Theses Series. You can always contact me at the email address given at my webpage.

Dear Vesselin Petkov

I agree with your answer about Mach principle, but I thought on more wide definition of Mach principle, where one option is Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion? I expect that this dissagrees with your view? On this view it is also based the graph theory of Fotini Markopolou. I think that gravity is quantized also because G helps to give that physics is dimensionless (similarly as Planck constant helps this.)

I intuitively like the idea that gravity is not a force, but I also like the Mach7 rule. So it seems that the elegant solution is that the virtual graviton does not exist.

Otherwise, I also like your opinion and example that mathematics is not only description in physics. I also mainly agree wih Stoica opinion about your essay, except that I think that spacetime is discretized on some way.

My essay

Best regards

Janko Kokosar

report post as inappropriate

I agree with your answer about Mach principle, but I thought on more wide definition of Mach principle, where one option is Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion? I expect that this dissagrees with your view? On this view it is also based the graph theory of Fotini Markopolou. I think that gravity is quantized also because G helps to give that physics is dimensionless (similarly as Planck constant helps this.)

I intuitively like the idea that gravity is not a force, but I also like the Mach7 rule. So it seems that the elegant solution is that the virtual graviton does not exist.

Otherwise, I also like your opinion and example that mathematics is not only description in physics. I also mainly agree wih Stoica opinion about your essay, except that I think that spacetime is discretized on some way.

My essay

Best regards

Janko Kokosar

report post as inappropriate

Dear Janko,

Regarding your question (at the end):

Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion?

You know that there exist matter-free universe solutions of Einstein’s equations. And it is not trivial at all to decide which solutions are “physical”.

However, I think it is, to a larger extent, a matter of what we will call matter - if we regard as matter everything that exists in the universe, the answer to your question is self-evident.

Best wishes,

Vesselin

Regarding your question (at the end):

Mach7 rule: ''If all matter is removed from our universe, universe does not exist any more''. What is your opinion?

You know that there exist matter-free universe solutions of Einstein’s equations. And it is not trivial at all to decide which solutions are “physical”.

However, I think it is, to a larger extent, a matter of what we will call matter - if we regard as matter everything that exists in the universe, the answer to your question is self-evident.

Best wishes,

Vesselin

Dear Vesselin,

Thank you for your very interesting essay, one of the best in the contest. I have nothing to add to your essay’s conclusions, especially: “the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world.”

I take the opportunity and propose the mathematical entities and their counterparts in my essay, engaging the set of Thurston geometries (the geometrization conjecture ) with metrics. I treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime. In three dimensions, it is not always possible to assign a single geometry to a whole space. So, the geometrization conjecture states that every closed 3-manifold can be decomposed into pieces that each have one of eight types of geometric structure, resulting in an emergence of some attributes that we can observe. As you probably know, Thurston geometries include: S3, E3, H3, S2 × R, H2 × R, SL(2, R), Nil and Solv geometry. The constant curvature geometries arise as steady states of the Ricci flow, the other five arise naturally where the dynamics of the Ricci flow is more complicated and where topological changes (neck pinching or surgery) happen. I have tried to attribute the geometries to interactions and fermions, except of five exotic ones (so far). You will probably find interesting Torsten Asselmeyer-Maluga’s publications that deal with details of similar approach. Interesting is also the proof of the geometrization conjecture, sketched in 2003 by Grigori Perelman, showing that the Ricci flow can be continued past the singularities.

If you are interested you can find details in my essay.

I would appreciate your comments however I would understand if you were tired with the contest. You deserve the high rating what you can observe in a moment.

Jacek

report post as inappropriate

Thank you for your very interesting essay, one of the best in the contest. I have nothing to add to your essay’s conclusions, especially: “the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world.”

I take the opportunity and propose the mathematical entities and their counterparts in my essay, engaging the set of Thurston geometries (the geometrization conjecture ) with metrics. I treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime. In three dimensions, it is not always possible to assign a single geometry to a whole space. So, the geometrization conjecture states that every closed 3-manifold can be decomposed into pieces that each have one of eight types of geometric structure, resulting in an emergence of some attributes that we can observe. As you probably know, Thurston geometries include: S3, E3, H3, S2 × R, H2 × R, SL(2, R), Nil and Solv geometry. The constant curvature geometries arise as steady states of the Ricci flow, the other five arise naturally where the dynamics of the Ricci flow is more complicated and where topological changes (neck pinching or surgery) happen. I have tried to attribute the geometries to interactions and fermions, except of five exotic ones (so far). You will probably find interesting Torsten Asselmeyer-Maluga’s publications that deal with details of similar approach. Interesting is also the proof of the geometrization conjecture, sketched in 2003 by Grigori Perelman, showing that the Ricci flow can be continued past the singularities.

If you are interested you can find details in my essay.

I would appreciate your comments however I would understand if you were tired with the contest. You deserve the high rating what you can observe in a moment.

Jacek

report post as inappropriate

Vesselin,

Nice to hear from you again. In your essay, you wrote/spoke like a true physicist. Physics is the study of this special relationship between the observer and his reality that we call “experience”.

This experience only exists by the interaction between the observer and what is really out there, the substance. By opposition to “experience”, the substance of the universe does not need us in order to exist.

We have known this long enough to stop beating around the “black box” and guess right away what’s in it. The truth is not something to look for anymore. It is something we have to be able to look at.

All the bests,

Marcel,

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Nice to hear from you again. In your essay, you wrote/spoke like a true physicist. Physics is the study of this special relationship between the observer and his reality that we call “experience”.

This experience only exists by the interaction between the observer and what is really out there, the substance. By opposition to “experience”, the substance of the universe does not need us in order to exist.

We have known this long enough to stop beating around the “black box” and guess right away what’s in it. The truth is not something to look for anymore. It is something we have to be able to look at.

All the bests,

Marcel,

report post as inappropriate

Marcel,

Nice to hear from you too. Regarding your:

"In your essay, you wrote/spoke**like** a true physicist. "

I hope you meant**as**, not **like**. English is not my first language either, but I have always tried hard to learn such delicate differences.

However, if you did mean**like**, then you could consult my webpage given above,

Best wishes,

Vesselin

Nice to hear from you too. Regarding your:

"In your essay, you wrote/spoke

I hope you meant

However, if you did mean

Best wishes,

Vesselin

Dear Vesselin,

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

report post as inappropriate

Dear Vesselin,

I read with great interest your depth analytical essays in the spirit of the Cartesian doubt with extremely important conclusion, which I fully agree:

"…mathematics in physics is not merely a description and that part of the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world. Also, despite that the issue...

view entire post

I read with great interest your depth analytical essays in the spirit of the Cartesian doubt with extremely important conclusion, which I fully agree:

"…mathematics in physics is not merely a description and that part of the exciting art of doing physics is to determine which mathematical entities have counterparts in the physical world. Also, despite that the issue...

view entire post

report post as inappropriate

Dear Vesselin,

You make a compelling case as to how equivalent theories contribute to hiding the nature of the foundational properties of the physical world. I found enlightening the idea that one may have equally correct theories but only one of them is closer to the heart of things and can be used as a foundation for future research. It's an idea that*feels* true. You have a very enjoyable and clear writing style which benefits the presentation very much. I am very enthusiastic about your essay. One thing I found a bit confusing is that I always though that relativity implies that there is no interaction but only geometry, however you seem to say something a bit different (page 8, the last paragraph "Had he lived longer, Minkowski himself might have arrived at this radical possibility"). But maybe I'm just reading it wrong.

Anyway, I loved your idea and your writing style so I am rating this essay accordingly. Should you have the necessary time, do read my essay and let me know what you think.

Warm regards,

Alma

report post as inappropriate

You make a compelling case as to how equivalent theories contribute to hiding the nature of the foundational properties of the physical world. I found enlightening the idea that one may have equally correct theories but only one of them is closer to the heart of things and can be used as a foundation for future research. It's an idea that

Anyway, I loved your idea and your writing style so I am rating this essay accordingly. Should you have the necessary time, do read my essay and let me know what you think.

Warm regards,

Alma

report post as inappropriate

You are very much gelled with the concepts.

Great.

- Sincerely

Miss. Sujatha Jagannathan

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Great.

- Sincerely

Miss. Sujatha Jagannathan

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Thank you all for your comments. Due to some urgent issues in the last ten days and this week I hope to be able to do something enjoyable next weekend - reading essays.

Vesselin Petkov

P.S. Thanks a lot Alma. What I meant is that if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident “fact” that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics).

Vesselin Petkov

P.S. Thanks a lot Alma. What I meant is that if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident “fact” that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics).

Dear Vesselin,

Thank you very much for explaining, now it makes perfect sense. I did suspect I misunderstood what you meant. I wish you good luck and I hope the issues you are attending will be resolved soon!

Have a great day and a successful week!

Alma

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Thank you very much for explaining, now it makes perfect sense. I did suspect I misunderstood what you meant. I wish you good luck and I hope the issues you are attending will be resolved soon!

Have a great day and a successful week!

Alma

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Vesselin,

Great essay. Tom flagged it up for me. It was on my list but I've failed to hit my target so got promotion! (and a top score), but only a 'speed read' so lowfi and I've marked it for a return.

I'm sure you'll like mine, no worries on scoring, but I'd greatly appreciate your views. There's a link to the main paper co-authored with John Minkowski. Our main work has been in the 'discrete field' model of SR, but this is a result of the implications of that model on QM.

There's also a short video on my string I hope you'll look at and discuss.

best wishes.

Peter

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Great essay. Tom flagged it up for me. It was on my list but I've failed to hit my target so got promotion! (and a top score), but only a 'speed read' so lowfi and I've marked it for a return.

I'm sure you'll like mine, no worries on scoring, but I'd greatly appreciate your views. There's a link to the main paper co-authored with John Minkowski. Our main work has been in the 'discrete field' model of SR, but this is a result of the implications of that model on QM.

There's also a short video on my string I hope you'll look at and discuss.

best wishes.

Peter

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Dear Vesselin,

I very much enjoyed your essay! You offer convincing arguments that mathematics in physics is not merely a description. I agree with your opinion that metatheoretical misconceptions might delay the advancement of fundamental physics.

Best regards and good luck,

Milen

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I very much enjoyed your essay! You offer convincing arguments that mathematics in physics is not merely a description. I agree with your opinion that metatheoretical misconceptions might delay the advancement of fundamental physics.

Best regards and good luck,

Milen

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