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**Ivan Zhogin**: *on* 4/21/15 at 14:01pm UTC, wrote Dear Vladimir, thanks for comments. I’ve read your essay; it was not...

**Vladimir Rogozhin**: *on* 4/11/15 at 20:13pm UTC, wrote Dear Ivan, I totally agree with you: "Physical laws, on the contrary, are...

**Ivan Zhogin**: *on* 4/11/15 at 19:01pm UTC, wrote Dear James Putnam, thanks for greetings. Dear all. I have looked at the...

**Joe Fisher**: *on* 4/9/15 at 16:00pm UTC, wrote Dear Ivan, I think Newton was wrong about abstract gravity; Einstein was...

**Sujatha Jagannathan**: *on* 4/5/15 at 18:34pm UTC, wrote You exhibit more projection in your work with more interpretations crossing...

**James Putnam**: *on* 4/3/15 at 18:59pm UTC, wrote Dr. Ivan Zhogin, Welcome and thank you for your essay. Professionally...

**Ivan Zhogin**: *on* 3/30/15 at 19:57pm UTC, wrote Well, here was a post by Joe Fisher (on 3/23/15 at 16:37pm UTC, wrote Dear...

**Jonathan Dickau**: *on* 3/22/15 at 21:50pm UTC, wrote You might want to check out... On Michael Goodband's personal web-site, he...

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Philosophers, physicists and neuroscientists discuss how our sense of time’s flow might arise through our interactions with external stimuli—despite suggestions from Einstein's relativity that our perception of the passage of time is an illusion.

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FQXi FORUM

October 15, 2019

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

TOPIC: Physics as a (unique) nonlinear math which is free of infinities in solutions by Ivan L Zhogin [refresh]

TOPIC: Physics as a (unique) nonlinear math which is free of infinities in solutions by Ivan L Zhogin [refresh]

The fundamental physical theory should be nonlinear (to describe interactions) but that leads to problems, infinities in solutions – both for classical and quantum theories (not so toy, able to include gravity). String theory changes the very topology of Feynman diagrams, but still remains just a program, a design on a (complete) theory. On the other hand, Einstein’s research did not stop on Special and General relativities – he also considered (compatible, second order) field equations whose symmetry group united symmetries of both relativity theories. Among such equations (mostly non-Lagrangian) one can find a unique one (no free parameters, D=5) which solutions last forever (no breaks on singularities). Many features of this equation and its solutions are interesting indeed (three linearly unstable polarizations, plus longitudinal one, which add nothing to D-momentum; topological charges and quasi-charges) and give rise to a new interpretation of Quantum Mechanics and new 4th-order Lagrangian gravity.

Ivan Zhogin (graduated from Novosibirsk University; PhD from Tomsk University, see the book below) is a Senior Researcher in the department of sorters at Bourevestnik, Petersburg. He is author of the book "Old and new research on the Absolute Parallelism theory" (gr-qc/0412130v2). Among the standpoints “Einstein did not understand QM” and “Nobody understands QM”, he prefers the second one (maybe Einstein was just more honest and responsible).

Intriguing offering Ivan,

I strongly agree with, and have championed, some of the points you make - but I have some criticism too, and can't give you full credit. You are quite correct that the fundamental theory must be non-linear to reflect the actual reality of nature. Too many times; people have made limiting assumptions in order to find linear equations, which are solvable, and then forgotten that this limits their range of applicability. So the true Physics remains non-linear, and the linearized equation is only partially true.

I know that absolute parallelism solves a lot of problems, such as flatness, but it remains an unpopular answer. Perhaps some of this is due to the unreasonable claims of G.I. Shipov, regarding the local reception of distant information - that may have extended his funding, and was seized on by believers in psychic phenomena, but left most serious scientists convinced he is a crackpot. There are some serious deficiencies in his Math too, which I suspect is due in part to an attempt to build his framework exclusively out of tensors - which fails to properly represent topological torsion. You don't fall into the same traps, though.

You may find interesting Joy Christian's book on the Disproof of Bell's theorem, and you'll find some resonant concepts in the essays of Michael Goodband and Edwin Klingman. I have enjoyed this introduction to your work, but I feel that you failed to adequately show why this theory connects back to the essay question. It seems like you are saying that the Math you developed is automatically selected by nature. If you feel strongly, that the lack of singularities signals that this unique solution is the right one, you need to spell that out better - or explain why you feel that way.

Regards,

Jonathan

report post as inappropriate

I strongly agree with, and have championed, some of the points you make - but I have some criticism too, and can't give you full credit. You are quite correct that the fundamental theory must be non-linear to reflect the actual reality of nature. Too many times; people have made limiting assumptions in order to find linear equations, which are solvable, and then forgotten that this limits their range of applicability. So the true Physics remains non-linear, and the linearized equation is only partially true.

I know that absolute parallelism solves a lot of problems, such as flatness, but it remains an unpopular answer. Perhaps some of this is due to the unreasonable claims of G.I. Shipov, regarding the local reception of distant information - that may have extended his funding, and was seized on by believers in psychic phenomena, but left most serious scientists convinced he is a crackpot. There are some serious deficiencies in his Math too, which I suspect is due in part to an attempt to build his framework exclusively out of tensors - which fails to properly represent topological torsion. You don't fall into the same traps, though.

You may find interesting Joy Christian's book on the Disproof of Bell's theorem, and you'll find some resonant concepts in the essays of Michael Goodband and Edwin Klingman. I have enjoyed this introduction to your work, but I feel that you failed to adequately show why this theory connects back to the essay question. It seems like you are saying that the Math you developed is automatically selected by nature. If you feel strongly, that the lack of singularities signals that this unique solution is the right one, you need to spell that out better - or explain why you feel that way.

Regards,

Jonathan

report post as inappropriate

Jonathan,

my preferred Math is a unique (and non-Lagrangian) variant of “clear” Absolute Parallelism (or primeval AP, as was used by Einstein-Mayer: single field - frame field, irreducibility; no other fields) which solutions are seemingly free of singularities; that’s of exceptional rarity. And I try to indicate other interesting features of this math.

It seems you are writing about some other AP (not primeval) where I am not a specialist.

Long-long ago I ran through couple of Shipov’s papers (in Izvestiya VUZov; V.R.Kaigorodov once mentioned him) and, frankly, found nothing interesting (as I can remember): that was not clear-AP, plus Lagrangian equations; no mentioning of topological charges and quasicharges; no tracks of compatibility theory; and all.

(BTW, Lagrangian-ness of equations in AP guarantees the presence of an identity but not their compatibility; and some researchers (e.g. Hehl) considered a pathological, incompatible variant of Lagrangian equations of AP.)

Sure, I am unable to discuss wordings and trifles of Shipov, or, say, the present interpretation of (the) Einstein-Cartan theory (which seemingly preserves nothing from AP and Einstein).

Next, I believe that QM works well, so one needs just (instead of disproving the Bell’s inequalities) to give an explanation of the superposition principle and a convincing understanding (interpretation) of QM.

You are right that my exposition of this Math is much less elegant than the Math itself (and, frankly, many items relating to the combinatorics of topological (quasi)particles and the scenario of appearance of a SM-like QFT are unclear yet).

Regards,

Ivan

my preferred Math is a unique (and non-Lagrangian) variant of “clear” Absolute Parallelism (or primeval AP, as was used by Einstein-Mayer: single field - frame field, irreducibility; no other fields) which solutions are seemingly free of singularities; that’s of exceptional rarity. And I try to indicate other interesting features of this math.

It seems you are writing about some other AP (not primeval) where I am not a specialist.

Long-long ago I ran through couple of Shipov’s papers (in Izvestiya VUZov; V.R.Kaigorodov once mentioned him) and, frankly, found nothing interesting (as I can remember): that was not clear-AP, plus Lagrangian equations; no mentioning of topological charges and quasicharges; no tracks of compatibility theory; and all.

(BTW, Lagrangian-ness of equations in AP guarantees the presence of an identity but not their compatibility; and some researchers (e.g. Hehl) considered a pathological, incompatible variant of Lagrangian equations of AP.)

Sure, I am unable to discuss wordings and trifles of Shipov, or, say, the present interpretation of (the) Einstein-Cartan theory (which seemingly preserves nothing from AP and Einstein).

Next, I believe that QM works well, so one needs just (instead of disproving the Bell’s inequalities) to give an explanation of the superposition principle and a convincing understanding (interpretation) of QM.

You are right that my exposition of this Math is much less elegant than the Math itself (and, frankly, many items relating to the combinatorics of topological (quasi)particles and the scenario of appearance of a SM-like QFT are unclear yet).

Regards,

Ivan

Thanks for replying Ivan,

I like what you have done so far, and to my mind this approach has merit, but there are people who feel otherwise. I mention Dr. Christian and Gennady Shipov because it illustrates why, and to what extent, people are suspicious of AP as a serious explanation of anything. I think Shipov was rightly labeled a charlatan, but Dr. Christian is a serious scientist trying to explain correlations observed in QM, and it looks like he was chased away by other FQXi members and harsh negative opinions.

Though Einstein and Cartan considered AP, and though Einstein and Infeld used the Ether metaphor to illustrate the fundamentals of Relativity effectively; both ideas have come into disfavor. So the fact that Shipov's work was discredited, and that it refers repeatedly to Absolute Parallelism and a Physical Vacuum, may unfairly predispose people against your work. However; you seem to be moving in a fruitful direction, and I hope you continue to explore this avenue of explanation.

Regards,

Jonathan

report post as inappropriate

I like what you have done so far, and to my mind this approach has merit, but there are people who feel otherwise. I mention Dr. Christian and Gennady Shipov because it illustrates why, and to what extent, people are suspicious of AP as a serious explanation of anything. I think Shipov was rightly labeled a charlatan, but Dr. Christian is a serious scientist trying to explain correlations observed in QM, and it looks like he was chased away by other FQXi members and harsh negative opinions.

Though Einstein and Cartan considered AP, and though Einstein and Infeld used the Ether metaphor to illustrate the fundamentals of Relativity effectively; both ideas have come into disfavor. So the fact that Shipov's work was discredited, and that it refers repeatedly to Absolute Parallelism and a Physical Vacuum, may unfairly predispose people against your work. However; you seem to be moving in a fruitful direction, and I hope you continue to explore this avenue of explanation.

Regards,

Jonathan

report post as inappropriate

You might want to check out...

On Michael Goodband's personal web-site, he has a paper on an S10 QFT that might be to your liking, or give you ideas to proceed on. It should show up in a web search, or you can ask him on his essay page.

All the Best,

Jonathan

report post as inappropriate

On Michael Goodband's personal web-site, he has a paper on an S10 QFT that might be to your liking, or give you ideas to proceed on. It should show up in a web search, or you can ask him on his essay page.

All the Best,

Jonathan

report post as inappropriate

Well, here was a post by Joe Fisher (on 3/23/15 at 16:37pm UTC, wrote Dear Dr. Zhogin, I do not wish to disrespect you or your essay, but I do...).

At present the post miraculously disappeared - nevertheless I'll try to answer:

Dear Joe Fisher, in absence of tracks of any math, I feel as should judge about a piece of poetry (or philology, or philosophy, if you prefer); and that is not an easy deal for me.

You would (could) look at the text of the dialog between Rabindranath Tagore and Albert Einstein. They agreed that, in absence of humans, Apollo Belvedere would not be handsome (the sample of beauty) any more. However Einstein suggested that the concept of truth is of another sort, truth (relating to physics) should be free of any subjectivity.

In some other place Einstein wrote that (approximately, as I remember) “a priori we might expect that events of the visual environment (outward world) are just slightly ordered – like letters in words (or maybe words in phrases, not sure); however our experience unveils much more rigid links between events (or processes), which only approximately can be expressed in terms of cause and effect”.

So, I would prefer a math (yes, without infinities!)

At present the post miraculously disappeared - nevertheless I'll try to answer:

Dear Joe Fisher, in absence of tracks of any math, I feel as should judge about a piece of poetry (or philology, or philosophy, if you prefer); and that is not an easy deal for me.

You would (could) look at the text of the dialog between Rabindranath Tagore and Albert Einstein. They agreed that, in absence of humans, Apollo Belvedere would not be handsome (the sample of beauty) any more. However Einstein suggested that the concept of truth is of another sort, truth (relating to physics) should be free of any subjectivity.

In some other place Einstein wrote that (approximately, as I remember) “a priori we might expect that events of the visual environment (outward world) are just slightly ordered – like letters in words (or maybe words in phrases, not sure); however our experience unveils much more rigid links between events (or processes), which only approximately can be expressed in terms of cause and effect”.

So, I would prefer a math (yes, without infinities!)

Dr. Ivan Zhogin,

Welcome and thank you for your essay. Professionally prepared alternatives are in need to emphasize the weaknesses of mainstream theories that dominate contests such as this one. What I am able to understand from your presentation looks logical to me. I hope your work attracts further discussion among professionals.

James Putnam

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Welcome and thank you for your essay. Professionally prepared alternatives are in need to emphasize the weaknesses of mainstream theories that dominate contests such as this one. What I am able to understand from your presentation looks logical to me. I hope your work attracts further discussion among professionals.

James Putnam

report post as inappropriate

You exhibit more projection in your work with more interpretations crossing different lines at different mediums.

- Regards,

Miss. Sujatha Jagannathan

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- Regards,

Miss. Sujatha Jagannathan

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Dear Ivan,

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

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 James Putnam,

thanks for greetings.

Dear all.

I have looked at the discussion around some essays, and let me say a few words about the speed of light and the Lorentz group (and sure about Minkowski spacetime as well).

Well, it is better to consider the speed of light simply as a conversion factor (say, between seconds and meters, or foots if someone prefers)....

view entire post

thanks for greetings.

Dear all.

I have looked at the discussion around some essays, and let me say a few words about the speed of light and the Lorentz group (and sure about Minkowski spacetime as well).

Well, it is better to consider the speed of light simply as a conversion factor (say, between seconds and meters, or foots if someone prefers)....

view entire post

Dear Ivan,

I totally agree with you:

"Physical laws, on the contrary, are seemingly invariable, and hardly ignorable; supposedly, they should be united in a single law, the fundamental theory (FT). "

Good question and answer, which clearly indicates the path to the fundamental theory:

"But how on earth can that tiny and simple part hold information on all those “fundamental constants”? Perhaps, FT should have no arbitrary parameters (being perfect and beautiful indeed) – otherwise it’s a huge set of similar theories, not a single theory at all. “Constants” might emerge as slowly varying and globally extended parameters of solutions, not of the theory itself (if simple, FT should be absolutely comprehensible). "

Solution to the problem of ontology and dialectics "metalaw" - "constants" outputs to nature of fundamental constants, and ultimately on the basis of fundamental knowledge and the primordial structure of the Universe as a whole. There are also important ontology of idea of absolute parallelism that you develop in research. I looked further your report "the absolute parallelism and a new picture of the world", in which you state that "The world picture is far from unity and needs to be replaced." I fully agree with you.

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld" (E.Husserl), as a picture of the world poets and philosophers.

Kind regards,

Vladimir

report post as inappropriate

I totally agree with you:

"Physical laws, on the contrary, are seemingly invariable, and hardly ignorable; supposedly, they should be united in a single law, the fundamental theory (FT). "

Good question and answer, which clearly indicates the path to the fundamental theory:

"But how on earth can that tiny and simple part hold information on all those “fundamental constants”? Perhaps, FT should have no arbitrary parameters (being perfect and beautiful indeed) – otherwise it’s a huge set of similar theories, not a single theory at all. “Constants” might emerge as slowly varying and globally extended parameters of solutions, not of the theory itself (if simple, FT should be absolutely comprehensible). "

Solution to the problem of ontology and dialectics "metalaw" - "constants" outputs to nature of fundamental constants, and ultimately on the basis of fundamental knowledge and the primordial structure of the Universe as a whole. There are also important ontology of idea of absolute parallelism that you develop in research. I looked further your report "the absolute parallelism and a new picture of the world", in which you state that "The world picture is far from unity and needs to be replaced." I fully agree with you.

I invite you to see my analysis of the philosophical foundations of mathematics and physics, the method of ontological constructing of the primordial generating structure, "La Structure mère" as the ontological framework, carcass and foundation of knowledge, the core of which - the ontological (structural, cosmic) memory and information - polyvalent phenomenon of the ontological (structural) memory of Universum as a whole. I believe that the scientific picture of the world should be the same rich senses of the "LifeWorld" (E.Husserl), as a picture of the world poets and philosophers.

Kind regards,

Vladimir

report post as inappropriate

Dear Vladimir,

thanks for comments.

I’ve read your essay; it was not simple reading, and I did not catch very much.

An attempt to substantiate all of mathematics seems to me like telling for all Odessa. Mathematics is toov diverse and must meet different demands of the human practice (incorrect inverse problems, computer science, etc). Physics (fundamental) is another deal and should engage some special, dedicated math, especially beautiful and worthy math, and be the only possible choice in a sense.

There is a natural need in parceling the world, the being, into parts, smaller and smaller pieces, down to a point. Following this way we arrive to the concepts of continuum and field theory. Earlier, in natural philosophy, there were an empty space (absolute, and the absolute time) and material points; according to Newton, the body weight was determined by the number of material points in the body.

At present, the Lorentz group is a sort of engineering science, and it is not good idea to consider the time separately (from the space-time).

Absolute parallelism in fact is not a very good name; the better name is just the frame field theory. The name AP is due to the fact that the field equations can be written using a covariant differentiation with asymmetric connection which is "compatible" with the frame (i.e. the frame can be brought through this differentiation, changing Greek indices to Latin ones, and vice-versa). The curvature tensor for such a differentiation (with asymm. connection) is obviously zero.

However there are the metric and the usual covariant differentiation with symmetrical connection (Levi-Civita), for which the curvature tensor (Riemann tensor) is not zero. In my opinion, it is better to use this usual covariant differentiation, because it leads to the energy-momentum tensor, Riemanian geodesic lines, etc.

By the way, any linear combination of two connections is a connection too, so the range of covariant differentiations in AP is really great; but the symmetry of connection is the most important feature, that simplifies matters!

In general, the AP theory is about the fact that the general covariance (the group of coordinate diffeomorphisms) can coexist with the Lorentz group (however, generally, without inertial coordinates).

One can try to say something about AP in philosophical terms (philosophy is supposed to help in understanding the meaning of some math that tries to describe the objective reality, the being).

Well, the Hegel's statement about the identity of the being and not-being can be stated in a bit more concrete form: locally, or rather, at a point, in zero jets, the being is identical to the not-being.

That is, staying in a point, without differentiating, at one point, it is impossible to distinguish the being from the not-being.

In the AP, sure, the not-being means the trivial solution, the Minkowski space-time, where there are absolutely no differences between the points, nothing able to catch the eye. And the being is a solution of general position (of some perfect field equations) where all points are regular (there are no emergent singular points where the rank of the frame matrix drops per unit).

In vacuum General relativity (no fields other than the metric) it would seem that there is a stronger similarity of points: even in the first jets all points are indistinguishable from each other and from a point of the trivial empty space-time.

However, in solutions of the GRT (of general position) singular points do appear, points where the covariant metric is singular (of co-rang 1). And, of course, these singular points are sharply different from regular points (and points of the not-being).

Best regards

thanks for comments.

I’ve read your essay; it was not simple reading, and I did not catch very much.

An attempt to substantiate all of mathematics seems to me like telling for all Odessa. Mathematics is toov diverse and must meet different demands of the human practice (incorrect inverse problems, computer science, etc). Physics (fundamental) is another deal and should engage some special, dedicated math, especially beautiful and worthy math, and be the only possible choice in a sense.

There is a natural need in parceling the world, the being, into parts, smaller and smaller pieces, down to a point. Following this way we arrive to the concepts of continuum and field theory. Earlier, in natural philosophy, there were an empty space (absolute, and the absolute time) and material points; according to Newton, the body weight was determined by the number of material points in the body.

At present, the Lorentz group is a sort of engineering science, and it is not good idea to consider the time separately (from the space-time).

Absolute parallelism in fact is not a very good name; the better name is just the frame field theory. The name AP is due to the fact that the field equations can be written using a covariant differentiation with asymmetric connection which is "compatible" with the frame (i.e. the frame can be brought through this differentiation, changing Greek indices to Latin ones, and vice-versa). The curvature tensor for such a differentiation (with asymm. connection) is obviously zero.

However there are the metric and the usual covariant differentiation with symmetrical connection (Levi-Civita), for which the curvature tensor (Riemann tensor) is not zero. In my opinion, it is better to use this usual covariant differentiation, because it leads to the energy-momentum tensor, Riemanian geodesic lines, etc.

By the way, any linear combination of two connections is a connection too, so the range of covariant differentiations in AP is really great; but the symmetry of connection is the most important feature, that simplifies matters!

In general, the AP theory is about the fact that the general covariance (the group of coordinate diffeomorphisms) can coexist with the Lorentz group (however, generally, without inertial coordinates).

One can try to say something about AP in philosophical terms (philosophy is supposed to help in understanding the meaning of some math that tries to describe the objective reality, the being).

Well, the Hegel's statement about the identity of the being and not-being can be stated in a bit more concrete form: locally, or rather, at a point, in zero jets, the being is identical to the not-being.

That is, staying in a point, without differentiating, at one point, it is impossible to distinguish the being from the not-being.

In the AP, sure, the not-being means the trivial solution, the Minkowski space-time, where there are absolutely no differences between the points, nothing able to catch the eye. And the being is a solution of general position (of some perfect field equations) where all points are regular (there are no emergent singular points where the rank of the frame matrix drops per unit).

In vacuum General relativity (no fields other than the metric) it would seem that there is a stronger similarity of points: even in the first jets all points are indistinguishable from each other and from a point of the trivial empty space-time.

However, in solutions of the GRT (of general position) singular points do appear, points where the covariant metric is singular (of co-rang 1). And, of course, these singular points are sharply different from regular points (and points of the not-being).

Best regards

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