What Mathematics Is Most Pertinent For Describing Nature? by Felix M Lev

Dr. Lev ... thank you very much for your thoughtful reply. One problem with being a nice person is that people tend to take advantage of you, as I shall do now. This is a quote from a paper by Brukner and Zeilinger (see cite below). I'm wondering if you agree or not, or agree/disagree in part ...

"Clearly, a number of important questions remain open. Of these, we mention here two. The first refers to continuous variables. The problem there is that with continuous variables, one has in principle an infinite number of complementary observables. One might tackle this question by generalizing the definition of (3.4) to infinite sets. This, while mathematically possible, leads to conceptually difficult situations. The conceptual problem is in our view related to the fact that we wish to define all notions on operationally verifiable bases or foundations, that is, on foundations which can be verified directly in experiment. In our opinion, it is therefore suggestive that the concept of an infinite number of complementary observables and therefore, indirectly, the assumption of continuous variables, are just mathematical constructions which might not have a place in a final formulation of quantum mechanics.

"This leads to the second question, namely, how to derive the Schrödinger equation. ...."

from: "Quantum Physics as a Science of Information" (2005)

http://tinyurl.com/26dwfel

Dear Dr. Lev,

Thanks again. I certainly thought so, which is why I made the connection. There's plenty of material out there to choose from but very little of it anywhere near as apposite. But of course the devil (or God, if you're Mies van der Rohe) is in the nevertheless-not-entirely-spiritual details.

I know that both of these guys are Community members and possible contest voters so not to press you further.

Dear Felix,

You did a nice exploration and exposition of a possible application of finite fields in quantum theory. Your article on arxiv shows that you developed extensively this idea. Since I do not know any field in fundamental physics which is closed, or at least which accounts for all observations, I think that we should not demand new-born theories to be perfect and answer all questions. Let's let them grow up so that we can really compare them with others which were developed during one century by so many scientists. I think it is good to question them and to compare them with experiment even from the beginning, but I don't think that their value should be judged before their maturity.

I will ask some questions about your essay, if you don't mind. Please, if you feel that we disagree at some points, consider my questions as a proof of interest and curiosity.

Best regards,

Cristi Stoica

Dear Felix,

I confess that I do not perceive the standard mathematics as being wrong, and the discrete or finite one as the only justified. I don't think I have enough information to decide whether our world is discrete or continuous. This is why I salute both directions of research, and I am interested in the arguments or evidence of each of them.

You said: "Standard mathematics is based on axioms about infinite sets (e.g., Zorn's lemma or Zermelo's axiom of choice), which are accepted without proof. Our belief that these axioms are correct is based on the fact that sciences using standard mathematics (physics, chemistry etc.) describe nature with a very high accuracy."

This triggered in my head the following questions (I would be pleased to receive answers from other readers too):

[?] As far as I know, Zorn's lemma and the axiom of choice are independent of the other axioms in set theory (although they are equivalent for example in Zermello-Fraenkel's system). Would it be possible to interpret one of the known experiments, or to devise a new one, so that we can check if they are valid from our world?

[?] All mathematical physics uses mathematics based on some axioms. Were some of these axioms tested directly, or only through their consequences (predictions)? Would it be possible, at least in principle, a physics based on axioms which are tested directly?

Best regards,

Cristi Stoica

Dear Felix M. Lev,

Mathematics is a blind tool designed mainly to follow physics and describe the products made by physisists, but not a tool to discover something in physics; There are a few examples only when mathematical methods discovered something in physics, but a many thousands of erroneous mathematical papers and false mathematical "proofs". It is dangerous for physics because a lot of people mask their false and erroneous papers under mathematical formulas and mathematical theories.

I have examined some your papers in order to find what this mathematical instrument can really discover in PHYSICS; However, the most of your papers deals mainly with Galois fields. Even in your paper "A POSSIBLE MECHANISM OF GRAVITY" I don't found any physical mechanism of gravitation - mathematics only; Gravity is a manifestation of Galois fields? Can you explain how this manifestation of Calois fields can curve spacetime and slow down time? Also some your papers repeats the same information, for example the figure "Relation between Fp and the ring of integers" I saw in 3 your different papers.

Sincerely,

Constantin

Dear Felix,

could my question "Would it be possible, at least in principle, a physics based on axioms which are tested directly?" be answered positively by a physics based on finite fields?

Could the habitants of a finite universe know everything about their world, just because there is a finite number of things to be known? It seems to me that they are "more finite" than the knowledge about their world. So, I would incline towards the second possibility you mentioned.

Dear Constantin,

You write: "Mathematics is a blind tool designed mainly to follow physics and describe the products made by physisists, but not a tool to discover something in physics" and so on. This is really nonsense.

I noticed that sometimes the authority argument works better than a more rational one.

Isaac Newton was Lucasian Professor of Mathematics at the University of Cambridge. His contemporary and archenemy Gottfried Wilhelm Leibniz was a mathematician as well. His Monadology, considered to be utterly unphysical, started the research program which ended with the invention of the computer and of the www (namely the http).

Coming back to Lev paper, it is certainly nothing wrong, IN PRINCIPLE, to suggest that a physical phenomenon "is a manifestation of Galois fields", because, look, Newton himself had to invent differential calculus in order to establish his theory.

(Leibniz invented the same mathematical "blind instrument" simultaneously and better than Newton, for reasons which were independent of physics.)

Dear Marius Buliga and Cristi Stoica,

I agree that there are a few examples of successful predictions in physics made by mathematics, against the thousands of wrong predictions on the other hand; I can show that about 70 percents of all theoretical papers made by mathematicians in physics are wrong. For example, about hundreds of different theories of gravitation have been published in the academic journals, but it is self-evident that one or two similar gravitational theories only can be true at the same time, but not hundreds of theories. It is self-evident that 99 percents of all published gravitational theories are erroneous. Meanwhile all these erroneous theories have the "PERFECT MATHEMATICS" and "mathematical proofs" and are accepted by peer reviewed journals and physics community. Also the same situation arise in other areas of physics: about 70 percents of all theoretical papers in physics made by mathematicians are wrong. For example, let us analyze this paper this paper published in Physical Review Letters: I found tens of errors here whereas this paper has been supported by Physical Review Letters and NASA. You see, the authors try to prove their erroneous papers by help of mathematics; Thus, the mathematical proofs in physical theories must be in doubt. All the Standard Model is a mathematical model only that can compute only but explain nothing. The invasion of mathematicians will stop the development of Physics. That situation arise because peer reviewed Journals accepts papers with mathematical content only. Journals should accept that a physical logic (reasoning) must have equal rights with mathematical proofs.

Dear Felix M Lev

Yes, your mathematical approach tries to describe the EXISTING already physical phenomena only. Your results confirm my point of view that mathematics must be a tool to describe quantitatively products (theories and phenomena) made/discovered by physicists only, but it is not a indicator for physicists what they must do. Because physics is directed by mathematics, it is a cause of modern crisis in physics.

Sincerely,

Constantin

[I apologize to Felix, I do not want to monopolize this thread. I would kindly ask a FQXi admin who validates the comments to move the discussion to a different thread, if it is off topic. Or perhaps to move this comment and the father comment as children to the discussion opened by Constantin Leshan, so that the discussion gets collapsed and does not occupy too much of this page.]

Dear Constantin Leshan,

you say "I agree that there are a few examples of successful predictions in physics made by mathematics"

The examples I gave cover a very wide part of fundamental physics, and I think that we can go on with such examples to cover most of it. But I did not claim that those mathematical theories which found applications in physics were predictions. Well, in some cases they are, for example Riemann, Hamilton and Clifford intended to obtain a mathematical description of space and time, although the result was not exactly as they expected. But most of them - for example, the Hilbert space - were not made with the physical applications in mind. It was only discovered later that they can be applied, probably, as I said, because physicists realized that these tools can be borrowed and used with success.

You say "I can show that about 70 percents of all theoretical papers made by mathematicians in physics are wrong. For example, about hundreds of different theories of gravitation have been published in the academic journals, but it is self-evident that one or two similar gravitational theories only can be true at the same time, but not hundreds of theories."

Should I understand that these hundreds of different theories of gravitation are published by mathematicians and not physicists? I was thinking that physicists are those publishing them. If you are right, then it is simple to find the correct theory of gravity: just look at the resume of various authors, exclude the theories invented by mathematicians, and keep those discovered by physicists. If they are one or two, it should be easy to identify them.

My guess is that the percentage of wrong theories, let's say 70% as you say, although I think it is larger, is the same for physicists and for mathematicians. Or it would be so if mathematicians would be interesting in making theories of gravity.

My viewpoint* is that physicists are those doing physics. Mathematical physicists develop the theories discovered by physicists, or try to express them in different mathematical formalisms, in order to find the best fit. Mathematicians which are not particularly interested in physics, develop and generalize and solve various particular cases and classify the solutions etc., without caring about the applications. From time to time, a purely abstract mathematical theory is found to provide a good formulation of a concrete physical problem.

I apologize if I let the impression that I claim that all the work in physics is done by mathematicians. This is far from truth, and I would not do such a discrimination. In fact, most of my heroes in science are physicists rather than mathematicians.

Best regards,

Cristi

__________________________________

* Oversimplified and stereotypical, of course, but if I would like to be correct in detail, I should never speak :-).

Dear Cristi Stoica,

The border between mathematicians and physicists is very thin; therefore by papers of mathematicians I mean papers were the percentage of mathematics is more than 40 of volume, or all proofs are mathematical; From this point of view, almost all gravitational theories are mathematical theories, made by mathematicians. Also, I do not accuse all mathematical world; I say that all false physical theories have mathematical proofs, consequently mathematical proofs in physical theories must be in doubt. Therefore, it is mathematics' fault that the most of published physical papers are wrong.

It is because journals accept papers with mathematical content only. I'm sure that the percentage of false theories may fall, if the journals allow physical reasoning instead of mathematical proofs. Thus, Journals must allow to physicists to publish their papers with physical proofs instead of mathematical. Since the Standard Model is more mathematical model than physical, therefore I accuse mathematics. We'll never find any Higgs boson because SM is a mathematical model only that may fall in nearest future. The future Physics will be based on physical reasoning rather than on mathematical proofs.

About moving this comment to the discussion opened by Constantin Leshan: soon I'll send my essay to FQXI. I invite you to find logical errors in my theory.

Sincerely,

Constantin Leshan

Dear Constantin,

I am sympathetic to your viewpoint that these day physics is too much math without physical content. I stop now because I took too much space from Felix with my off topic comments. We can continue by email. Good luck with your forthcoming essay.

Cristi

Dear Felix,

Sorry for the delayed answer, I was caught up in a lot of work recently. Let me start by clarifying my intention. First and foremost I am interested in understanding your approach because I work in a different number system for QM myself. Second, I am interested in your essay entry. Let me repeat that I find your essay interesting, otherwise I would not spend my time trying to understand your ideas. Also you have strong claims, and strong claims deserve strong scrutiny, IMHO.

I am puzzled by your statements: "Let me also repeat that if I understand you correctly and you are interested only in discussing physics then the present forum is not an appropriate place for this discussion. " and "I believe that my essay is fully in the spirit of this essay contest entitled "Is Reality Digital or Analog?" So I discuss mathematics." First, this is a physics contest and FQXi is mostly a physics organization. Second, mathematical statements without physics support are irrelevant to deciding if nature is digital or analog. Mathematical (or any other kinds of) statements without agreement with reality are just marks on paper.

To me, discussing from the physics point of view it is the only thing which makes sense and interests me. But if you find this inappropriate, I will respect your wishes and not continue to ask questions. But if you want to continue the physics discussion, I am available.

Hi all,

Congratulations for your beautiful essay dear Felix,The finite groups of Galois are relevants in my humble opinion when we want calculate rationally the quantic number and all its proportionalities.This system has a finite serie at my opinion.

To all, very relevant discussions.Don't stop dear Friends, hhihihi Laplace, Poisson and Gauss shall be happy to see these discussions and they shall say,; don't forget the theory of errors and the dispersions.....a kind of precison and sorting appears in the same rational logic.Like an Occam Raozr applied to maths for rational physics.

That permits to see better the serie towards the Planck scale and its finite number.

The infinity , the 0 and the - must be rationalized in the pure physicality and its pure laws in 3 Dimensions and a time constant of evolution.I d say even ,they doesn't really exist, if we add them yes, but not in our pure uniqueness, and their finite system and their pure number.

We can for example add or multiplicate our cosmological spheres, that doesn't mean that their number changes...their pure number inside an evolutive Unievrse rests like it is.It's the same for our quantum number, we can add or multiplicate them ,their pure number rests.It's a little like a proportional approximation in fact with rational limits.

Regards

Steve

Hi all,

dear Felix,

You are welcome.

Indeed we have different points of vue(as many here on FQXi,the sharing of ideas seems essential), but the most important is this universality behind.

I like finite groups, and I think that maths must be analyzed with the biggest rationality when we analyze physics in its details.

I utilize algebras with an ocaam razzor,it exists several methods ,interestings and relevants.I add or superimpose them.

But I don't rest in one method.

In fact lie algebras, Clifford's alg.,.....are interestings when they respect the foundamental theorem of algebras.Now of course the physicality is the physicality.And the number is the number.

I see the quantum entanglement a little as our universe.Now if the entanglement of spheres is specific....the volumes are important and the number is the same and finite as the serie of volumes.The begining is a fractal of the main central sphere.Now I ask me how is the serie between 1 and our number of cosmological spheres.My problem is about the spheres between the center and our planets.And between 1 and 2 and 3........the volumes decrease on a specific harmonous serie.

Yes of course here is mine , a simple google mail.We can speak here you know I am transparent.

Ps sorry for my poor litteral english.

dufournybionature@gmail.com

Regards

Steve

I like the idea of using the Galois fields in physics. Are you aware of the result that it is possible to construct a complete set of mutually unbiased basis for finite dimensional quantum systems if and only if the base is indexed by a Galois field?