Популярно о конечной математике и ее интересных применениях в квантовой теории

Глава 16. Попытки опубликовать строгое доказательство что конечная квантовая теория и конечная математика более фундаментальны чем стандартная квантовая теория и классическая математика соответственно

Выше я приводил аргументы, что FQM более общая (фундаментальная) чем стандартная квантовая теория и что конечная математика более общая (фундаментальная) чем классическая. Эти аргументы были даны на уровне строгости общепринятом в теорфизике. Можно сказать, что раз проблема фундаментальная, то она должна быть доказана строго. И я нашел строгое доказательство. Казалось бы, раз дано строгое доказательство такого фундаментального факта, то любой журнал должен быть рад опубликовать это доказательство. Но оказалось, что публикация такого фундаментального результата – большая проблема. Ниже я описываю свои долгие злоключения с публикацией этого фундаментального (и даже фундаментальнейшего) результата.

Одна из попыток обсудить с математиками мой подход была такая. Jose Manuel Rodriguez Caballero написал мне, что при New York University есть форум FOM – Foundations of Mathematics. Описание его политики такое.

FOM is an automated e-mail list for discussing foundations of mathematics. It is a closed, moderated list, subscriptions and postings must be approved by the moderator, currently Martin Davis. Approval of a posting does not imply agreement with the views expressed in the posting. FOM subscribers typically have advanced training in mathematics, philosophy, computer science or related fields, and either have professional activity in one of these directions or are preparing for such a career. The FOM list is intended to provide a venue for discussing the provocative, sometimes controversial, ideas which drive contemporary research in foundations of mathematics and which often do not find their way into journal articles. FOM postings must be highly relevant to issues and programs in foundations of mathematics. They should reflect high intellectual and scholarly standards. However, FOM is not a venue for papers that should be submitted to journals. Generally, detailed proofs and technical details are not welcome. Of course, pointers to more extensive accounts, published in print or on the Web are welcome. Postings should be thoughtful, well-reasoned, and lively. Although controversy is both expected and desired, personal invective and other irrelevant discussions will not be permitted. Quotation from previous postings should be limited to what is absolutely needed for understanding, and quotations within quotations are particularly to be avoided. All postings are available in full on the archive. FOM postings must consist of single-spaced, plain text and have an informative subject line in the e-mail header. Extended quotes from other FOM postings should be avoided.

Postings to FOM (by subscribers only) should be addressed to fom@cs.nyu.edu

The FOM Editorial Board currently consists of:

Stephen Simpson

Harvey Friedman

Martin Davis

Andreas Blass

William Tait

John Baldwin

Alasdair Urquhart

Т.е., опять произносятся очень хорошие слова о том, что разные подходы приветствуются, даже “the provocative, sometimes controversial, ideas which drive contemporary research in foundations of mathematics and which often do not find their way into journal articles.” Эти слова похожи на те, которые произносятся в editorial policy of Foundations of Physics и от них тоже дух захватывает. FOM – это не журнал, а форум для обсуждения разных идей, поэтому политика FOM выглядит очень привлекательно. Большинство начальников FOM против стандартной математики и за так наз. finitism, т.е., подход когда нет бесконечностей. Но, с другой стороны, в той математике, которую они пропагандируют нет и операций по модулю числа. Так происходит, например в Robinson arithmetic и Peano arithmetic. Эти арифметики считаются неполными и в приложениях не применяются. Но в целом мне казалось, что то что я пытаюсь делать они должны приветствовать. Ясно, что когда я узнал про FOM, то сразу захотел в нем участвовать. Но – это не открытый форум, и вначале надо, чтобы начальники FOM одобрили твое участие. Т.е., проблема типа arxiv-vixra.

Я послал в FOM такой application:

From Felix Lev:

I am a physicist. For many years I’m working on a quantum theory over finite math. The results are published in known physics journals. In addition, in my papers for physicists I argue that finite math is more fundamental than standard one: the latter is a special degenerated case of the former in a formal limit when the characteristic of the field or ring p in finite math goes to infinity. Since I am a physicist, I can post my mathematical results in the mathematical section of arxiv only if someone agrees to endorse, while many my papers can be found in the physics section of arxiv if you search the author F Lev.

In my last paper http://vixra.org/abs/1811.0044 I give a simple rigorous proof of the above fact. In general, introducing infinity automatically implies transition to a degenerate theory because in that case operations modulo a number are lost. So, even from the pure mathematical point of view (i.e. to say nothing about the fact that in nature there are no infinitely small and infinitely large quantities, no continuity etc.) the notion of infinity cannot be fundamental, and theories involving infinities can be only approximations of more general theories. In particular, standard quantum theory is a special degenerate case of quantum theory over finite math when p→∞. In many cases math with infinities works with a high accuracy because at the present stage of the Universe the number p is huge. At the same time, as shown in my papers, several physics phenomena can be explained only if p is finite. In particular, in my approach gravity is a consequence of the fact that p is finite: the gravitational constant is proportional to 1/lnp, i.e. gravity disappears in the formal limit p→∞. My estimation is that p is of the order of exp(1080) but since the gravitational constant depends on lnp, the effect of finite p is observable.

I graduated from the Moscow Institute for Physics and Technology, got a PhD from the Institute of Theoretical and Experimental Physics in Moscow, and Dr. Sci. degree (in Russia there are two doctoral degrees) from the Institute for High Energy Physics (also known as the Serpukhov Accelerator). In Russia I worked at the Joint Institute for Nuclear Research (Dubna, Moscow Region). Now I live in LA CA and work at a software company.

Ответ на мою просьбу был такой: Your request to the FOM mailing list

Subscription request has been rejected by the list moderator. The moderator gave the following reason for rejecting your request: "Your interests aren't an appropriate match for this list. " Any questions or comments should be directed to the list administrator at: fom-owner@cs.nyu.edu

Мой ответ:

Dear fom-owner,

The reason for rejecting my request is: "Your interests aren't an appropriate match for this list." This reasons seems very strange to me because in my papers I argue that finite math is fundamental while standard math is a special degenerate case of finite one. This approach seems to be fully in the spirit of the FOM forum. I would understand if, for example, the reason was that my results are erroneous etc. If the Editors think so I would be very grateful if they explain this opinion. However, the actual reason for rejecting seems very strange. Could you please tell me whether this is a collective opinion of all Editors or only one of them proposed this formulation?

Ответ на мой ответ:

Dear Felix Lev,

The decision and the wording were mine after consulting the editors. Of course, you are welcome to write them yourself. They are:

Alasdair Urquhart, urquhart@cs.toronto.edu,

John Baldwin, jbaldwin@uic.edu,

Harvey Friedman, hmflogic@gmail.com,

Steve Simpson, simpson@math.psu.edu,

John Burgess, jburgess@princeton.edu,

Andreas Blass, ablass@umich.edu,

Best wishes,

Мой ответ на это письмо:

Dear Professor Davis,

Thank you for your response to my query. So, in my understanding, none of the Editors found anything erroneous in my papers. Then the decision is fully unclear to me. As I noted, in my papers I argue that finite math is the most fundamental and standard math is a special degenerated case of finite one. Needless to say that this fact is fundamental for foundation of math. In my understanding, this fact is fully in the spirit of the FOM forum, and the goal of the forum is just to find strong arguments in favor of this fact. Of course there can be different approaches in this direction but in my understanding it is just the goal of the forum to discuss different approaches.

My results are published in known journals on physics and mathematical physics and, for example, my paper in Finite Fields and Their Applications is one of the three most downloaded. So I do not see any reasonable explanation of the Editorial decision. I will apologize if I am wrong but the only reason which comes to mind is that the Editors allow only their approaches and do not want the participants to know about other approaches.

I would be grateful if the Editorial decision is reconsidered.

Наконец, окончательный отказ такой:

Dear Felix Lev,

We have read your archiv article. The physics is not relevant to f.o.m. We found the mathematical claims to be unsubstantiated.

Best wishes,

В этом отказе два утверждения. Во-первых, что физика не относится к FOM. Но я использую физику только для иллюстрации, а претендую только на свои математические результаты. Я утверждаю, что, в отличие от своих предыдущих работ, где доказательство фундаментальности конечной математики было дано на уровне более-менее принятом в теорфизике, в новой статье дано чисто математическое доказательство. Второе утверждение – что мои результаты необоснованные. Но никаких объяснений нет, т. е. как обычно, такие мелочи как научная этика их не волнуют. Но даже это не укладывается в логику. Ведь FOM – это не журнал, а форум, а цель моей работы такая же как у них – привести аргументы, что бесконечности не нужны. И, если я ошибаюсь, то, казалось бы, они должны объяснить всем участникам форума, что мой подход неправильный и ни к чему не приведет. Поэтому теперь я не сомневаюсь, что в моем письме к ним привел правильную причину: начальники не хотят, чтобы участники форума знали о моем подходе. Мой подход неявно говорит, что их подход большого смысла не имеет, так что начальники не хотят, чтобы участники форума засомневались в том действительно ли начальники такие великие.

Jose Manuel Rodriguez Caballero написал начальникам FOM такое письмо в мою поддержку:

Dear FOM Editors,

As a member of FOM and a young researcher with publications in important journals, e.g.,

Caballero, Jose Manuel Rodríguez. "On a function introduced by Erdös and Nicolas. " Journal of Number Theory 194 (2019): 381–389. https://www.sciencedirect.com/science/article/pii/S0022314X18301999

Caballero, José Manuel Rodríguez. "On Kassel-Reutenauer q-analog of the sum of divisors and the ring F3 [X]/X2F3 [X]. " Finite Fields and Their Applications 51 (2018): 183–190.https://www.sciencedirect.com/science/article/pii/S1071579718300169

I would like to support the possibility of subscription of Dr. Felix Lev in FOM mailing list. In my own research, motivated just by mathematics, not by physics, I studied some of Dr. Lev mathematical publications, e.g.,

Lev, Felix M. "Why is quantum physics based on complex numbers?. " Finite Fields and Their Applications 12.3 (2006): 336–356.

https://www.sciencedirect.com/science/article/pii/S1071579705000687

I consider that it is very important for both, the foundations of mathematics and physics, to have researchers, like Dr. Lev, who are interested in learning about the progress in both fields. I remember that it was very important for the foundations of mathematics to have mathematicians interested in both number theory on the one hand and computability theory, on the other hand, e.g., in the resolution of Hilbert's tenth problem. So, I celebrate the inclusion of researchers with diverse interests and I hope they will contribute to the solution of new open problems in the future, putting together knowledge from several seemly unrelated fields.

I consider that to be aware of the progress in non-standard models of natural numbers, a subject related to FOM, will be useful for the development of Dr. Lev's research concerning his finitist reformulation of quantum mechanics. Indeed, I remarked that some post from FOM are related to biology, e.g., Rene Vestergaard's post "Proofs of life" (see below).

Finally, the CV of Dr. Lev is superior than the CV of some of the young members of FOM, including myself.

Sincerely yours,

но это письмо не помогло.

Еще одной попыткой опубликовать эту работу, было послать ее в arXiv. Т.к. они разрешают мне посылать только в gen-ph, то, чтобы послать в Number Theory, надо было, чтобы кто-то endorse и, по моей просьбе, это сделал Дима Логачев. Ответ arxiv был такой:

Dear arXiv user,

Our moderators determined that your submission is on a topic not covered by arXiv. As a result, we have removed this submission. While arXiv serves a variety of scientific communities, not all subjects are currently covered. Submissions that do not fit well into our current classification scheme may be removed. We encourage you to find another open access forum that serves your discipline.

Т.е., отвергают не потому, что что-то неправильно, а потому, что “your submission is on a topic not covered by arXiv”! Т.е., проблема, является ли конечная математика более фундаментальной чем стандартная математика, не входит в раздел Mathematics! Ясно, что это полная бессмыслица, и эта тупая и, главное, злобная мафия должна была найти повод, чтобы отфутболить, и ничего более умного они не нашли.

ArXiv содержит an arXiv Math Advisory Committee, который включает известных математиков. Казалось бы, задача этого Комитета высказывать свое мнение по научным вопросам. Один из членов этого Комитета – Professor Iosevich. Я написал ему об отношении к моим статьям:

Dear Professor Iosevich,

You are a member of the arXiv Math Advisory Committee, and I would be grateful for your advice on my problems with arXiv.

I have many papers published in known journals, 49 papers in arXiv, and Springer published my monograph: Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Application to Gravity and Particle theory. ISBN 978–3–030–61101–9. Springer, https://www.springer.com/us/book/9783030611002 (2020). More detailed information about me can be found in my ORCID: https://orcid.org/0000–0002–4476–3080.

My main area of research is quantum theory based on finite rings or fields. So, arXiv treated my papers as belonging to physics. Before 2009 they placed my papers in sections which I proposed. However, then their attitude to my papers significantly changed. They often required that my papers can be posted only after publications in known journals, and this, obviously, contradicts the very meaning of arXiv. However, even when a paper was published, they placed it in physics.gen-ph and several of my papers were rejected altogether. The only exception was that in 2012 they agreed to reclassify my paper published in Physical Review D to hep-th. It is obvious that quantum theory based on finite mathematics has nothing to do with general physics. I wrote many appeals but typically they were ignored.

I worked with physicists for many years and know their way of thinking. Unfortunately, when many physicists see a paper with mathematics which they don’t know, they immediately conclude that this is pathology or exotics which has nothing to do with physics. Most physicists are not familiar even with the very basics of finite mathematics. This is not a drawback because everybody knows something and does not know something, and it’s impossible to know everything. But typically, those physicists do not accept that in science different approaches should be allowed.

My understanding is that the goal of arXiv is to let scientists know what other scientists are doing. But in my case, the impression is that their goal is the opposite. The matter is that if a paper is posted in gen-ph then it is not allowed to cross-list the paper to other sections, and physicists and mathematicians interested in quantum theory over finite mathematics do not go to gen-ph.

Let me describe two latest examples.

My paper “Discussion of foundation of mathematics and quantum theory” published in Open Mathematics https://doi.org/10.1515/math-2022–0011 is in fact a popular description of some results of my book. I requested to post this paper in quant-ph and math.HO. However, they again posted the paper in gen-ph although it is obvious that the problems of foundation of mathematics and quantum theory have nothing to do with general physics. I wrote an appeal and after a month they informed me that they reclassified the paper to physics.gen-ph quant-ph. So, they refused to reclassify the paper to math.HO, and the paper was not posted in sections new and recent of quant-ph. Moreover, since the primary section is still gen-ph, I have no right to cross-list the paper to other sections.

Another example is the following. I had a talk "Obtaining information about nature with finite mathematics" at the international online conference organized by known universities, in particular by UCLA. The talk was published in Proceedings, MDPI, 2022, 81 (1), pp.8.

10.3390/proceedings2022081008. Nevertheless, arXiv rejected my submission with the following motivation: "Thank you for submitting your work to arXiv. We regret to inform you that arXiv’s moderators have determined that your submission will not be accepted and made public; Our moderators determined that your submission does not contain sufficient original or substantive scholarly research and is not of interest to arXiv. " This motivation is given without any explanation and has no hint that the moderators tried to understand the submission or were able to understand. It also contradicts their rules that the moderators are not referees. And the phrase that the submission is not of interest to arXiv contradicts scientific ethics because if the moderators do not understand the submission, it does not mean that it is not of interest for arXiv readers. Fortunately, I have no problems with the French archive HAL and here it is posted as https://hal.archives-ouvertes.fr/hal-03605174.

In summary, the attitude of arXiv to my submissions fully contradicts scientific ethics and does not give a hint that they understand what the submissions are about.

I would be grateful if you tell me about your opinion on whether it is possible to convince the moderators that their decisions are not based on scientific criteria, and they should be reconsidered.

Thank you.

Но не получил никакого ответа.

Председатель этого комитета – Professor Kuperberg. После того как я не получил ответ от Professor Iosevich, я написал ему тоже:

Dear Professor Kuperberg,

You are a chair of the arXiv Math Advisory Committee. I believe that the attitude of arXiv to my submissions fully contradicts scientific ethics and does not give a hint that they understand what the submissions are about. I described my problems in a letter to Professor Iosevich but he did not respond. Please find attached my letter to Professor Iosevich. I would be very grateful for your help.

Thank you.

но тоже не получил никакого ответа. Поэтому непонятно зачем этот Комитет существует, что ученые делают в этом Комитете, если они никак не реагируют на очевидные попытки нарушения научной этики.

Еще одной попыткой опубликовать эту работу было послать ее в Finite Fields and Their Application. Она была там месяц и ответ был такой:

Dear Dr. Lev,

Thank you for your submission to Finite Fields and Their Applications. Unfortunately, the Editors feel that your paper is not suitable for publication in the journal and unlikely to be favorably reviewed by the referees. We suggest you consider submitting the paper to another more appropriate journal.

Thank you for your interest in Finite Fields and Their Applications.

Sincerely,

Т.е., он не говорит, что статья не по теме журнала, а что так чувствуют редакторы. Казалось бы, зачем говорить о том, что чувствуют редакторы: есть редакционная политика, и надо просто сказать, статья соответствует ей или нет. А вторая часть предложения совсем бессмысленная. Казалось бы, почему просто не послать кому-то на рецензию и посмотреть какой будет отзыв? Я думаю, что единственное объяснение такое: он боялся, что вдруг отзыв будет положительный, а печатать статью он не хочет. И, чтобы написать этот глубокомысленный ответ нужен был месяц.

Еще у меня была переписка с Harald Niederreiter, который известный математик, автор книги по конечным полям и член редколлегии Finite Fields and Their Applications. Когда я написал ему о своей статье в Дубне, он ответил:

Dear Dr. Lev:

Thank you very much for your message and the link to your paper. I find your article highly interesting and the ideas enunciated therein truly original. As you can imagine, I also like a discrete and finite view of the world, with the continuous models of physics being the limit as the cardinalities of the finite models tend to infinity. It is fascinating that this can be proved rigorously!

With best regards,

Этот ответ меня обрадовал т.к. оказалось, что известный математик в целом меня поддерживает. Он пишет, что был очень рад, что фундаментальность конечной математики можно строго доказать. Но когда я написал ему о статье, где это строго доказано, он ответил:

Dear Dr. Lev:

Thank you for your message and the link to your paper. Actually, after studying your paper, I came to the conclusion that in the final analysis your work is really of more interest to physicists than to mathematicians. For a mathematician, the notion of infinity needs no explanation or interpretation, it is covered by cardinality theory. For a physicist, who deals with nature as it is and not with abstractions, the situation is different, and so I think your paper is better placed in the physics community.

Т.е., теперь он пишет, что для математиков понятие бесконечности не нуждается в объяснении или интерпретации; это важно только для физиков, которые имеют дело с реальностью. Т.е., фактически он говорит, что теория множеств – чисто абстрактная наука, которая не имеет отношения к реальной жизни. Это противоречит тому, что он писал в первом ответе. Почему вначале он писал одно, а потом совсем другое?

Еще одной попыткой опубликовать статью было послать ее в Forum of Mathematics, Pi. В своей редакционной политике они пишут, что “Forum of Mathematics, Pi is the open access alternative to the leading generalist mathematics journals”. Т. е. они намекают, что, вроде, они отличаются от establishment. У них есть раздел Foundations, т.е., опять-таки, вроде бы, моя статья полностью соответствует их правилам. Там надо предложить редактора, ответственного за статью, и я предложил Terence Tao. Он – звезда в математике и имеет много наград. И я получил такой ответ:

Dear Professor Lev,

This message concerns the manuscript A Simple Proof That Finite Mathematics Is More Fundamental Than Classical One by Felix Lev submitted to Forum of Mathematics, Pi. Unfortunately, we are uable to accept it for publication.

Sincerely,

Видимо, он хотел быстро отфутболить и даже не проверил, есть ли в ответе ошибки. И, как и в предыдущих примерах, тот факт, что он великий ученый, совсем не означает, что он утруждает себя соблюдением хотя бы минимальных правил научной этики. Он даже не пишет, соответствует ли статья правилам журнала и не делает никакой попытки объяснить почему “we are uable to accept it for publication”. Опять-таки, вроде как роль журналов не просто отвечать берут или нет. Вроде бы, предполагается, что когда автор посылает статью в журнал, то он хочет знать не только возьмут статью или нет, но и мнение квалифицированных ученых. Но, как и в предыдущих примерах, этого нет и в помине.