Популярно о конечной математике и ее интересных применениях в квантовой теории

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(10

) 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?

    Thank you. Sincerely, Felix Lev.

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,

    Martin Davis, Moderator

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.

    Thank you. Sincerely, Felix Lev.

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,

    Martin Davis

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 Rodr?guez. "On a function introduced by Erd?s and Nicolas. " Journal of Number Theory 194 (2019): 381–389. https://www.sciencedirect.com/science/article/pii/S0022314X18301999

Caballero, Josе Manuel Rodr?guez. "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,

    Jose Manuel Rodriguez Caballero

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.