Популярно о конечной математике и ее интересных применениях в квантовой теории - Феликс Лев

Надеюсь, что среди физиков есть и такие, которые могут применять какую-то теорию не только веря, что она правильная, но и если они сами в этом убедятся. Исторически, как правило, новые физические теории возникали когда привлекалась математика, которая раньше в физике не применялась. Например, до квантовой теории Гильбертовы пространства не применялись в физике. Наверное, Рецензент не сомневается, что Дирак – великий физик. Приведу его слова, которые, с точки зрения Рецензента, являются полной крамолой: «I learned to distrust all physical concepts as a basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting an interesting mathematics.» Отмечу также, что ЭЧАЯ публикует много работ, в которых рассматриваются чисто математические проблемы квантовой теории, т. е. предполагается, что есть физики, для которых математика представляет не только академический интерес.

Что мне понравилось в подходе этого рецензента: он не играет в дипломатию, режет правду-матку (как он ее понимает) и не боится, что выяснится, что он чего-то не понимает. Поэтому отвечать на его рецензии легко т.к. ясно, что он утверждает. Например, западные рецензенты обычно намного хитрее. Когда они понимают, что некомпетентны, то стараются так обойти углы, чтобы это не проявилось, поэтому произносят какие-то общие слова и надо думать как ответить, чтобы было ясно, что рецензент без понятия.

После этого ответа получил рецензию второго рецензента:

Review of the article by Felix M. Lev

"Finite mathematics, finite quantum theory and a conjecture on the nature of time"

The author considers an extremely non-standard approach to quantum theory (QT) based on finite ring or field with characteristic p1 (the finite quantum theory (FQT). Author, in particular, shows that the conventional QT is a limiting case of FQT as p1. In the QFT approach, the characteristic $p$ is a fundamental evolving [!] parameter which defines how the classical equations of motions arise as a consequence of changing of p; moreover, p may be (this is an author's conjecture) the “precursor" of notion of time itself (»…the existence of classical time is a consequence of the fact [!?] that p changes»). Well, although our physiology (and/or psychology?) does not provide a chance to understand what is evolution of Universe (or its part) out of time, the reader may believe that the author understand it and then try to follow the formal (finite) mathematics. Nonetheless, if p changes, there must be even more fundamental cause governing this «fact»… but let's stop the metaphysics. Obviously, the very unconventional concepts formulated in the paper under review (as well as in the previous publications by the author (Refs. [1–3]) are highly disputable, but they are nontrivial and thus interesting. So these concepts must be presented to the community at least as a subject of criticism, controversy… or silence. A handicap of the paper (from my personal point of view) is its volume together with too lengthy explanations of comparatively simple and known things and too lapidary discussion of the specific axiomatics and (even more important) implications and (potentially) falsifying effects of the FQT.

1 The article looks like a novel about Cabbages and Kings (in other words, about everything known to the author). I guess that many items could be ejected in order to simplify understanding of the main ideas and results and to classify the ins and outs of the theory; this is not a demand but just a suggestion. In fact I have a lot of questions and even objections against the author's categorical statements, but I would not like to force a further increase in the length of the text. In conclusion, I think that the writeup under review is of interest for the community and thus is suitable for publication.

And yes, «Viennese School's philosophy» still predominates in physics, if we are able to separate postulates and consequences. This philosophy simply suggests to compare the consequences (and not the postulates) with the relevant empirical facts, but it does not demand to test the axioms of mathematics.

Я благодарен рецензенту за эту рецензию, после которой откорректированный вариант статьи был принят и опубликован в [21].

Глава 15. Попытка опубликовать монографию в Springer

15.1. Предложение о монографии

Свой подход к квантовой теории и свои результаты решил изложить в монографии. Мое предложение о монографии, посланное в Springer такое:

Dear Dr. Lahee,

Please consider my monograph proposal. The monograph will be based on my paper https://arxiv.org/abs/1104.4647 which contains 259 pages. Probably the final version will be longer but not considerably. The title of the monograph is:

Finite Quantum Theory and Applications to Gravity and Particle Theory and the abstract is:

We argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by continuous mathematics. Moreover, the ultimate physical theory cannot be based on continuous mathematics because it has its own foundational problems which cannot be resolved (as follows, in particular, from Gödel's incompleteness theorems). In the first part of the work we discuss inconsistencies in standard quantum theory and reformulate the theory such that it can be naturally generalized to a formulation based on finite mathematics. It is shown that: a) as a consequence of inconsistent definition of standard position operator, predictions of the theory contradict the data on observations of stars; b) the cosmological acceleration and gravity can be treated simply as kinematical manifestations of de Sitter symmetry on quantum level (i.e. for describing those phenomena the notions of dark energy, space-time background and gravitational interaction are not needed). In the second part we consider a quantum theory based on finite mathematics with a large characteristic p. In this approach the de Sitter gravitational constant depends on p and disappears in the formal limit p→∞, i.e. gravity is a consequence of finiteness of nature. The application