Популярно о конечной математике и ее интересных применениях в квантовой теории

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.