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

get around the criticized issues». I do not see any meaning in this statement because the reviewer does not say specifically what is not clear to him/her and, as noted above, there is no indication that he/she has at least a basic understanding of my approach. Scientific ethics imply that any negative statement should be substantiated, i.e. the words «too commonplace», «unspecific», «not really clear», «speculative» and others should be explained.

In summary, the report of Reviewer 1 contains nothing specific, contradicts scientific ethics and fully contradicts the FTPH policy because he/she recommends rejection without any understanding of my approach and results.

The report of Reviewer 2 also does not follow standards of scientific ethics. He/she says that I ignore «80 years of successful quantum theory». This is a very serious accusation but no explanation is given. Does he/she think that any attempt to improve the theory means ignoring it? In particular, does he/she think that relativistic mechanics ignores nonrelativistic one? Or does quantum theory ignore classical one? He/she also thinks «that the proposal is kind of esoteric» but again does not explain why he/she thinks so.

In contrast to Reviewer 1, Reviewer 2 acknowledges that there are problems with the photon position operator and with infinities but says that «the author is only focusing on those». This immediately shows that, in full contradiction to the FTPH policy, Reviewer 2 even did not carefully read my abstract where it is indicated what problems are discussed. Reviewer 2 says: «But the first question one would have to address is, when one wants to change the world, how does the world in which we actually live fit into that. This sentence is fully puzzled. Why does he/she think that I want to change the world? If I show that standard photon position operator is inconsistent then does it mean that I want to change the world? Does it mean that any improvement of standard theory means changing the world?

Reviewer 2 says The author ignores that or hides the discussion somewhere, where it is hard to find». Why was it hard for the reviewer to find? Was it hard to read the title of paper [15]?

Then he/she writes: «…the book is all words, hardly formulas, almost like a book of philosophy». Probably Reviewer 1 read only the introductory chapter because the other chapters contain extensive mathematical derivations of new results which have never been published. The existing version of the manuscript contains 259 pages. Again, in contradiction to scientific ethics, Reviewer 2 does not explain how many pages he/she treats as «all words» and how many as «hardly formulas».

In summary, my conclusion on the report of Reviewer 2 is absolutely the same as the conclusion on the report of Reviewer 1.

In view of the FTPH policy, the author should submit to FTPH a fundamentally new approach, not just a variation of mainstream one. So the reviewers should be ready that standard mentality is not sufficient for understanding the proposal. In particular, standard mentality that discrete is only an approximation to continuous, does not imply in the given case. In my proposal I tried to explain this point and below will try to explain again.

The notions of infinitely small, continuity etc. were proposed by Newton and Leibniz approximately 370 years ago. At that time people did not know about atoms and elementary particles and believed that any object can be divided by arbitrarily large numbers of arbitrarily small parts. But now it is obvious that when we reach the level of atoms and elementary particles then standard division loses its meaning and one cannot obtain arbitrarily small parts. It is immediately clear from this observation that the notions of infinitely small and continuity are not fundamental on quantum level. Moreover, it is rather strange to think that fundamental quantum theory should be based on mathematics involving infinitely small and continuity. The founders of quantum theory were highly educated physicists but they used only standard continuous mathematics, and even now discrete and finite mathematics is not a part of standard mathematical education at physics departments. For understanding my statement that finite mathematics is more fundamental than standard continuous one and that the latter is a degenerated special case of the former (see e.g. paper[16]), at least a very basic knowledge of finite mathematics is needed. The reviewer reports show that the reviewers do not have this knowledge. As I note above, this is not a drawback. However, scientific ethics implies that it is not decent to judge an approach without having at least very basic knowledge about the approach.

In particular, finite mathematics does not involve continuity, derivatives or integrals; those notions are approximations which might or might not work in different situations. In finite mathematics finite sums are possible. In some cases such sums can be approximated by integrals. So in this case not discrete is an approximation of continuous but vice versa. In my proposal I also explain that the continuous spectrum is an approximation of the discrete one but not vice versa.

После этого ответа Angela Lahee написала мне, чтобы я прислал ей свои предложения о рецензентах. Я их прислал и думал, что теперь мне надо ждать что напишут рецензенты и что она скажет. Но неожиданно получил такой емайл:

I have now received back some further comments on your manuscript. Although two of the reviews by persons you had suggested were positive about the work you present, I’m afraid that other established researchers in quantum theory remain skeptical. In particular they question the sense of applying finite mathematics to QFT in place of the well established renormalisation theory.

They are nonetheless open to new approaches. But they propose (and I agree) that the better way to disseminate new ideas of this kind is first to publish a series of short(er) self-contained papers demonstrating the power of this approach. If the published results have some