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

limiting theories, based on two examples: Newtonian mechanics as a limiting case of special relativity, and the classical limit of quantum mechanics. The related notions of physical dimensions and units of measurement are systematically confused throughout the paper (I recommend https://arxiv.org/abs/physics/0110060 for a clear discussion of the subject).

The Author claims that deSitter and Anti-deSitter spacetimes are more “fundamental” than Minkowski spacetime, since the latter can be obtained as a particular case when the cosmological constant (or, equivalently, the curvature radius) is sent to zero. However, this only shows that dS and AdS spacetime are more general than Minkowski. Neither the former are more symmetric than the latter, as claimed on page 6 (all of them are maximally symmetric spacetimes). It is simply incorrect to speak of a given spacetime geometry as being more fundamental than another; rather, the attribute “fundamental” should be used with reference to a dynamical theory having a broader regime of applicability compared to a particular limit. Moreover, neither the value nor the sign of the cosmological constant can be fixed following the arguments in the paper.

Without a theory (as given by, e.g., an action principle), there is no reason to assume a particular spacetime geometry (e.g. deSitter) as being a valid description for the vacuum. Moreover, it is quite challenging to build a theory of gravity where the cosmological constant (or, equivalently, the deSitter radius) matches the observed value without introducing new tunable parameters: finding such a theory could in fact be regarded as a solution of the cosmological constant problem. Such a crucial aspect is not discussed at all in the paper, and the Author does not propose any theory to frame his discussion.

Из этого отзыва сразу видно, что рецензент – чисто классический физик и то, что написано в статье с точки зрения квантовой теории ему понять не дано. Он мыслит только в терминах spacetime geometry и считает, что проблема очень важная. Кроме того, вопреки научной этике, он делает отрицательные утверждения без всякого обоснования. Например, он пишет, что обсуждение размерностей наивно и даже рекомендует мне эту известную статью трех авторов. Но не пишет в чем наивность, есть ли расхождения с этими авторами и т.д. Да и ясно, что он статью не понимает т.к. в этой статье три автора высказывают кардинально разные взгляды, а он не пишет, какую точку зрения он предпочитает. Но теперь ясно, что даже совершенно не важно что он пишет, но Silvestri нашла такой повод для отклонения статьи: из трех рецензий две были отрицательными. Конечно, я написал appeal, в котором, в частности, отметил, что 1) вполне возможно, что оба отрицательных отзыва принадлежат одному и тому же рецензенту; 2) в любом случае, на данный вариант статьи есть два рецензента. И написал почему отзыв бессмысленный:

Ref: DARK_2019_25_R1

Title: Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry, by F. Lev

Author’s appeal on editorial decision

The decision is based on reports of Reviewer 1 and Reviewer 3. Reviewer 1 did not say that the paper should not be published. He/she said that it could not be published in the present form because in his/her opinion the paper contained nothing essentially new in comparison with my previous papers. In view of this remark, I considerably revised the paper and now I explicitly explain why the new paper is fundamentally new. So in fact the decision is based only on the report of Reviewer 3.

At the beginning of the report, Reviewer 3 says the same words as Reviewer 1 without any substantiation. Regardless whether or not Reviewer 1 is the same person as Reviewer 3, for the current version of the paper there were two reviewers with fully opposite recommendations. In such cases in my practice the paper was usually sent to adjudicator. However, in the given case the preference was given to one of the reviewers. Reviewer 3 says that “The related notions of physical dimensions and units of measurement are systematically confused throughout the paper (I recommend https://arxiv.org/abs/physics/0110060 for a clear discussion of the subject).” However, nothing specific is said on what is “systematically confused” and so it is fully unclear whether Reviewer 3 understands what is written about physical dimensions. He/she says nothing on whether or not my paper contradicts this reference. This reference is known and I discuss it in my monograph project https://arxiv.org/abs/1104.4647. The three authors propose considerably different opinions on the problem, and Reviewer 3 says nothing on what opinion (if any) he/she prefers. One of the authors (M. J. Duff) states that the most fundamental physical theory should not contain arbitrary constants at all, and in Sec. 2 I also argue in favor of this statement.

The next part of the report also shows no sign that Reviewer 3 understands my results. First he/she says that "Section 2 is a naive, incomplete and unnecessarily lengthy…" but nothing specific is said on what is naïve, incomplete etc. Reviewer 3 writes: "The Author claims that deSitter and Anti-deSitter spacetimes are more “fundamental” than Minkowski spacetime…" but there is no such a claim in the paper and the comparison of those spacetimes is not discussed at all. I don't know whether Reviewer 3 understands basic facts of quantum theory, whether he/she works in the framework of this theory or he/she works only in the framework of classical theory. As I noted in my previous emails, many physicists do not understand that spacetime is only a classical notion, and spacetime description is only a consequence of quantum theory in semiclassical approximation.

On quantum level symmetry is defined by the commutation relations in the symmetry algebra as explicitly explained in Sec. 2, and in the formulation of this symmetry nothing is said about spacetime. In the theory of Lie groups and algebras a well-established fact is that if symmetry B is obtained from symmetry A by contraction then symmetry A is higher than symmetry B. In Sec. 2 I refer to famous Dyson’s paper [7] where this fact is explained