Популярно о конечной математике и ее интересных применениях в квантовой теории

Ясно, что я пытался опубликовать свои статьи по Λ в arXiv. Прежде чем описывать эту попытку – несколько замечаний о моих отношения с arXiv. Вначале отношения были идеальными. Они принимали все мои статьи в те разделы куда я хотел и даже советовали в каком разделе может быть больше читателей. Но все изменилось в 2009 г. Не знаю что было основной причиной, но они все мои статьи стали публиковать в разделе "общая физика" (gen-ph), хотя, кажется очевидным, что статьи по квантовой теории над конечной математикой и по Λ никакого отношения к общей физике не имеют. Причем, делали они это и тогда когда мой endorser рекомендовал другой раздел.

Проблема с gen-ph такая. Если, например, у тебя статья в hep-th, а ты думаешь, что она может быть интересна и читателям по гравитации (gr-qg), то можешь сделать cross-listing. А из gen-ph cross-listing сделать нельзя. Т. е. впечатление такое, что для них gen-ph – это как мусорный ящик, куда они сбрасывают то от чего хотят отделаться. И ясно, что если кто-то интересуется теми же проблемами, что и я, то он не пойдет gen-ph, т. е. вероятность, что мои статьи прочитают в gen-ph – намного меньше, чем, например, в hep-th. Ясно, что я просил их опубликовать статью в том разделе, который считал более подходящим, но они отказывали под предлогом, что их решение основано на совете какого-то moderator. Они имеют так наз. moderation system, описание которой такое:

arXiv is an openly accessible, moderated repository for scholarly papers in specific scientific disciplines. Material submitted to arXiv is expected to be of interest, relevance, and value to those disciplines. arXiv reserves the right to reject or reclassify any submission.

Причем они говорят, что moderator – не рецензент, и они не обязаны объяснять почему они решили так, а не иначе.

Philip Gibbs считает (совершенно справедливо), что такая система не соответствует научным принципам. Он организовал свой сайт и назвал его vixra. Это слово получается из arxiv, если читать его в обратном порядке. Он абсолютно прав в том, что если ты не можешь привести аргументы против статьи, то не имеешь морального права рекомендовать, чтобы статью не взяли. Поэтому любая научная статья может быть принята в vixra. Так что любой автор может быть уверен, что его статья увидит свет, и это важно не только с точки зрения того, признают ее физики или нет, а и с точки зрения авторского права. Я тоже послал много своих статей в vixra. Хотя в идеале подход vixra совершенно справедлив, при этом возникают проблемы. Т.к. никакого барьера нет, то много статей в vixra – полная мура и многие авторы там очень низкоквалифицированные. В arXiv тоже много всякой муры, но все же, видимо, ее меньше чем в vixra. Но все равно, не может быть оправдания системе когда всё решают модераторы, которые исходят непонятно из каких принципов и, когда я писал appeal с аргументами, что их решение ненаучное, они отвергали мои аргументы без всяких объяснений.

Итак, как я писал, начиная с 2009 г. все мои статьи arXiv переводил в gen-ph. Но статью по Λ не взяли даже туда. Как обычно, была стандартная отписка, что moderator считает, что статья не подходит для arXiv. Казалось бы, тема Λ сейчас одна из самых животрепещущих в современной физике, поэтому, если эта тема не подходит, то непонятно, что подходит. И ясно, что я написал протест. Ответ был удивительный. Они написали что возьмут только если статья будет вначале опубликована в каком-то журнале. Это, конечно, полностью противоречит идее архива как электронного препринта, где статьи выходят до их появления в журнале.

Т.к. мои попытки опубликовать статью в каком-либо «престижном» журнале были неудачными, я послал ее в Journal of Modern Physics. Рецензенты у них отовсюду, но журнал издается в Китае. Рецензия была по существу, я немного статью изменил, ее взяли и за open access я заплатил 600 долларов. Когда статья вышла, я написал в arXiv, что выполнил их требования и прошу взять статью. Но какой-то moderator мне ответил, что статья с ошибками и т.к. Journal of Modern Physics не является престижным журналом, то они статью не берут. Ну а т. к. мнение модератора – это не рецензия, то никаких возражений больше не принимается. Так что в целом все мои попытки опубликовать статьи по Λ закончились неудачно т.к. статьи вышли только в vixra и Journal of Modern Physics. На фоне того, что по dark energy пишут много статей, готовят эксперименты, проводят конференции и т.д., думаю, что причина понятна.

Еще одна попытка опубликовать статью по dark energy – Physics of the Dark Universe. Этот журнал считается очень престижным – у него impact factor 6.5. Редактором ответственным за мою статью была назначена Alessandra Silvestri. Первый отзыв был мало осмысленным, и статья была отклонена. Я ответил, что, по правилам журнала, должно быть по крайней мере два рецензента. После этого она предложила мне переделать статью, а на новый вариант было уже два рецензента. Один из отзывов был полностью положительный, а второй был такой:

I cannot recommend publication of this paper due to the following reasons:

Essentially, the results discussed in the paper are not new, being largely based on previously published work by the same author, e.g. Ref. [9]. The paper does not address the cosmological constant problem, neither it shows convincingly that “the problem does not arise”, as claimed in the abstract. Therefore, this work does not lead to any significant advance of our understanding of dark energy, and for this reason I can hardly see how it would be of interest to the Journal’s readership.

Section 2 is a naive, incomplete and unnecessarily lengthy discussion of the subject of 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 for groups and I explain this fact for algebras. Since Poincare algebra can be obtained from dS or AdS algebra by contraction, this automatically implies that dS and AdS symmetries are more fundamental than Poincare symmetry, and this has nothing to do with the relation between de Sitter and Minkowski spaces. The notion of contraction is a fundamental notion of the theory of Lie groups and algebras, and the report shows no sign that Reviewer 3 has a basic knowledge in this theory.

Reviewer 3 says ”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.”. Again, as noted above, I do not discuss spacetime at all because this is only a classical notion. In Sec. 2 I give Definition when theory A is more general than theory B, and this definition explicitly says that a more general theory has a broader regime of applicability compared to a particular limit. So a question arises whether Reviewer 3 read my Definition and whether he/she tried to understand it.

Reviewer 3 says: “Moreover, neither the value nor the sign of the cosmological constant can be fixed following the arguments in the paper.” As I explain in detail, the problem of the value of Λ does not arise for the same reasons as the problems of the values of c and ћ do not arise. Indeed this statement contradicts the usual dogma that Λ should be somehow fixed. However, Reviewer 3 says nothing specific on why in his/her opinion my explanation is incorrect or unacceptable, and so his/her objection cannot be treated as a scientific argument. It is known that relativistic quantum theory itself does not need the values of c and ћ, and in all textbooks on this theory the presentation is given in units c=ћ=1. The numerical values of c and ћ are needed only if one wants to express some quantities in (kg,m,s). The notion of the system of units was proposed many years ago when quantum theory and relativity did not exist. The notion of (kg,m,s) is pure classical and physical quantities are expressed in these units only for convenience. The problem why the values of c and ћ in units (kg,m,s) are as are does not exist since the answer is: because people want to measure c and ћ in these units.

Reviewer 3 writes: "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…". As explained in Sec. 2, quantum dS or AdS theories themselves do not need the numerical value of Λ for the same reasons as relativistic quantum theory does not need the numerical values of c and ћ. I also explain the known fact that even for classical dS and AdS theories themselves the numerical value of R is not needed. Since Reviewer 3 again raises this question, I will try to explain this obvious point again.

Suppose for simplicity that our world is a surface of two-dimensional sphere. Then the coordinates on the sphere can be described by two dimensionless polar angles (φ,θ). For the description of geometry we do not need the radius of the sphere R and we can assume that R=1. The quantity R in meters has the meaning of the radius of the sphere seen from the three-dimensional space where the sphere is embedded in. But we know nothing and do not need to know about this space and its coordinates. Those coordinates are of interest only when we want to attribute to R some value and consider a formal limit R→∞. In this limit a vicinity of the Northern pole of the sphere becomes the flat two-dimensional space.

Analogously, for dS or AdS theories themselves the value of R is not important; we can assume that R=1 and describe geometry on dS or AdS space by using only dimensionless polar and hyperbolic angles. The value of R becomes important only when we consider transition from dS or AdS space to Minkowski one. So the desire to describe R in meters does not have a fundamental physical meaning. The question why R is as is does not arise since the answer is: because people want to measure R in meters.

The only problem which is indeed important is whether dS quantum theory is more fundamental than AdS one or vice versa. I discuss this problem in my paper in J. Phys. A [9] and in my papers published in J.Math. Phys., Finite Fields and Applications, Phys. Rev. D and other journals where I argue that a quantum theory based on a finite ring or field is more fundamental than standard quantum theory based on complex numbers.

The cosmological constant problem is purely artificial. One first tries to build quantum gravity from Poincare invariance because it is associated with Minkowski background. Then he/she realizes that the expression for the vacuum energy-momentum tensor strongly diverges, and after the cutoff which is called reasonable he/she obtains that Λ is of the order of 1/G as expected. However, as noted above, on quantum level Poincare symmetry is a special degenerate case of dS or AdS symmetry not because Minkowski space is less symmetric than dS or AdS space but because Poincare algebra can be obtained from dS or AdS algebra by contraction. With the same success one can discuss the speed of light problem or the Planck constant problem.

Finally, let me note the following. Reviewer 3 claims that my paper is of no interest for the readers of Physics of Dark Universe and for this reason he/she does not want the readers to know about my results. I believe, however, that the readers are interested in knowing different approaches to the problems of their interest. My paper shows that a known problem can be tackled from a fully different approach. I believe that for the readers it would be extremely interesting to know that the result of General Relativity on cosmological acceleration obtained from dS space can be obtained from semiclassical approximation of dS quantum mechanics without using dS space at all (i.e. its metric, connection etc.). This result is obviously more general than the result of General Relativity because any classical result should be a consequence of quantum theory in semiclassical approximation. As I note in my explanations, while in [9] this result has been obtained after lengthy mathematical calculations, in the present paper I give a short description on three pages such that the reader will understand the necessary steps.

Let me also note that my paper is fully in the scope of Physics of the Dark Universe because the editorial policy contains "cosmic acceleration and its alternative explanations". At the same time, Reviewer 3 does not allow alternative explanations and accepts only those approaches which are in the spirit of his/her mentality.

The report cannot be treated as a scientific recommendation because: 1) it contains no sign that Reviewer 3 understands what is done in the paper; 2) scientific ethics implies that all negative statements in the report should be substantiated but all of them are made without any substantiation; 3) the report contains no specific statement on why anything in my paper is incorrect or unacceptable, my only “fault” is that my statements contradict known dogmas which have no physical justification. For those reasons I would appreciate if the editorial decision is reconsidered. I am also grateful to Reviewer 2 for the recommendation to publish the paper and for important remarks which will be taken into account in the next version of the paper.

Кроме того, написал ей такое письмо:

Dear Professor Silvestri,

Thank you for the info about your decision on my paper. Of course I believe that the decision is not fair. Please find my appeal attached. I think that the main problem is not that Reviewer 3 understands nothing in my paper and obviously cannot refute my derivations. Everybody knows something and does not know something, and it is impossible to know everything. In my opinion, if a scientist is proposed to review a paper which he/she does not understand then he/she should either decline from being a reviewer or say that different approaches have a right to exist. However, Reviewer 3 believes that only papers done in the spirit of his/her mentality can be published and all other papers should be prohibited such that the readers even should not know about their existence. Reviewer 3 does not understand that it is disgraceful to make negative statements without any substantiation. As explained in the appeal, I believe that my results will be extremely interesting for the readers of Physics of the Dark Universe, and my paper is fully in the scope of the journal. However, if your final decision is that my paper cannot be published in the usual way, I would be grateful if you consider the following possibility. My paper is published but along with the paper you or any reviewer writes a paper or comments explaining why my approach is unacceptable. In particular, the report of Reviewer 3 can be published. I believe this will be extremely important for the readers because they will be given an opportunity to make a judgment and will understand pros and cons of different approaches. Maybe my understanding of Reviewer 3’s intentions is not correct and he/she will appreciate the opportunity to express his/her opinion.

Thank you. Sincerely, Felix Lev.

Но сразу получил такой ответ:

Dear Dr. Lev,

I understand your disappointment, every decision if of course questionable, but our decision is final.

Kind regards,

Т.е., она даже не хочет играть в игру, что, якобы, она честно пытается разобраться. Она начальник группы, которая пишет, якобы, высоконаучные статьи по dark energy. В этих статьях никакой квантовой теории нет и в помине, все основано на классической ОТО, статьи печатает Phys. Rev. и другие журналы, так что видимость большой науки соблюдается.

Все это заняло три месяца и теперь ясно, что с самого начала она искала только повод, чтобы отфутболить. После этого я написал главному редактору журнала:

Dear Professor Tait,

I regret that you decided not to respond to my seminar proposal. The proposal had nothing to do with the fact that my paper was rejected. I believe the results are fundamental and my hope was that physicists at UCI would be interested. In this situation I decided to describe my experience with your journal. For the first time in my practice the editor even did not try to make an appearance of fair treatment.

First the paper was rejected because Reviewer 1 wrote a short (and meaningless) review stating that the paper contains nothing new. According to the editorial policy, a paper should be reviewed by at least two reviewers but this requirement was ignored. When I pointed out to this requirement the editor changed her opinion and proposed me to revise the paper.

After revision the editor found two reviewers. The report of Reviewer 2 was positive and the report of Reviewer 3 was negative. Then the editor found the pretext for rejecting the paper that two of three reviews were negative. The pretext obviously is not reasonable for the following reasons. First, it is quite probable that Reviewer 1 is the same person as Reviewer 3. But regardless whether or not this is the case, for the current version there were two reviewer reports, positive and negative. In that case the paper is usually sent to adjudicator or a board member writes a report. But in this case, in contrast to standard practice, the editor immediately rejected the paper without any additional reports.

The report of Reviewer 3 had no sign that he/she understands what is done in the paper. In addition, Reviewer 3 does not understand that it is disgraceful to make negative statements without any substantiation. I wrote an appeal but again, in contrast to the usual practice, the editor even did not want to consider the appeal and informed me that her decision was final. Ignoring author’s appeal fully contradicts scientific ethics.

Let me say a few words about the dark energy problem. Usually physicists working on this problem believe that since this a macroscopic problem then there is no need to involve quantum theory and the problem can be tackled exclusively in the framework of classical theory. And many physicists working on this problem are not even familiar with very basics of quantum theory. In particular, the report of Reviewer 3 shows no sign that he/she understands basic facts of quantum theory. He/she tried to reinterpret my statement in terms of classical physics but he/she does not understand that quantum theory cannot be interpreted in terms of classical physics.

Meanwhile, as shown in my paper, it is obvious from quantum theory that the cosmological constant problem (or dark energy problem) does not exist. I tried to explain this obvious fact in my several papers. Some of them have been published (e.g. in Phys. Rev. D) but the papers devoted exclusively to this problem have been rejected even by arXiv. However, I believe that the arguments given in the last version of the paper are so convincing that now arXiv has accepted my paper https://arxiv.org/abs/1905.02788. I would be grateful if you inform physicists about that paper.