The considered paper is the second version of the paper http://arXiv.org/abs/0811.4562v2. The remarks of the referees concern the first version of the paper, which is shorter, than the present version. The first version began from the second paragraph of the fourth page (In the end of nineteenth century the physics… see http://arXiv.org/abs/0811.4562v1 ) The present version is a result of a revision, founded on the remarks of the referees.
The name of the journal is coded by AAA. It is devoted to conceptual problems of physics.
The first referee:
The paper is aimed at describing the dynamics of point-like particles within the framework of non-Riemannian geometry.
The hypothesis of a granular geometry allows one to describe discrete features of elementary particles without the paradigm of quantum
mechanics. The case of a 5D Kaluza-Klein model is also envisaged.
Consideration of the granular geometry is NOT A HYPOTHESIS. It is simply a consideration of a more general case of
the space-time geometry.
The first referee:
The paper is rather technical, so that I do not recommend it for the Letter Section.
The work does not refer to previous or contemporary literature, and the connection with all other developments of Physics
is not explained.The average reader of Journal AAA would not therefore in principle be able to appreciate the content of the
It is quite reasonable, that my paper does not contain a reference to contemporary literature, because the
contemporary literature is based on the "quantum paradigm", whereas my paper is based on the "geometric paradigm".
There is nothing common beween these paradigms. My paper is not a development of contemporary papers. Appearance
of the quantum paradigm took place in the beginning of the 19th century, and papers of Kaluza-Klein were the last
papers, which does not concern the quantum paradigm.
As to average readers, I agree with the referee, that the study of the new paradigm may be difficult for average reader.
However, the journal AAA is devoted to conceptual problems of physics, and the reader of such a journal must be ready for
investigation of new approaches and new paradigms.
The first referee:
Because of all the technicalities, the concern with Particle Physics is missed. In fact, many features are not clear.
1) How does this formalism allow one to distinguish between Fermions and Bosons?
2) According to 1.13, how are massless particles treated? Please explain, within this formalism, the difference between
Photons and other gauge bosons. Please, explain also the difference between massive neutrinos and massles neutrinos and their
properties within this formalism, and possible experimental predictions.
3) Is it possible to extend this formalism for other compactification mechanisms and/or for other exrtaD scenarios?
4) In the case of Fermions, the approach should be compared with the Dirac approach both in 4 dimensions and in
5 dimensions. The discussion in lines 45-54 page 9 is not satisfactory at all.
Furthermore, it should also be compared with the Papapetrou approach both in 4 and in 5 dimensions.
5) The description of the q/m problem in the KK approach has not been addressed. Can this formalism add new elements
for the q/m puzzle, which affects KK models?
6) Eq.s 5.5 and 5.6, for example, should refer to some KK scenario. Anyhow, it is difficult to distinguish the term
accounting for the 5th dimension, and how the compactification scale enters the dynamics.
The referee suggests to test different corollaries of the particle dynamics in the non-Riemannian space-time geometry.
I agree, that such a test would be useful. But why is this test a condition of the paper publication? The dynamical
laws are formulated in the coordinateless form. They do not refer to the space-time dimension, compactification,
particle mass and other details of the space-time geometry and those of considered particle characteristics. In the
Riemannian space-time the particle dynamics coincide with the known classical dynamical laws. The suggested
dynamics in the non-Riemannian space-time does not need a consideration of details for its rationale. It is
true, that the quantum dynamics was constructed by parts (at first, the Schroedinger equation, thereafter
the Dirac equataion...) But why must the more general dynamics be constructed by parts as the quantum dynamics?
The particle dynamics is formulated at once (but not by parts), and it is a denomination of the dynamics (but not
its defect). There is answer for the most important question, how Fermions (Dirac particle) are described in
the suggested dynamics. However, it is a large article (reference 7 of the second version), which could not be included
in the text of manuscript. Another important question on influence of compactification on dynamics is also considered
in the large article (reference 10 of the second version). Detailed investigation of this question cannot be included in the text of
Pretensions of the referee are unfounded. They would be well-founded, if I have invented a new hypothesis, and the
particle dynamics were constructed by parts. But I have only corrected a mistake in the geometry, when one considers,
that only axoimatizable geometries are possible (The experimental test is nesessary, when the theory is constructed by
method of fitting). If the theory is constructed as a correction of a mistake, there is no necessity to test this
correction by experiment. (Such a test looks as an experimental test of the binomial formula).
I agree with the referee, that it would desirable to fulfil the program, suggested by the referee. But it is impossible
in the framework of one paper, and fulfilment of this program cannot be a condition of my paper publishing.
Some points of the program, suggested by the referee are fulfilled in other papers. For instance, the difference between
the Fermions (Dirac particle) and Boson lies in the fact that the Boson is described by a timelike world chain, whereas
the Fermion is described by a spacelike world chain, which form a helix with timelike axis (reference 7 of the second version).
Some points are essential in the quantum paradigm, however, they have no sense in the geometric paradigm.
For instance, epicycles are essential concepts in the Ptolemaic doctrine and epicycles are not mention in the
doctrine of Copernicus.
The first referee:
7) The reference list is extremely poor and solipsistic. In fact, six references refer to the same author, and only one
of them has been published on a journal, while the others are arXiv e-prints. The remaining two references trace back to the Twenties,
and are the basic references for KK.
It is true, that the manuscript contains references mainly to my own papers. It is connected with the fact, that only
I myself develop the "geometric paradigm". I know nobody, who develops the "geometric paradigm". References to papers,
dealing with the conventional "quantum paradigm" have no relation to the considered problem. The fact, that nobody deals
with the "geometric paradigm", is conditioned by the circumstance, that the discovery of a mistake in the geometry needs
a very high qualification.
My papers are published as arXiv e-prints, and this fact is conditioned by pioneer character of my papers. The
peer review journals rejected to publish such papers. The journal rejected to publish papers in two cases
(1) when the manuscript is of low quality and (2) when there are no reviewers, whose qualification is sufficient for a
correct estimation of the manuscript. Everybody knows the first point, whereas the situation, connected with the second
point, is known only to those authors, who write pioneer papers. Thus, although my papers are published as e-prints, this
fact, does not mean, that these papers are pithless.
The first referee:
English is quite poor, but this fact does not affect the comprehension of the work.
The style of lines 36-53 page 1 is not appropriate for a scientific discussion. References should be added, and sentences
The use of the verb 'demonstrate' line 33 page 2 is not correct.
The terms 'orthodox' and 'orthodoxy', lines 31 and 33 page 13, are not appropriate for Physics.
The use of the article 'the' should be reconsidered, in particular with respect to technical sentences, i.e. line 40 page
11 'geometry of the index 1'.
The use of punctuation is in conflict with English rules throughout the paper. In particular, sentences like 'we did not
know, how one can...' (line 41 page 1) should be amended throughout the paper.
I agree with remarks of the referee, concerning my English spelling. I think, that all orthographic mistakes can be
corrected, if the paper will be accepted for publication.
The first referee:
I do not recommend publication of the paper in its present form. The author(s) should follow points 1-6 and
update and enlarge the reference list to explain, at least at ground level, how this work can
be conceived within the framework of modern Theoretical Physics, and to what extent the work can
add new perspectives. After that, the paper can be reconsidered for publication.
I shall not try to follow the points 1-6, because it is not possible in the framework of one paper. Besides, I should
like to describe arrangement and structure of elementary particles. It is impossible in the framework of the contemporary
elementary particle theory. The fact is that, the contemporary elementary particle theory is a theory which systematizes
the phenomenological properties of the elementary particles. Although it predicts sometimes new elementary particles,
but it cannot describe their structure. In the same way the periodical system of chemical elements systematizes
chemical elements and predicted new chemical elements, but contribution of the periodic system into our knowledge
on the structure of atoms is equal to zero.
The second referee:
According to the title this is a work on the ``generalization of relativistic particle dynamics to the case of a
non-Riemannian space-time geometry''. While the study of the dynamics of matter in geometries which go beyond the concept
of a Riemannian spacetime, usually encountered in non-standard theories of gravitation, is certainly a topic in
contemporary gravitational physics, it is not clear how the present work is linked to this field of research.
In the submitted paper only problem of particle dynamics in the FIXED space-time geometry is considered. Influence of
the particle distribution on the space-time geometry is a very important problem, which is beyond the framework of the
submitted paper. The referee is quite right in the relation, that there exists the problem of a generalization of the gravitational theory
on the case of non-Riemannian space-time geometry. It is a very serious problem which is beyond the framework of the
submitted paper. I am planning to investigate this problem, but not in the framework of this paper.
The second referee:
The line of reasoning in the work under consideration is -- at least to me -- incomprehensible. Different notions from
geometry, topology, and physics are mixed in a misleading way. Furthermore, the work is almost devoid of any references to
the existing literature, the only two exceptions being references to the early works of T. Kaluza (1921) and O. Klein
(1926). There is no critical discussion of the findings in the present work and the results of other authors. The language
appears not to be sufficiently clear for an international journal.
I agree with the referee. Apparently, it is very difficult to understand the paper, when only axiomatizable geometries
are known, and the technique of the geometry description in terms of the world function is unknown. But I cannot help
at this point. Study nonaxiomatizable geometries and new approach to geometry.
The first version of the paper was revised. It was resubmitted to journal AAA with the following letter to the editor
I should like to submit revised version of my manuscript "Generalization of relativistic
particle dynamics on the case of non-Riemannian space-time geometry" for publication
in the journal AAA.
Revision concerns only the introduction, where I try to explain, that my paper is simply
a generalization of dynamics in the Riemannian space-time geometry on the case of arbitrary
non-Riemannian space-time geometry. The paper does not pretend to determination of true space-time geometry.
It formulates simply the CLASSICAL particle dynamics in the arbitrary (non-Riemannian) space-time geometry.
The considered examples of the space-time geometries are used only for demonstration of capacities of
classical dynamics in the non-Riemannian space-time geometry.
Unfortunately, the first referee decided, that my paper pretended to determination of the true space-time geometry.
He suggested a voluminous program, which I should realize in order my manuscript be published. This voluminous program
cannot be realized in the framework of one paper. I am not going to fulfill recommendation of the referee,
because the goal of my paper is restricted. I construct the technique of dynamics in arbitrary space-time geometry.
I suppose, that construction of such a technique is sufficiently important problem. I suppose, that solution
of this problem is sufficient for publication of the paper. The dynamic principles are formulated in
any space-time geometry independently of, whether or not this geometry is true. Test of the trueness of the
space-time geometry is needless in the considered case..
The second referee did not understand that my investigations relate to the "geometrical paradigm",
whereas all conventional papers are written in the framework of the "quantum paradigm". In the quantum papradigm
the space-time geometry (geometry of Minkowski) is fixed and principles of dynamic are varied (transition from
the classical dynamics to the quantum one). In the framework of the geometrical pardigm the classical principles
of dynamics are fixed, whereas the space-time geometry is varied. Connection between the two paradigms is absent
practically. Working in the framework of the geometrical paradigm, it is meaningless to refer to the papers,
written in the framework of the quantum paradigm. Unfortunately, the second referee did not take into account this circumstance.
In the revised version I try to explain existence of the two paradigms and absence of a connection between them.
The second referee writes that the paper is incomprehensible. It is rather reasonable, when the paper, written in
the framework of the GEOMETRICAL PARADIGM is considered from the viewpoint of the QUANTUM PARADIGM. I understand,
that a consideration of the geometrical paradigm is difficult for both the referees and the readers of the Journal, who
use the quantum paradigm. However, publication of such a paper in the journal AAA seems for me to be
admissible, because this journal is devoted to conceptual problems of physics.
The revised version of the manuscript was rejected by the following letter.
Dear Yuri Rylov,
We have received the reports from our advisors on your manuscript "Generalization of relativistic
particle dynamics on the case of non-Riemannian space-time geometry".
With regret, I must inform you that, based on the advice received, the Editors have decided that your manuscript
cannot be accepted for publication in the journal AAA. This manuscript is a resubmission of a manuscript
that was previously rejected by the Editors. Manuscripts that have been rejected cannot be resubmitted.
Below, please find the comments for your perusal.
I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every
success in finding an alternative place of publication.
With kind regards,
Comments for the Author:
The foundational content of the manuscript is too weak. The connection to physics and the motivation for introducing
granual geometries are insufficiently explicated. This manuscript would be more suitable in a journal on mathematical
physics. It is not appropriate for the journal AAA.