"Generalization of relativistic particle dynamics on the case of non-Riemannian space-time geometry",

submitted to a scientific journal, devoted to conceptual problems of physics.


The considered paper is the second version of the paper 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 )  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.


My comment:


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



My comment:


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.


My comment:


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.


My comment:


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

Rephrased accordingly.

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.


My comment:


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.


My comments:


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.


My comments:


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.


My comments:


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


Dear 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.


Sinceerely yours,

Yuri Rylov


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,


Chief Editor


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.