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.*

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*

*work.*

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

manuscript.

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.*