Ref.: Ms. No. GERG-D-07-00084
COSMOLOGICAL IMPLICATIONS OF CLASSICAL KALUZA RELATIVITY
General Relativity and Gravitation

Dear Dr williams,

Reviewers' comments on your work have now been received. You will see that they are advising against publication of your work. Therefore I must reject it.

For your guidance, I append the reviewers' comments below.

Thank you for giving us the opportunity to consider your work.

Yours sincerely

George Ellis, Ph.D.
Editor-in-Chief
General Relativity and Gravitation

Reviewers' comments:

Reviewer #1: This paper resurrects Kaluza's original theory without
attempting to address any of the arguments against that theory, which
have long since led to its abandonment. I do not recommend it for
publication in General Relativity and Gravitation.

Briefly:

1) the cylinder condition is imposed "by fiat"; no explanation is
given why the extra coordinate is to be treated differently from the
others. Such a procedure may have been acceptable in 1921, but it
was already out of date by 1926 when Klein provided the first physical
explanation for cylindricity (namely compactification). The author
of the present paper offers no such explanation, instead justifying
the assumption of the cylinder condition as a "minimal form of the
theory which reproduces standard 4D theory." This is not a scientific
approach.

2) even if some mechanism such as compactification is supposed, a
paper reviving Kaluza's theory must address another of the historical
reasons for its abandonment; namely, the hierarchy problem. When one
follows Klein's approach, leading to a hierarchy of "Kaluza-Klein
modes" for every particle, it is natural to hope that the same
hierarchy would account for the quantization of electric charges, as
well as masses of elementary particles. However, the charge-to-mass
ratios of the n=1 modes turn out to be all wrong for describing,
e.g., electrons and protons (as Klein had originally hoped). The
practice later on was instead to associate observed particles with
n=0 modes. These are, however, massless at the level of the field
equations, and one has to go through additional steps to endow them
with mass, so that the whole theory becomes a great deal more
complicated (and, to some perhaps, more artificial).

3) the author seems confused about scalar fields, the third great
reason why Kaluza's idea never caught on historically. In some
places, he seems to want to set the scalar equal to a constant, which
is of course necessary if one wants to get Maxwell electromagnetism
out of Kaluza's theory in 4D. But a scalar field that is everywhere
constant is no scalar at all, and completely artificial from a modern
point of view. (It was occasionally considered in the context of
certain problems, e.g. by Bergmann in his book [Ref. 6], but he
introduced "special coordinate systems" for this purpose, obviously
not a covariant approach.)In other places, the author wants to let
the scalar field vary with time. Then one no longer gets
electromagnetism from the Kaluza mechanism. The author proceeds
nonetheless, and finds that the gravitational "constant" G evolves
like t squared. Such a variation would be in gross disagreement with
observational bounds from, e.g., the Mars Viking lander experiments.

I do not see any way to remedy this paper so as to make it suitable
for publication in GRG. Generations of physicists have wrestled with
Kaluza's beautiful idea in the hope of building a unified theory of
fundamental interactions. Those who would push this work further
must first understand what has gone before.

Reviewer #2:
The author revises the classical Kaluza-Klein theory arguing that
the fifth diagonal element of the metric, a scalar field, is constant
on non-cosmological scales. This, it is claimed, is a natural
consequence of the theory and does not need to be imposed a priori.
The author then studies the cosmological implications of the theory:

-The gravitational constant is directly related to a universal
charge to mass ratio, eq.(16);
-The gravitational constant relates the 5th dimensional coupling of
the electromagnetic field to gravity;
-The electric charge arises from motion along the 5th dimension and
it is not a conserved quantity, eq.(19);
-The scale factor of the universe can vary proportionally to cosmic
time during the radiation dominated epoch.

I worry, however, whether the theory can provide a viable
cosmological scenario. Surely if the scale factor varies
proportionally to the cosmic time during radiation domination, the
rate of expansion must be significantly different from the standard
one at the time of nucleosynthesis which can potentially be dangerous
for the nucleosynthesis predictions of the light elements abundances.