🚀 go-pugleaf

On Sep 13, 10:18 pm, PD <thedraperfam...@gmail.com> wrote:
> On Sep 13, 6:28 am, Pentcho Valev <pva...@yahoo.com> wrote:
>
> > Premise: Einstein's equivalence principle
>
> > Conclusions:
> > If the speed of light varies with the gravitational potential V in
> > accordance with Einstein's 1911 equation c'=c(1+V/c^2) given by
> > Newton's emission theory of light, then the speed of light varies with
> > the speed of the light source v in accordance with the equation c'=c+v
> > given again by Newton's emission theory of light, that is, Einstein's
> > 1905 light postulate is false.
>
> > If the speed of light varies with the gravitational potential V in
> > accordance with Einstein's 1915 equation c'=c(1+2V/c^2), then the
> > speed of light varies with the speed of the light source v in
> > accordance with the equation c'=c+2v, that is, Einstein's 1905 light
> > postulate is false.
>
> Nonsense, Pentcho. The variation of light speed as observed across a
> gravitational potential is clearly a statement made in a non-inertial
> frame.
> The second postulate explicitly refers to the speed of light being
> invariant in *inertial* reference frames.

A light source on top of a tower of height h emits light with
frequency f, speed c (relative to the source) and wavelength L. A
receiver on the ground receives light with frequency f', speed
c' (relative to the receiver) and wavelength L'. According to Newton's
emission theory of light:

f'=f(1+gh/c^2); c'=c(1+gh/c^2); L'=L

A rocket of length h accelerates with acceleration g. A light source
at the front end emits light with frequency f, speed c (relative to
the source) and wavelength L. A receiver at the back end receives
light with frequency f', speed c' (relative to the receiver) and
wavelength L'. At the moment of reception, the receiver has speed v
relative to the light source at the moment of emission. According to
Newton's emission theory of light:

f'=f(1+v/c); c'=c+v; L'=L

Einstein did not offer any reasonable alternative to the variation of
the speed of light in a gravitational field predicted by the emission
theory. Initially he was just using the equation c'=c(1+gh/c^2), then
quite stupidly (or dishonestly) replaced it with c'=c(1+2gh/c^2):

http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is not constant in
a gravitational field [which, by the equivalence principle, applies as
well to accelerating (non-inertial) frames of reference]. If this were
not so, there would be no bending of light by the gravitational field
of stars....Indeed, this is exactly how Einstein did the calculation
in: 'On the Influence of Gravitation on the Propagation of Light,'
Annalen der Physik, 35, 1911. which predated the full formal
development of general relativity by about four years. This paper is
widely available in English. You can find a copy beginning on page 99
of the Dover book 'The Principle of Relativity.' You will find in
section 3 of that paper, Einstein's derivation of the (variable) speed
of light in a gravitational potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."

http://www.mathpages.com/rr/s6-01/6-01.htm
"In geometrical units we define c_0 = 1, so Einstein's 1911 formula
can be written simply as c=1+phi. However, this formula for the speed
of light (not to mention this whole approach to gravity) turned out to
be incorrect, as Einstein realized during the years leading up to 1915
and the completion of the general theory. In fact, the general theory
of relativity doesn't give any equation for the speed of light at a
particular location, because the effect of gravity cannot be
represented by a simple scalar field of c values. Instead, the "speed
of light" at a each point depends on the direction of the light ray
through that point, as well as on the choice of coordinate systems, so
we can't generally talk about the value of c at a given point in a non-
vanishing gravitational field. However, if we consider just radial
light rays near a spherically symmetrical (and non- rotating) mass,
and if we agree to use a specific set of coordinates, namely those in
which the metric coefficients are independent of t, then we can read a
formula analogous to Einstein's 1911 formula directly from the
Schwarzschild metric. (...) In the Newtonian limit the classical
gravitational potential at a distance r from mass m is phi=-m/r, so if
we let c_r = dr/dt denote the radial speed of light in Schwarzschild
coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
equation, except that we have a factor of 2 instead of 1 on the
potential term."

Pentcho Valev
pvalev@yahoo.com