🚀 go-pugleaf

On Mar 27, 9:10 am, Pentcho Valev <pva...@yahoo.com> wrote:
> 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."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German (download from:
http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1911_35_898-908.pdf).
It predated the full formal development of general relativity by about
four years. You can find an English translation of this paper in the
Dover book 'The Principle of Relativity' beginning on page 99; 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+phi/c^2) where phi is the gravitational potential
relative to the point where the speed of light co is measured......You
can find a more sophisticated derivation later by Einstein (1955) from
the full theory of general relativity in the weak field
approximation....For the 1955 results but not in coordinates see page
93, eqn (6.28): c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation
shows a variation in km/sec twice as much as first predicted in 1911."

Sooner or later Einsteinians will have to answer the simple question:
The gravitational redshift factor 1+phi/c^2 experimentally confirmed
by Pound and Rebka is consistent with:

(A) Einstein's 1911 equation c'=c(1+phi/c^2) given by Newton's
emission theory of light?

(B) Einstein's 1955 equation c'=c(1+2phi/c^2)?

Then Einsteinians will have to explain why they have been so silent
about this simple problem for so long.

Pentcho Valev
pvalev@yahoo.com