Speed of light is variable says Einstein

On 10 Aug, 17:52, Tom Roberts wrote:
qbit wrote:
To see the steps how Einstein theorized that the speed of light in a
gravitational field is actually not a constant, but rather a variable
depending upon the reference frame of the observer:
'On the Influence of Gravitation on the Propagation of Light',
Annalen der Physik, 35, 1911. Einstein wrote this paper in 1911 in German
http://www.physik.uni-augsburg.de/an...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' = c * (1 + phi / c^2)
Where phi is the gravitational potential relative to the point where
the speed of light c is measured. Simply put:
Light appears to travel slower in stronger gravitational fields (near bigger mass).
[...]

[Bewa Pentcho Valev obsesses about that equation, and
posts endless articles about it around here, ALL WRONG.]

That 1911 article was documenting a portion of Einstein's arduous trek
from SR to GR. The above formula does not hold in GR, except in certain
approximations for specific physical situations; it is not a general
formula at all. In GR, the speed of light (in vacuum) is c in EVERY
locally inertial frame (when measured with standard clocks and rulers).
But due to the curvature of spacetime, when measured over a non-local
distance one can obtain other values. The above formula purports to
describe the speed of light "there" when measured by an observer "here"
-- in GR that in general makes no sense; in the small-field
APPROXIMATION to GR it does make sense, and that formula holds
APPROXIMATELY for certain specific measurements (even in the small-field
approximation it is not a general formula).

So yes, there are cases where the speed of light is not c (in vacuum).
But it is considerably more subtle than you seem to think.

Tom Roberts

Bravo Roberts bravo Tom bravo Albert Einstein of our generation
(Hawking is no longer the Albert Einstein of our generation etc.).
From now on your zombies will know everything about Einstein's 1911
formula

c' = c * (1 + phi / c^2)

and what is even more important Roberts Roberts, your explanation is
so clear and unambiguous that even other hypnotists' zombies will be
able to learn something from it (you used to say Einstein's formula
was wrong but now you do not wish to be so rude). Yet there is a small
detail you forgot to explain clearly and unambiguously: there is an
equivalent formula proved experimentally by Pound and Rebka and
showing how the frequency varies with the gravitational potential:

f' = f * (1 + phi / c^2)

I say the two formulas are "equivalent" because they are related by
the textbook equation

frequency = (speed of light)/(wavelength)

So Roberts Roberts the danger is not over: unless you offer more clear
and unambiguous explanations, even your zombies will find that the two
formulas are JUST TRUE, confirmed by experiment, and will also find,
by applying Einstein's equivalence principle, that

c' = c * (1 + phi / c^2)

is equivalent to

c' = c + v

where c is the initial speed of photons relative to the light source
and v is the relative speed of the light source and the observer, in
the absence of a gravitational field.

Pentcho Valev