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On May 9, 4:54 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote in
sci.physics.relativity:
> mluttg...@orange.fr wrote:
> > one can quibble 'ad nauseam'
> > about the relativistic mass of the photon.
> > http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence:
> > "Even a single photon traveling in empty space has a relativistic
> > mass, which is its energy divided by c2."
>
> > One can quibble about such claim, but the relativistic mass
> > m = E/c^2 = hNu/c^2 of the photon can be used to interpret
> > results of a series of experiments, for instance those obtained
> > by Pound & Rebka.
>
> Certainly a photon has a non-zero "relativistic mass". Just remember
> that "relativistic mass" does NOT refer to what we now mean by mass, but
> rather is a synonym for ENERGY. The name "relativistic mass" is an
> anachronism, coined in the past, before the subtleties were fully
> understood; in the manner of textbooks it lives on in elementary
> discussions.
>
> Tom Roberts

Honest Roberts why don't you abandon all those red herrings? Just
choose between (1) and (2) below:

(1) The photon behaves like all massive particles: in a gravitational
field, its speed varies in accordance with Einstein's 1911 equation
c'=c(1+V/c^2) given by Newton's emission theory of light:

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.blazelabs.com/f-g-gcont.asp
"So, faced with this evidence most readers must be wondering why we
learn about the importance of the constancy of speed of light. Did
Einstein miss this? Sometimes I find out that what's written in our
textbooks is just a biased version taken from the original work, so
after searching within the original text of the theory of GR by
Einstein, I found this quote: "In the second place our result shows
that, according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
and to which we have already frequently referred, cannot claim any
unlimited validity. A curvature of rays of light can only take place
when the velocity of propagation of light varies with position. Now we
might think that as a consequence of this, the special theory of
relativity and with it the whole theory of relativity would be laid in
the dust. But in reality this is not the case. We can only conclude
that the special theory of relativity cannot claim an unlimited domain
of validity ; its results hold only so long as we are able to
disregard the influences of gravitational fields on the phenomena
(e.g. of light)." - Albert Einstein (1879-1955) - The General Theory
of Relativity: Chapter 22 - A Few Inferences from the General
Principle of Relativity-. Today we find that since the Special Theory
of Relativity unfortunately became part of the so called mainstream
science, it is considered a sacrilege to even suggest that the speed
of light be anything other than a constant. This is somewhat
surprising since even Einstein himself suggested in a paper "On the
Influence of Gravitation on the Propagation of Light," Annalen der
Physik, 35, 1911, that the speed of light might vary with the
gravitational potential. Indeed, the variation of the speed of light
in a vacuum or space is explicitly shown in Einstein's calculation for
the angle at which light should bend upon the influence of gravity.
One can find his calculation in his paper. The result is c'=c(1+V/c^2)
where V is the gravitational potential relative to the point where the
measurement is taken. 1+V/c^2 is also known as the GRAVITATIONAL
REDSHIFT FACTOR."

(2) The photon is more sensitive to gravity than ordinary massive
particles: in a gravitational field, its speed varies in accordance
with Einstein's 1915 (or 1955) equation c'=c(1+2V/c^2):

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."

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