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If the speed of the photon varies with the gravitational potential V
in conformity with the equation c'=c(1+V/c^2), then, in a sense, the
photon behaves like a cannonball and its speed will vary with the
speed of the light source v in conformity with the equation c'=c+v.

In 1911 Divine Albert explicitly established the truth of the
antecedent and he also knew that, by applying the equivalence
principle, one would be able to easily prove the validity of the above
conditional:

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."

So in 1911 Divine Albert badly needed a new protective belt that would
deflect any attack against his 1905 false light postulate, an attack
relying on the variability of the speed of light in a gravitational
field. And he did build a new belt: GRAVITATIONAL TIME DILATION. This
protective belt presupposes that rates of clocks vary with the
gravitational potential while the speed of light remains constant.

Nowadays only silly Einsteinians insist that the speed of light is
constant in a gravitational field. Einsteiniana's highest priests
admit the variability but know that any hint at Einstein's 1911
protective belt makes this variability harmless:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
". . . 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
[. . .] 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." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. (...) In general
relativity, the appropriate generalisation is that the speed of light
is constant in any freely falling reference frame (in a region small
enough that tidal effects can be neglected).  In this passage,
Einstein is not talking about a freely falling frame, but rather about
a frame at rest relative to a source of gravity.  In such a frame, the
speed of light can differ from c, basically because of THE EFFECT OF
GRAVITY (spacetime curvature) ON CLOCKS and rulers."

Pentcho Valev wrote:

http://bertie.ccsu.edu/~dsb/naturesci/PhilSci/Lakatos.html
"Lakatos distinguished between two parts of a scientific theory: its
"hard core" which contains its basic assumptions (or axioms, when set
out formally and explicitly), and its "protective belt", a surrounding
defensive set of "ad hoc" (produced for the occasion) hypotheses.
(...) In Lakatos' model, we have to explicitly take into account the
"ad hoc hypotheses" which serve as the protective belt. The protective
belt serves to deflect "refuting" propositions from the core
assumptions..."

http://www.physics.queensu.ca/~phys242/Section2_3.pdf
"Because the GTs [Galilean transformations] are clearly not consistent
with Einstein's two postulates, we are going to have to develop a new
set of transformations: the Lorentz transformations."

Historically the protective belt (Lorentz transformations) was created
before the hard core (Divine Albert's 1905 postulates). Without the
protective belt, Divine Albert's postulates (more precisely, his light
postulate) would have been immediately refuted by the Michelson-Morley
experiment:

http://philsci-archive.pitt.edu/archive/00001743/02/Norton.pdf
John Norton: "Einstein regarded the Michelson-Morley experiment as
evidence for the principle of relativity, whereas later writers almost
universally use it as support for the light postulate of special
relativity......THE MICHELSON-MORLEY EXPERIMENT IS FULLY COMPATIBLE
WITH AN EMISSION THEORY OF LIGHT THAT CONTRADICTS THE LIGHT
POSTULATE."

http://books.google.com/books?id=JokgnS1JtmMC
"Relativity and Its Roots" By Banesh Hoffmann
p.92: "Moreover, if light consists of particles, as Einstein had
suggested in his paper submitted just thirteen weeks before this one,
the second principle seems absurd: A stone thrown from a speeding
train can do far more damage than one thrown from a train at rest; the
speed of the particle is not independent of the motion of the object
emitting it. And if we take light to consist of particles and assume
that these particles obey Newton's laws, they will conform to
Newtonian relativity and thus automatically account for the null
result of the Michelson-Morley experiment without recourse to
contracting lengths, local time, or Lorentz transformations. Yet, as
we have seen, Einstein resisted the temptation to account for the null
result in terms of particles of light and simple, familiar Newtonian
ideas, and introduced as his second postulate something that was more
or less obvious when thought of in terms of waves in an ether."

James H. Smith "Introduction à la relativité" EDISCIENCE 1969 pp.
39-41: "Si la lumière était un flot de particules mécaniques obéissant
aux lois de la mécanique, il n'y aurait aucune difficulté à comprendre
les résultats de l'expérience de Michelson-Morley.... Supposons, par
exemple, qu'une fusée se déplace avec une vitesse (1/2)c par rapport à
un observateur et qu'un rayon de lumière parte de son nez. Si la
vitesse de la lumière signifiait vitesse des "particules" de la
lumière par rapport à leur source, alors ces "particules" de lumière
se déplaceraient à la vitesse c/2+c=(3/2)c par rapport à
l'observateur. Mais ce comportement ne ressemble pas du tout à celui
d'une onde, car les ondes se propagent à une certaine vitesse par
rapport au milieu dans lequel elles se développent et non pas à une
certaine vitesse par rapport à leur source..... Il nous faut insister
sur le fait suivant: QUAND EINSTEIN PROPOSA QUE LA VITESSE DE LA
LUMIERE SOIT INDEPENDANTE DE CELLE DE LA SOURCE, IL N'EN EXISTAIT
AUCUNE PREUVE EXPERIMENTALE. IL LE POSTULA PAR PURE NECESSITE
LOGIQUE."

Pentcho Valev
pvalev@yahoo.com