Initially Newton the Villain managed to convince Divine Albert that,
in a gravitational field, the speed of photons varies in exactly the
same way that the speed of cannonballs does:
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."
Then in 1915 the situation became unbearable: Divine Albert was still
unable to offer a better formula and outdo Newton the Villain. In
despair, Divine Albert suddenly declared: "The speed of photons varies
twice as fast as the speed of cannonballs and that's it!":
http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. 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. (...) ...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."
Today's high priests in Einsteiniana don't like Divine Albert's 1915
panicky decision to make the speed of photons vary faster than the
speed of cannonballs. They simply teach: "In both the presence and
absence of a gravitational field, the speed of photons is constant and
that's it!":
http://www.amazon.com/Brief-History-.../dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 6:
"Under the theory that light is made up of waves, it was not clear how
it would respond to gravity. But if light is composed of particles,
one might expect them to be affected by gravity in the same way that
cannonballs, rockets, and planets are.....In fact, it is not really
consistent to treat light like cannonballs in Newton's theory of
gravity because the speed of light is fixed. (A cannonball fired
upward from the earth will be slowed down by gravity and will
eventually stop and fall back; a photon, however, must continue upward
at a constant speed...)"
http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Is c, the speed of light in vacuum, constant? At the
1983 Conference Generale des Poids et Mesures, the following SI
(Systeme International) definition of the metre was adopted: The metre
is the length of the path travelled by light in vacuum during a time
interval of 1/299 792 458 of a second. This defines the speed of light
in vacuum to be exactly 299,792,458 m/s. This provides a very short
answer to the question "Is c constant": Yes, c is constant by
definition! (...) 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. This interpretation
is perfectly valid and makes good physical sense, but a more modern
interpretation is that the speed of light is constant in general
relativity."
Believers invariably sing "Divine Einstein" and "Yes we all believe in
relativity, relativity, relativity":
http://www.haverford.edu/physics/songs/divine.htm
No-one's as dee-vine as Albert Einstein
Not Maxwell, Curie, or Bohr!
He explained the photo-electric effect,
And launched quantum physics with his intellect!
His fame went glo-bell, he won the Nobel --
He should have been given four!
No-one's as dee-vine as Albert Einstein,
Professor with brains galore!
No-one could outshine Professor Einstein --
Egad, could that guy derive!
He gave us special relativity,
That's always made him a hero to me!
Brownian motion, my true devotion,
He mastered back in aught-five!
No-one's as dee-vine as Albert Einstein,
Professor in overdrive!
http://www.youtube.com/watch?v=5PkLLXhONvQ
We all believe in relativity, relativity, relativity.
Yes we all believe in relativity, 8.033, relativity.
Einstein's postulates imply
That planes are shorter when they fly.
Their clocks are slowed by time dilation
And look warped from aberration.
We all believe in relativity, relativity, relativity.
Yes we all believe in relativity, 8.033, relativity.
Pentcho Valev