In 1905 Einstein developed his theory of special relativity. It was an explanation
of how speed affects mass, time and space. It included a way for the speed of light to define
the relationship between energy and matter. In it he defined that the speed of light was constant.
What many people may not be aware of is that Einstein did not hold this view for
long and would start to develop a theory which would allow for a variable speed of light.
Two years after publishing his paper on special relativity he wrote the following
in a paper on the relativity principle and the conclusions drawn from it:
"These equations too have the same form as the corresponding equations
of the nonaccelerated or gravitation-free space; however, c is here replaced by the
value c[1 + γξ/c²] = c[1 + Φ/c²]. From this, it follows that those light rays
that do not propagate along the ξ-axis are bent by the gravitational field. "
This shows his thinking towards a concept where the velocity of light is altered by
the gravitational potential. In 1911 he wrote a paper on the influence of
gravity on the propagation of light and said the following:
"If c₀ denotes the velocity of light at the coordinate origin, then the velocity of light
c at a point with a gravitational potential Φ will be given by the relation c = c₀(1 + Φ/c²).
The principle of the constancy of the velocity of light does not hold in this theory in the
formulation in which it is normally used as the basis of the ordinary theory of relativity"
Some might claim that Einstein developed his theory of the Variable Speed of light and
then abandoned it but if follow his writings we find he keeps going on about this point:
1912: "On the other hand I am of the view that the principle of the
constancy of the velocity of light can be maintained only insofar as one restricts
oneself to spatio-temporal regions of constant gravitational potential"
1913: "I arrived at the result that the velocity of light is not to be regarded as
independent of the gravitational potential. Thus the principle of the constancy of the
velocity of light is incompatible with the equivalence hypothesis."
1914: "In the case where we drop the postulate of the constancy of the velocity of light,
there exists, a priori, no privileged coordinate system"
1915: "the writer of these lines is of the opinion
that the theory of relativity is still in need of generalisation,
in the sense that the principle of the constancy of the velocity of light is to be abandoned"
1916: "In the second place our result shows that, according to the general theory of relativity,
the law of 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."
1920: "Second, this consequence shows that the law of constancy of the speed
of light no longer holds, according to the general theory of relativity,
in spaces that have gravitational fields. As a simple geometric consideration shows,
the curvature of light rays occurs only in spaces where the speed of light is spatially variable."
Einstein's ideas remained relatively unknown because of a series of coincidences. In 1919
Eddington's solar eclipse observations were seen as a confirmation of Einstein's 1915
form of general relativity where the curvature of spacetime caused a bending of the light.
This overshadows Einstein's continued efforts to have a variable speed of light.
In Einstein's variable speed of light, the bending is caused by the gravitational gradient much like
that of light which is refracted in a dense medium. Einstein attempted to calculate the
deviation using his variable speed of light theory but as he had not considered length scales he got
the incorrect value. It would take until 1957 for Robert Dicke to spot the mistake. In that paper,
Dicke remarked that when he included length scales, the variable speed of
light formulation of general relativity was in agreement with the classical tests.
In the period from the 1920's until the 1960 relativistic physics was in
hibernation mainly due to the fact that theoretical work had
outstripped technology and experimental possibilities, and, as a consequence,
the field stagnated and was relegated to the backwaters of physics and astronomy.
In 1964 Irwin Shapiro wrote an article about the Fourth
Test of General Relativity and said the following:
"Because, according to the general theory, the speed of a light wave depends on the strength
of the gravitational potential along its path, these time delays should thereby
increase by almost sx10^-04 seconds when the radar pulse pass near the sun. Such a change,
equivalent to 60km in distance, could now be measured over the
required path length to within about 5 to 10% with presently obtained equipment."
The first test of this was performed in 1966 when a radar beam was bounced off
the surface of Venus and Mercury and they were able to measure the round trip delay.
It is important to note that in Shapiro's paper he specifically mentions that the speed
of a light wave depends on the strength of the gravitational potential along its path and yet
the Shapiro effect's cause when googled is given as a time delay caused by spacetime dilation,
which increases the time it takes light to travel a given distance. Changing the emphasis
away from the speed of light and back on to the ability of time to flow at a different rate.
Peter Bergmann was Einstein's research assistant in Princeton between 1926 and
1941 and did not agree with Einstein's view on a variable velocity of light.
Bergmann had left this dispute out of his first book on general relativity published
in 1942 this presumably allowed him to get Einstein's endorsement. In 1968,
after Einstein died, he wrote a new book and in it claimed that vector light velocity
could change direction but not speed. Since then this has become the prevailing opinion.
Now you may ask... If the speed of light does vary then surely we would be able to measure this?
Here it is important to understand how we measure the speed of light. In order
to measure the speed we need to be able to measure distance and time. The unit of
time is defined by an oscillating system or the frequency of an atomic transition, and the unit
of space is defined in terms of the distance travelled by light in the unit of time. We,
therefore, have a situation akin to saying that the speed of light is 'one light-year per year'.
To appreciate the circular argument and fallacy in thinking our measure
of time is not directly connected to the speed of
light consider the atomic clock and how it is used to define a second.
Modern caesium clocks form by releasing a gas of caesium atoms into a vacuum chamber.
Six infrared laser beams are directed at right angles to each other at the centre
of the chamber. The lasers are used to push and contain the caesium atoms into a ball.
Two vertical lasers are then used to push the atoms up into a microwave cavity chamber.
Under gravity, the ball of atoms falls back down. Some of the atoms might have changed state. When
they fall back down another laser is pointed at the ball of atoms. All those atoms that did
change state then emit a photon which is counted by a detector. This process is repeated many times
while the frequency in the chamber is changed. Once the resonant frequency of the caesium atom
is achieved and the maximum number of atoms are forced into higher energy states the second can
be defined as the duration of 9,192,631,770 periods of radiation corresponding to the
transition between the two hyperfine levels of the ground state of the caesium 133 atom.
The problem is that in essence we are counting light waves going by and when
you get 9,192,631,770 you say that a second has elapsed. You then use the second along
with the speed of light to define a metre. So the metre is defined as "the length of
the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second"
This concept sets in concrete the idea that the speed of light is fixed but allows for
time variations. Let's just consider what the results might tell us if we
take into consideration that a gravitational potential can slow down the speed of light.
At a lower elevation, we would measure the transition. Light goes slower so that second
should appear to last longer. At higher altitudes, light travels faster and therefore the second will
appear to be shorter. By comparison at a higher altitude, the photon is able to travel quicker
meaning that it is able to reach its count quicker compared to at a lower altitude. Time
has not magically changed just the speed of light allowing for a quicker completion of the count.
Consider as well the definition of the second and the meter at lower elevation.
When the light travels slower the second appears larger but these two exactly
cancel each other out leaving the metre unchanged. So using these definition all
calculations will yield that the speed of light is 299,792,458 m/s. So no matter if
you measure at a lower or higher altitude the answer will always come out to be the same.
As the official measurement of the length of a second is determined by the frequency
needed to make electrons jump between two specific energy levels in a caesium atom
and the metre is defined through the distance light travels in the fraction
determined by the idea of a fixed speed of light it is impossible to measure the
speed of light if the speed of light varies with gravitational potential.
You will always get the same value as speed slows the time increases cancelling each other out.
But the situation is far worse than just the speed of light. The majority of SI units have
definitions that mention either the second or other units defined using the second. So every
base unit with the exception of the mole, and every named derived unit except the Coulomb,
Ohm, Siemens, Weber, Gray, Sievert, Radian, and Steradian have values that
are implicitly defined by properties of the caesium-133 hyperfine transition radiation.
There is no time flowing inside an optical clock. Time cannot flow faster or slower.
An optical clock appears to go slower when it's lower because light goes slower when
it's lower. Light bends around gravitational potentials because of this slowing effect,
similar to the way light rays refract and bend in an optically more dense medium,
but not because some magical fabric if being bent by gravity.
In Einstein's 1920 Leyden Address, he said the following:
“According to this theory the metrical qualities of the continuum of space-time
differ in the environment of different points of space-time, and are partly conditioned by the
matter existing outside of the territory under consideration. This space-time variability of
the reciprocal relations of the standards of space and time, or, perhaps, the recognition
of the fact that ’empty space’ in its physical relation is neither homogeneous nor isotropic,
compelling us to describe its state by ten functions (the gravitation potentials gμν), has,
I think, finally disposed of the view that space is physically empty”.
Einstein didn’t talk about spacetime curvature. Instead, he talked about
space that was neither homogeneous nor isotropic. He finished up by saying this:
“recapitulating, we may say that according to the general theory of relativity space is
endowed with physical qualities; in this sense, therefore, there exists an ether”
He also explicitly talked about “the refraction of light rays by the gravitational field”