CONSERVAPEDIA: COUNTEREXAMPLES TO RELATIVITY

Recently a Conservapedia entry stirred a controversy and Einsteinians
(those who don't know how to leave the sinking ship) felt uneasy:

http://conservapedia.com/Counterexamples_to_Relativity
Conservapedia: "Here is a list of 29 counterexamples: any one of them
shows that the theory [of relativity] is incorrect."

When a theory is an inconsistency, that is, when it makes
contradictory statements, it does not make much sense to look for
counterexamples (a counterexample to which one of the, say, three
incompatible statements made by the theory?). Imagine you have some
independent evidence showing how the speed of light varies with the
gravitational potential, and you want to use it as a counterexample
against Einstein's general relativity. But what does Einstein's
general relativity say about the variation of th speed of light in a
gravitational field? By searching in Internet, you may find
Einsteiniana's experts saying that the speed of light varies with the
gravitational potential in accordance with the equation c'=c(1+V/c^2)
given by Newton's emission theory of light and consistent with the
Pound-Rebka experiment showing that the frequency varies in accordance
with f'=f(1+V/c^2):

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."

Other experts of Einsteiniana would teach you that c'=c(1+V/c^2) is
wrong; in 1915 Einstein made the speed of light even more variable in
a gravitational field:

http://blogs.discovermagazine.com/co...ity-and-light/
"One of the most interesting predictions of Einstein's new theory of
relativity was that gravity would cause light to bend." I think it is
worth mentioning that the bending of light due to gravity was NOT a
prediction of general relativity. As early as 1704 in his Opticks,
Newton predicted the effect. However, the speed of light was not known
a the time (or even whether it was finite) so no quantitative
prediction could be made. This was rectified by the end of the 18th
century and the Newtonian calculation could be made, though
experimental limitations forbade any test at the time. In 1911
Einstein applied his early ideas of relativistic gravity to the
problem and got the same answer as the Newtonian model. In 1915, when
his theory was approaching completion, he realised the earlier
calculation was wrong, and the deviation of light should be twice the
Newtonian value."

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."

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/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'=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."

Then Stephen Hawking, the Albert Einstein of our generation, will
explain to you that, in a gravitational field, the speed of light is
not variable at all - the Michelson-Morley experiment has disproved
any variability. So, gravitational field or no gravitational field,
the speed of light 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://www.hawking.org.uk/index.php?...64&It emid=66
Stephen Hawking: "Interestingly enough, Laplace himself wrote a paper
in 1799 on how some stars could have a gravitational field so strong
that light could not escape, but would be dragged back onto the star.
He even calculated that a star of the same density as the Sun, but two
hundred and fifty times the size, would have this property. But
although Laplace may not have realised it, the same idea had been put
forward 16 years earlier by a Cambridge man, John Mitchell, in a paper
in the Philosophical Transactions of the Royal Society. Both Mitchell
and Laplace thought of light as consisting of particles, rather like
cannon balls, that could be slowed down by gravity, and made to fall
back on the star. But a famous experiment, carried out by two
Americans, Michelson and Morley in 1887, showed that light always
travelled at a speed of one hundred and eighty six thousand miles a
second, no matter where it came from. How then could gravity slow down
light, and make it fall back."

Stephen Hawking's ideas are further deveoped by other experts of
Einsteinana who will explain to you that the speed of light is not the
only constant - the frequency is constant as well (poor Pound and
Rebka - what did they measure?):

http://www.answers.com/topic/gravitational-redshift
"The gravitational weakening of light from high-gravity stars was
predicted by John Michell in 1783 and Pierre-Simon Laplace in 1796,
using Isaac Newton's concept of light corpuscles (see: emission
theory) and who predicted that some stars would have a gravity so
strong that light would not be able to escape. The effect of gravity
on light was then explored by Johann Georg von Soldner (1801), who
calculated the amount of deflection of a light ray by the sun,
arriving at the Newtonian answer which is half the value predicted by
general relativity. All of this early work assumed that light could
slow down and fall, which was inconsistent with the modern
understanding of light waves. Once it became accepted that light is an
electromagnetic wave, it was clear that the frequency of light should
not change from place to place, since waves from a source with a fixed
frequency keep the same frequency everywhere."

Finally, Steve Carlip, another Albert Einstein of our generation, will
put an end to your qualms by explaining to you that, in a
gravitational field, the speed of light is both variable and constant:

http://math.ucr.edu/home/baez/physic..._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. 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."

Pentcho Valev