Einsteinium's Lunacy-5
Do photons and cannonballs undergo the same acceleration in a
gravitational field? In the period 1907-1914 Einstein's answer was an
unambiguous "yes". However this meant that Newton's emission theory
of
light was correct: it is easy to show that, if the speeds of the
photon and the cannonball vary in the same way in a gravitational
field, then they vary in the same way in the absence of a
gravitational field. Precisely, both speeds obey the equation c'=c+v,
where c' is the speed of the photon/cannonball relative to the
observer, c is the speed of the photon/cannonball relative to the
emitter and v is the speed of the emitter relative to the observer.
In his 1915 (final) version of general relativity Einstein found it
pertinent to inform future believers that, in a gravitational field,
photons accelerate faster than cannonballs by a factor of two:
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/191...
). 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."
In the era of Postscientism believers do not express doubts but feel
uneasy sometimes:
"Divine Albert says that massless photons accelerate faster than
cannonballs?!?"
Einsteiniana's priests find this uneasiness dangerous and disperse it
by fiercely confusing believers' minds: some teach that in a
gravitational field the speed of light is variable, others that in a
gravitational field the speed of light is constant, Steve Carlip
teaches that in a gravitational field the speed of light is both
variable and constant:
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."
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.amazon.com/Brief-History-Time-Stephen-Hawking/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?option=com_content&view=article&i...
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."
http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes
effects
such as gravitational lensing), and it can change the energy of
light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_o...
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved
Pentcho Valev