A light source on top of a tower of height h emits light with
frequency f, speed c (relative to the source) and wavelength L. A
receiver on the ground receives light with frequency f', speed
c' (relative to the receiver) and wavelength L'. According to Newton's
emission theory of light:
f'=f(1+gh/c^2); c'=c(1+gh/c^2); L'=L
A rocket of length h accelerates with acceleration g. A light source
at the front end emits light with frequency f, speed c (relative to
the source) and wavelength L. A receiver at the back end receives
light with frequency f', speed c' (relative to the receiver) and
wavelength L'. At the moment of reception, the receiver has speed v
relative to the light source at the moment of emission. According to
Newton's emission theory of light:
f'=f(1+v/c); c'=c+v; L'=L
Einstein did not offer any reasonable alternative to the variation of
the speed of light in a gravitational field predicted by the emission
theory. Initially he was just using the emission theory equation
c'=c(1+gh/c^2), then quite stupidly (or dishonestly) replaced it with
c'=c(1+2gh/c^2). Here "stupidly" and "dishonestly" refer to the fact
that c'=c(1+2gh/c^2) is not consistent with the gravitational redshift
factor advanced by Einstein himself and experimentally confirmed by
Pound and Rebka:
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.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/1911_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."
Since the variability of the speed of light in a gravitational field
is a fundamental tenet of Einstein's general relativity, it would be
extremely difficult to camouflage it in a world where scientific
rationality still exists. In Einsteiniana's schizophrenic world no
camouflage is necessary: Einsteinians simply declare that the speed of
light is constant in a gravitational field and that's it (believers
sing "Divine Einstein" and "Yes we all believe in relativity,
relativity, relativity" all along):
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 Newtons 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&id=64&Itemid=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."
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. 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."
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!
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
***@yahoo.com