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On Mar 27, 9:10 am, Pentcho Valev <pva...@yahoo.com> wrote:
> 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 equation c'=c(1+gh/c^2), then
> quite stupidly (or dishonestly) replaced it with c'=c(1+2gh/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."
>
> 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."

In 1915 Einstein knew how to "outdo" Newton (by replacing the equation
c'=c(1+gh/c^2) given by Newton's emission theory of light with the
silly equation c'=c(1+2gh/c^2)) but in 1911 he was still desperately
trying to camouflage his involuntary allegiance to the emission
theory. So in 1911 Einstein devised "gravitational time dilation": an
absurd concept implying that, in a gravitational field, the frequency
and the wavelength change but the speed of light remains constant.
Spin-offs from this particular camouflage of Einstein's:

http://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 2:
"Another prediction of general relativity is that time should appear
to slower near a massive body like the earth. This is because there is
a relation between the energy of light and its frequency (that is, the
number of waves of light per second): the greater the energy, the
higher frequency. As light travels upward in the earth’s gravitational
field, it loses energy, and so its frequency goes down. (This means
that the length of time between one wave crest and the next goes up.)
To someone high up, it would appear that everything down below was
making longer to happen. This prediction was tested in 1962, using a
pair of very accurate clocks mounted at the top and bottom of a water
tower. The clock at the bottom, which was nearer the earth, was found
to run slower, in exact agreement with general relativity. The
difference in the speed of clocks at different heights above the earth
is now of considerable practical importance, with the advent of very
accurate navigation systems based on signals from satellites. If one
ignored the predictions of general relativity, the position that one
calculated would be wrong by several miles! (...) Consider a pair of
twins. Suppose that one twin goes to live on the top of a mountain
while the other stays at sea level. The first twin would age faster
than the second. Thus, if they met again, one would be older than the
other."

http://www.astronomynotes.com/relativity/s4.htm
"Prediction: light escaping from a large mass should lose energy---the
wavelength must increase since the speed of light is constant.
Stronger surface gravity produces a greater increase in the
wavelength. This is a consequence of time dilation. Suppose person A
on the massive object decides to send light of a specific frequency f
to person B all of the time. So every second, f wave crests leave
person A. The same wave crests are received by person B in an interval
of time interval of (1+z) seconds. He receives the waves at a
frequency of f/(1+z). Remember that the speed of light c = (the
frequency f) (the wavelength L). If the frequency is reduced by (1+z)
times, the wavelength must INcrease by (1+z) times: L_atB = (1+z)
L_atA. In the doppler effect, this lengthening of the wavelength is
called a redshift. For gravity, the effect is called a gravitational
redshift."

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

Pentcho Valev
pvalev@yahoo.com