LIGHT IN A GRAVITATIONAL FIELD : NO PLACE FOR EINSTEIN

The top of a tower of height h emits light with frequency f, speed c and wavelength L (as measured by the emitter):

f = c/L

An observer on the ground measures the frequency to be f', the speed of light to be c' and the wavelength to be L':

f' = c'/L'

Crucial questions:

f' = ?

c' = ?

L' = ?

Newton's emission theory of light:

f' = f(1+gh/c^2) (confirmed by Pound and Rebka)

c' = c(1+gh/c^2)

L' = L

No reasonable alternative exists but of course Einsteinians are invited to try to answer the crucial questions. They can choose beween c'=c(1+2gh/c^2), Einstein's original (1915) prediction, and c'=c, a formula taught nowadays.

Pentcho Valev

The Albert Einstein Institute admitting that the gravitational redshift (measured in the Pound-Rebka experiment) is caused by the change in the speed of light predicted by Newton's emission theory of light:

http://www.einstein-online.info/spot...t_white_dwarfs
Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

Pentcho Valev

http://physics.ucsd.edu/students/cou...ecture5-11.pdf
"In 1960 Pound and Rebka and later, 1965, with an improved version Pound and Snider measured the gravitational redshift of light using the Harvard tower, h=22.6m. From the equivalence principle, at the instant the light is emitted from the transmitter, only a freely falling observer will measure the same value of f that was emitted by the transmitter. But the stationary receiver is not free falling. During the time it takes light to travel to the top of the tower, t=h/c, the receiver is traveling at a velocity, v=gt, away from a free falling receiver. Hence the measured frequency is: f'=f(1-v/c)=f(1-gh/c^2)."

The (initial) frequency measured at the bottom of the tower is f=c/L, where L is the wavelength. The frequency measured by the stationary receiver at the top of the tower is:

f' = f(1-gh/c^2) = (c/L)(1-gh/c^2) = c'/L

where c'=c(1-gh/c^2) is the speed of the light relative to that receiver. From the equivalence principle,

c' = c(1-gh/c^2) = c-v

is also the speed of the light relative to an observer/receiver moving, in gravitation-free space, away from the light source with speed v (relative to the source) and measuring the frequency to be f'=f(1-v/c)=f(1-gh/c^2)..

Clearly the Pound-Rebka experiment has refuted both general and special relativity.

Pentcho Valev

Top of a tower of height h emits light with frequency f, speed c and wavelength L (as measured by the emitter):

f = c/L

An observer on the ground measures the frequency to be f', the speed of light to be c' and the wavelength to be L':

f' = c'/L'

Crucial questions:

f' = ?

c' = ?

L' = ?

Newton's emission theory of light:

f' = f(1+gh/c^2) (confirmed by Pound and Rebka)

c' = c(1+gh/c^2)

L' = L

Einstein's general relativity:

f' = f(1+gh/c^2) (confirmed by Pound and Rebka)

c' = c(1+2gh/c^2)

L' = c'/f' (absurd!)

Clearly Einstein's predictions for f' and c' are incompatible. In other words, Einstein's general relativity is an inconsistency. In such cases any experimental confirmation is totally irrelevant:

http://cdn.preterhuman.net/texts/tho...%20science.pdf
W.H. Newton-Smith, THE RATIONALITY OF SCIENCE, 1981, p. 229: "A theory ought to be internally consistent. The grounds for including this factor are a priori. For given a realist construal of theories, our concern is with verisimilitude, and if a theory is inconsistent it will contain every sentence of the language, as the following simple argument shows. Let 'q' be an arbitrary sentence of the language and suppose that the theory is inconsistent.. This means that we can derive the sentence 'p and not-p'. From this 'p' follows. And from 'p' it follows that 'p or q' (if 'p' is true then 'p or q' will be true no matter whether 'q' is true or not). Equally, it follows from 'p and not-p' that 'not-p'. But 'not-p' together with 'p or q' entails 'q'. Thus once we admit an inconsistency into our theory we have to admit everything. And no theory of verisimilitude would be acceptable that did not give the lowest degree of verisimilitude to a theory which contained each sentence of the theory's language and its negation."

References showing that, according to Einstein's general relativity, the speed of light varies in a gravitational field in accordance with the equation c'=c(1+2gh/c^2):

http://arxiv.org/pdf/gr-qc/9909014v1.pdf
Steve Carlip: "It is well known that the deflection of light is twice that predicted by Newtonian theory; in this sense, at least, light falls with twice the acceleration of ordinary "slow" matter."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. (...) ...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. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.ita.uni-heidelberg.de/res...s/JeruLect.pdf
LECTURES ON GRAVITATIONAL LENSING, RAMESH NARAYAN AND MATTHIAS BARTELMANN, p. 3: " The effect of spacetime curvature on the light paths can then be expressed in terms of an effective index of refraction n, which is given by (e.g. Schneider et al. 1992):
n = 1-(2/c^2)phi = 1+(2/c^2)|phi|
Note that the Newtonian potential is negative if it is defined such that it approaches zero at infinity. As in normal geometrical optics, a refractive index n1 implies that light travels slower than in free vacuum. Thus, the effective speed of a ray of light in a gravitational field is:
v = c/n ~ c-(2/c)|phi| "

http://www.mathpages.com/rr/s6-01/6-01.htm
"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=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. (...) ...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://poincare.matf.bg.ac.rs/~rvikt..._Cosmology.pdf
Relativity, Gravitation, and Cosmology, T. Cheng

p.49: This implies that the speed of light as measured by the remote observer is reduced by gravity as

c(r) = (1 + phi(r)/c^2)c (3.39)

Namely, the speed of light will be seen by an observer (with his coordinate clock) to vary from position to position as the gravitational potential varies from position to position.

p.93: Namely, the retardation of a light signal is twice as large as that given in (3.39)

c(r) = (1 + 2phi(r)/c^2)c (6.28)
________________________________________________
[end of quotation]

Pentcho Valev