EINSTEIN : VARIABLE SPEED OF LIGHT IN GRAVITY

http://bartleby.net/173/22.html
Albert Einstein: "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."

The top of a tower of height h emits light with (initial) speed c, wavelength L and frequency f=c/L. An observer on the ground measures the speed to be c', the wavelength L' and the frequency:

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

the last result confirmed by the Pound-Rebka experiment. For c' and L' the following two combinations are conceivable:

(A) c' = c(1+gh/c^2) ; L' = L

(B) c' = c ; L' = L/(1+gh/c^2)

Which combination - A or B - is compatible with Einstein's text? Is there a third combination? Einsteinians?

Pentcho Valev

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..."

http://courses.physics.illinois.edu/...ctures/l13.pdf
University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values.. This is known as the gravitational red shift of light."

The top of a tower of height h emits light with (initial) speed c, wavelength L and frequency f=c/L. An observer on the ground measures the speed to be c', the wavelength L' and the frequency:

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

the last result confirmed by the Pound-Rebka experiment. For c' and L' the following two combinations are conceivable:

(A) c' = c(1+gh/c^2) ; L' = L

(B) c' = c ; L' = L/(1+gh/c^2)

Which combination - A or B - is compatible with the above two quotations? Is there a third combination? Einsteinians?

Pentcho Valev

http://www.youtube.com/watch?v=FJ2SVPahBzg
Video: "The light is perceived to be falling in a gravitational field just like a mechanical object would."

http://bartleby.net/173/22.html
Albert Einstein: "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."

Are the video and Einstein's text compatible?

The top of a tower of height h emits light with (initial) speed c, wavelength L and frequency f=c/L. An observer on the ground measures the speed to be c', the wavelength L' and the frequency:

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

the last result confirmed by the Pound-Rebka experiment. For c' and L' the following two combinations are conceivable:

(A) c' = c(1+gh/c^2) ; L' = L

(B) c' = c ; L' = L/(1+gh/c^2)

Which combination - A or B - is compatible with the above video? Is there a third combination? Einsteinians?

Pentcho Valev

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'=f(1+gh/c^2) (confirmed by Pound and Rebka), the speed of light to be c' and the wavelength to be L':

f' = c'/L'

Crucial questions:

c' = ?

L' = ?

Newton's emission theory of light says:

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

L' = c'/f' = L

Einstein's general relativity says:

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

L' = c'/f' L

The increase in wavelength (L'L) implied by general relativity is obviously absurd, which means that the Pound-Rebka experiment has actually confirmed Newton and refuted Einstein.

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

http://arxiv.org/ftp/arxiv/papers/1111/1111.6986.pdf
J.D. Franson, Physics Department, University of Maryland: "According to general relativity, the speed of light c as measured in a global reference frame is given by c=c0(1+2phi/c0^2), where c0 is the speed of light as measured in a local freely-falling reference frame."

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)
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Pentcho Valev