EINSTEIN'S VARIABLE SPEED OF LIGHT

[Pentcho Valev]

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."

Today's Einsteinians admit that Einstein's variable speed of light "is perfectly valid and makes good physical sense" but teach that after Einstein the speed of light became constant and is going to remain so forever:

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."

Pentcho Valev

[Pentcho Valev]

A confession that kills Einstein's relativity instantaneously:

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."

This fast fall is incompatible with the Pound-Rebka experiment.

Pentcho Valev

[Pentcho Valev]

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)

Since (A) is a prediction of Newton's emission theory of light, (B) must be a prediction of Einstein's general relativity. Yet it is not - for c' general relativity predicts:

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

which means that general relativity is actually refuted by the Pound-Rebka experiment.

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/research/bartelmann/Publications/Proceedings/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 n>1 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/~rviktor/kosmologija/Relativity_Gravitation_and_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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[end of quotation]

Pentcho Valev

[Pentcho Valev]

http://www.einstein-online.info/spotlights/redshift_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..."

That is, if in a gravitational field the speed of photons varies as the speed of ordinary falling objects, the resulting frequency shift will be that measured by Pound and Rebka. In this sense the Pound-Rebka experiment was consistent with the variable speed of light predicted by Newton's emission theory of light. In other words, in the gravitational field of the Earth, the experiment was consistent with acceleration g for photons.

Einstein's general relativity predicts a faster change of the speed of light - in the gravitational field of the Earth photons will fall with acceleration 2g, not just g:

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."

Needless to say, the Pound-Rebka experiment cannot be consistent with both g (Newton) and 2g (Einstein). Newton is right, Einstein is wrong.

Pentcho Valev

[Pentcho Valev]

http://www.relativitycalculator.com/pdfs/On_the_influence_of_Gravitation_on_the_Propagation_of_Light_English.pdf
On the Influence of Gravitation on the Propagation of Light, by A. Einstein. Annalen der Physik, 35, pp. 898-908, 1911: "...If we call the velocity of light at the origin of coordinates c_o, then the velocity of light c at a location with the gravitation potential phi will be given by the relation c = c_o(1+phi/c^2)."

Einstein plagiarized this (correct) equation from Newton's emission theory of light - the equation actually says that, in a gravitational field, the speed of light varies like the speed of ordinary falling matter. Then in the final 1915 version of general relativity the speed of light in a gravitational field became two times more variable than the speed of ordinary matter - the correct equation c = c_o(1+phi/c^2) was replaced by the absurd equation c = c_o(1+2phi/c^2). This greater variability of the speed of light predicted by general relativity is a grand secret between knowledgeable Einsteinians (I have found only a few references on internet where the secret is revealed). Most Einsteinians neither know nor care about it - they find it easier to teach that the speed of light in a gravitational field is constant, Divine Einstein, yes we all believe in relativity, relativity, relativity, that's the way ahah ahah we like it, ahah ahah:

http://www.oapt.ca/newsletter/2004-02%20Newsletter%20Searchable.pdf
Richard Epp: "One may imagine the photon losing energy as it climbs against the Earth's gravitational field much like a rock thrown upward loses kinetic energy as it slows down, the main difference being that the photon does not slow down; it always moves at the speed of light."

http://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168
Stephen Hawking, A Brief History of Time, Chapter 6: "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.amazon.com/Why-Does-mc2-Should-Care/dp/0306817586
Brian Cox, Jeff Forshaw, p. 236: "If the light falls in strict accord with the principle of equivalence, then, as it falls, its energy should increase by exactly the same fraction that it increases for any other thing we could imagine dropping. We need to know what happens to the light as it gains energy. In other words, what can Pound and Rebka expect to see at the bottom of their laboratory when the dropped light arrives? There is only one way for the light to increase its energy. We know that it cannot speed up, because it is already traveling at the universal speed limit, but it can increase its frequency."

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