VARIABLE SPEED OF LIGHT AFTER ALL

http://galileo.phys.virginia.edu/cla...elativity.html
Michael Fowler, University of Virginia: "What happens if we shine the pulse of light vertically down inside a freely falling elevator, from a laser in the center of the ceiling to a point in the center of the floor? Let us suppose the flash of light leaves the ceiling at the instant the elevator is released into free fall. If the elevator has height h, it takes time h/c to reach the floor. This means the floor is moving downwards at speed gh/c when the light hits. Question: Will an observer on the floor of the elevator see the light as Doppler shifted? The answer has to be no, because inside the elevator, by the Equivalence Principle, conditions are identical to those in an inertial frame with no fields present. There is nothing to change the frequency of the light. This implies, however, that to an outside observer, stationary in the earth's gravitational field, the frequency of the light will change. This is because he will agree with the elevator observer on what was the initial frequency f of the light as it left the laser in the ceiling (the elevator was at rest relative to the earth at that moment) so if the elevator operator maintains the light had the same frequency f as it hit the elevator floor, which is moving at gh/c relative to the earth at that instant, the earth observer will say the light has frequency f(1 + v/c) = f(1+gh/c^2), using the Doppler formula for very low speeds."

That is, the earth observer will measure the speed of light to be c'=f'(lambda)=cf'/f=c(1+gh/c^2), as predicted by Newton's emission theory of light. Equivalently, an observer in gravitation-free space accelerating against the flash of light with acceleration g will measure the speed of light to be c'=f'(lambda)=cf'/f=c+v. Needless to say, this is again a prediction of Newton's emission theory of light.

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."

http://adsabs.harvard.edu/abs/1964AmJPh..32...52O
Redshift and Deflection of Photons by Gravitation: A Comparison of Relativistic and Newtonian Treatments, O'Leary, Austin J., American Journal of Physics, Volume 32, Issue 1, pp. 52-55 (1964): "Gravitational redshift of photons from a star and gravitational bending of the path of photons grazing the sun can be derived by using only Newton's laws and the idea of a photon as a particle of mass hv/c^2. The difference between the relativistic and Newtonian equations for gravitational redshift is too small to be detected and, therefore, gravitational redshift does not provide experimental verification of the general theory of relativity."

But the speed of "a particle of mass hv/c^2" gradually decreases as the particle leaves the gravitational field of the emitter and remains constant but lower than c in gravitation-free space. Therefore, the "gravitational redshift of photons from a star" is a measure of this decrease. The higher the redshift, the lower the speed of the light coming from the star.

Pentcho Valev

http://physics.ucsd.edu/students/cou...ecture5-11.pdf
"Doppler Shift. As long as the velocity of the observer, v, is much smaller than the speed of light, c, (for the case of sound waves much smaller than the speed of sound) then the expression that we derived is a very good approximation. Taking into account v may be in the opposite direction: f'=f(1±v/c). At this point you might ask why the shift in direction from the discussion of the equivalence principle. Soon, as we shall see, we can put this together with the equivalence principle to derive the gravitational redshift of light! 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 receiver travelling at a velocity v=gt measures frequency f'=f(1-v/c)=f(1-gh/c^2), speed of light c' and wavelength L'. These are related by the equation f'=c'/L' which means that only two formulas, c'=c-v and c'=c, can be true insofar as the measured speed of light, c', is concerned:

(A) c' = c-v = c(1-gh/c^2) ; L' = L (Goodbye Einstein: the speed of light as measured by the receiver varies with the speed of the receiver).

(B) c' = c ; L' = L/(1-v/c) = L/(1-gh/c^2) (Goodbye Einstein: c'=c is incompatible with general relativity where the speed of light is VARIABLE and obeys the equation c'=c(1-2gh/c^2)).

Pentcho Valev

http://physics.aps.org/story/v16/st1
"Imagine a pulse of light emitted downward from the top of a cliff just as a diver jumps. By the time the light reaches the ground, the diver will have gained speed and will regard a detector stationed on the ground as moving upward. According to the diver, the light source was stationary when it emitted the pulse, but the detector is racing upwards toward the light pulse at the moment of detection. So the detector should see the light's frequency increased by the Doppler effect. Relativity says that only an observer in freefall, who is weightless and feels no acceleration or gravity, is in an "impartial" reference frame."

As judged from the frame of the diver (the "impartial" reference frame), at the moment of detection the detector is racing upwards with a speed v. So what is the relative speed, c', of the light pulse and the detector at the moment of detection, ACCORDING TO THE DIVER? Both antirelativists and (clever) relativists agree that the diver is correct in seeing the relative speed as variable:

c' = c + v

Accordingly, the diver predicts that the frequency with which the wavefronts hit the detector is:

f' = c'/L = (c + v)/L

where L is the (invariable) wavelength. The equation f'=(c+v)/L has been confirmed by the Pound-Rebka experiment.

Pentcho Valev

The Pound-Rebka experiment confirmed the Newtonian tenet that, as light falls in a gravitational well, its speed increases exactly as the speed of any falling particle does:

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..."

Is this compatibility between the Pound-Rebka experiment and Newton's emission theory of light dangerous for Einstein's theory? Many Einsteinians don't know the answer to that question and teach, just in case, that the speed of light does not increase at all:

http://www.amazon.com/Why-Does-mc2-S.../dp/0306817586
Why Does E=mc2?: (And Why Should We Care?), 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."

Pentcho Valev