VARIABLE SPEED OF LIGHT ON THE HORIZON

http://bogpaper.com/2013/10/06/scien...peed-of-light/
"Einstein started with the constant speed of light in 1905 when he was doing special relativity. But check this out: 1911: "If we call the velocity of light at the origin of coordinates co, then the velocity of light c at a place with the gravitation potential phi will be given by the relation c = co(1 + phi/c^2)". 1912: "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". 1913: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". 1915: "the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned". 1916: "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". (...) Light doesn't curve because it curves, and it doesn't curve because spacetime is curved. Einstein never said that. It curves because the speed of light varies with position."

Einsteinians? Not convinced? See also this:

http://sethi.lamar.edu/bahrim-cristi...t-lens_PPT.pdf
Dr. Cristian Bahrim: "If we accept the principle of equivalence, we must also accept that light falls in a gravitational field with the same acceleration as material bodies."

http://www.wfu.edu/~brehme/space.htm
Robert W. Brehme: "Light falls in a gravitational field just as do material objects."

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..."

And now something awful: If, in a gravitational field, the speed of light varies like the speed of material bodies, then, in gravitation-free space, it varies with the speed of the observer as predicted by Newton's emission theory of light and in violation of special relativity:

http://www.youtube.com/watch?v=FJ2SVPahBzg
"The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."

Integrating dc/dh=g/c gives:

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

Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed:

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

where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with both the gravitational potential and the speed of the observer, just as predicted by Newton's emission theory of light.

Pentcho Valev

http://www.pitt.edu/~jdnorton/teachi...way/index.html
John Norton: "In 1907, Einstein had also concluded that the speed of light, and not just its direction, would be affected by the gravitational field."

It is easy to see that, if the speed of light is "affected by the gravitational field", then, in gravitation-free space, it varies with the speed of the observer, in violation of special relativity. In 1907 Einstein knew that:

http://discovermagazine.com/2004/sep...ns-lonely-path
Lee Smolin: "Few people have appreciated how dissatisfied he was with his own theories of relativity. Special relativity grew out of Einstein's insight that the laws of electromagnetism cannot depend on relative motion and that the speed of light therefore must always be the same, no matter how the source or the observer moves. Among the consequences of that theory are that energy and mass are equivalent (the now-legendary relationship E = mc^2) and that time and distance are relative, not absolute. Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it. He rejected his own theory, even before most physicists had come to accept it, for reasons that only he cared about."

Pentcho Valev

http://www.pitt.edu/~jdnorton/teachi...way/index.html
John Norton: "In 1907, Einstein had also concluded that the speed of light, and not just its direction, would be affected by the gravitational field."

THEOREM: If the speed of light is "affected by the gravitational field", then, in gravitation-free space, it varies with the speed of the observer, in violation of special relativity.

An emitter at the bottom of a tower of height h sends light upwards:

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 frequency measured at the bottom of the tower is f=c/L, where L is the wavelength. The frequency measured by a stationary observer at the top of the tower is:

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

where c'=c-v is the speed of light relative to the observer at the top of the tower. From the equivalence principle, c'=c-v is also the speed of light relative to an observer moving, in gravitation-free space, away from the emitter with speed v (v is assumed to be small so that the relativistic corrections can be ignored).

Clearly the variation of the speed of light in a gravitational field topples special relativity.

Pentcho Valev

An inertial light source emits pulses the distance between which is L (as measured in the source frame).

THEOREM: If L remains unchanged when measured by an inertial observer moving at speed v relative to the source, then the speed of light relative to the observer varies with the speed of the observer, in violation of special relativity.

L obviously remains unchanged - otherwise special relativity would have given the transformation formula L'=f(L,v) which must predict distance-contraction when the observer moves towards the source but distance-elongation when the observer moves away from the source. The formula does not exist and even the Albert Einstein Institute admits that "the distances between subsequent pulses are not affected" by the motion of the receiver/observer:

http://www.einstein-online.info/spotlights/doppler
Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) Here is an animation of the receiver moving towards the source: (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."

Clearly if the receiver/observer is moving towards the source at one third the speed of the pulses themselves, the speed of light as measured by the receiver/observer is (4/3)c, in violation of special relativity. This conclusion is consistent with the classical Doppler effect but one can easily see that the relativistic corrections change essentially nothing - the speed of light relative to the receiver/observer remains different from c.

Pentcho Valev

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."

Substituting f=c/L (L is the wavelength) into Fowler's equation gives:

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

where f' is the frequency measured by both the observer "stationary in the earth's gravitational field" and an equivalent observer who, in gravitation-free space, moves with speed v=gh/c towards the emitter. Accordingly, c'=c+v=c(1+gh/c^2) is the speed of light relative to those two observers.. Clearly the frequency shift is due to a shift in the speed of light - the speed of light varies with both the gravitational potential and the speed of the observer just as predicted by Newton's emission theory of light.

Pentcho Valev