LIGHT FALLS WITH TWICE THE ACCELERATION OF ORDINARY MATTER ?

http://arxiv.org/pdf/gr-qc/9909014v1.pdf
Steve Carlip: "Light falls with twice the acceleration of ordinary matter."

If so, the Pound-Rebka experiment refutes Einstein's general relativity and confirms Newton's emission theory of light:

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) (the Pound-Rebka experiment), the speed of light to be c' and the wavelength to be L':

f' = c'/L'

The crucial questions a

c' = ? ; L' = ?

Newton's emission theory of light gives a straightforward answer:

Newton's answer: c' = c(1+gh/c^2) ; L' = L

Einstein's general relativity says that c'=c(1+2gh/c^2) ("Light falls with twice the acceleration of ordinary matter") so we have:

Einstein's answer: c'=c(1+2gh/c^2) ; L' = (c(1+2gh/c^2))/(f(1+gh/c^2))

Obviously, and Einsteinians admit that, Newton's answer is reasonable:

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..."

Einstein's answer is absurd - the idiotic variation of the wavelength with height has no physical justification.

Desperate Einsteinians may see some hope in the hypothesis that Steve Carlip's statement "Light falls with twice the acceleration of ordinary matter" is a joke, or, equivalently, the hypothesis that general relativity does not predict anything like c'=c(1+2gh/c^2). Here are references for them:

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.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."

Pentcho Valev

General relativity does indeed predict that, in a gravitational field, the speed of light varies twice as fast as the speed of ordinary matter. Yet the (Newtonian) truth is that the two variations are identical - the variation of the speed of light obeys the equation c'=c(1+gh/c^2) given by Newton's emission theory of light and explicitly used by Einstein in 1911. In the final version of general relativity however there is a factor of 2 on the potential term (c'=c(1+2gh/c^2)):

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| "

The Newtonian equation c'=c(1+gh/c^2) is obviously consistent with the frequency shift f'=f(1+gh/c^2) measured in the Pound-Rebka experiment. The Einsteinian equation c'=c(1+2gh/c^2) is obviously inconsistent with this frequency shift.

Pentcho Valev

Triplethink in Divine Albert's world:

1. The speed of light is constant in a gravitational field, c'=c, Divine Einstein, yes we all believe in relativity, relativity, relativity:

http://www.oapt.ca/newsletter/2004-0...Searchable.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-.../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-S.../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."

2. In a gravitational field, the speed of light varies like the speed of ordinary falling objects, c'=c(1+gh/c^2) (Einsteinians don't sing here - this is Newton's emission theory of light):

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."

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.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."

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

3. In a gravitational field, the speed of light varies twice as fast as the speed of ordinary falling objects, c'=c(1+2gh/c^2), Divine Einstein, yes we all believe in relativity, relativity, relativity:

http://arxiv.org/pdf/gr-qc/9909014v1.pdf
Steve Carlip: "Light falls with twice the acceleration of ordinary 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://images.techiezlounge.com/post/2010/09/7.jpg

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 (measured in the Pound-Rebka experiment) confirms the variable speed of light predicted by Newton's emission theory of light. This frequency shift is inconsistent with both the variable speed of light c'=c(1+2gh/c^2) predicted by Einstein's general relativity and the constant speed of light c'=c fiercely taught by Einsteinians all over the world.

Pentcho Valev