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VARIABLE SPEED OF LIGHT IN GRAVITY



 
 
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  #1  
Old December 28th 13, 06:16 PM posted to sci.astro
Pentcho Valev
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Default VARIABLE SPEED OF LIGHT IN GRAVITY

Both Newton's emission theory of light and Einstein's general relativity predict that the speed of light is variable in a gravitational field. However the emission theory gives the right and general relativity the wrong prediction. Here I am going to explain that in detail.

Newton's emission theory of light predicts that, if the top of a tower of height h emits light downwards, the light will fall with the acceleration of ordinary falling matter:

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. (...) 07:56 : (c+dc)/c = 1+(g/c^2)dh [as predicted by Newton's emission theory of light]"

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

http://bouteloup.pierre.free.fr/vulg/relge.pdf
"Considérons une fusée posée sur le sol terrestre, donc immobile dans un champ de gravitation. Déja, à cause du principe d'équivalence, la lumière tombe vers le bas avec la même accélération qu'un caillou, vue par un observateur immobile dans la fusée."

That is, an observer on the ground will measure the speed of the light to be:

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

This means that the frequency measured by the observer on the ground will be:

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

where f=c/L is the initial frequency (measured by an observer at the top of the tower) and L is the wavelength.

The frequency shift predicted by Newton's emission theory of light, f'=f(1+gh/c^2), is exactly the frequency shift that Pound and Rebka measured, that is, their experiment confirmed the emission theory in a straightforward way. Even Einsteinians admit that:

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."

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 general relativity predicts that, if the top of a tower of height h emits light downwards, the light will fall with twice the acceleration of ordinary falling matter. That is, an observer on the ground will measure the speed of the light to be:

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

This shift in the speed of light predicted by general relativity is incompatible with the frequency shift f'=f(1+gh/c^2) measured by Pound and Rebka, given the formula:

(frequency) = (speed of light)/(wavelength)

That is, the Pound-Rebka experiment, while confurming Newton's emission theory of light, has in effect REFUTED GENERAL RELATIVITY.

References showing that, according to Einstein's general relativity, the speed of light varies 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/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)
________________________________________________
[end of quotation]

Pentcho Valev
  #2  
Old January 13th 14, 05:21 PM posted to sci.astro
Pentcho Valev
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Posts: 8,078
Default VARIABLE SPEED OF LIGHT IN GRAVITY

The top of a tower of height h emits light downwards. As the light reaches the ground, its speed relative to the ground is:

A) c' = c(1+gh/c^2) (Newton's emission theory)

B) c' = c(1+2gh/c^2) (Einstein's general relativity)

C) c' = c (Richard Epp, Stephen Hawking, Brian Cox)

where c is the initial speed of the light (relative to the emitter). The frequency as measured by observers on the ground (e.g. Pound and Rebka) is:

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

where f is the initial frequency (as measured by the emitter). Clearly A' is compatible with A and incompatible with B and C. That is, the Pound-Rebka experiment actually confirmed the variation of the speed of light predicted by Newton's emission theory and refuted any different variation.

Pentcho Valev
  #3  
Old January 14th 14, 12:58 PM posted to sci.astro
Pentcho Valev
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Posts: 8,078
Default VARIABLE SPEED OF LIGHT IN GRAVITY

The top of a tower of height h emits light downwards. If, as the light reaches the ground, its speed relative to the ground is:

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

then, in gravitation-free space, as the observer starts moving towards the light source with (small) speed v, the speed of the light relative to the observer shifts from c to:

c' = c + kv

Newton's emission theory of light says k=1.

Einstein's general relativity says k=2.

Richard Epp, Stephen Hawking, Brian Cox and many other Einsteinians say k=0.

Clever Einsteinians know that k=1 is the only reasonable solution, and although they would not discuss the issue explicitly, k=1 is implicit in their interpretations of the gravitational and Doppler frequency shifts:

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. Both special and general relativity are violated.

Pentcho Valev
  #4  
Old January 16th 14, 12:42 PM posted to sci.astro
Pentcho Valev
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Posts: 8,078
Default VARIABLE SPEED OF LIGHT IN GRAVITY

A light source at the bottom of a tower of height h emits light upwards. As the light reaches a stationary receiver at the top of a tower, its speed relative to that receiver is:

A) c' = c(1-gh/c^2) (Newton's emission theory)

B) c' = c(1-2gh/c^2) (Einstein's general relativity)

C) c' = c (Richard Epp, Stephen Hawking, Brian Cox)

The following analysis clearly shows that A is correct while B and C are false predictions:

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 the stationary receiver at the top of the tower is:

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

where c'=c(1-gh/c^2) is the speed of the light relative to that receiver. From the equivalence principle, c'=c(1-gh/c^2)=c-v is also the speed of light relative to an observer/receiver moving, in gravitation-free space, away from the light source with speed v. Clearly both general and special relativity are false.

Pentcho Valev
 




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