HOW DOES THE SPEED OF LIGHT VARY IN GRAVITY, EINSTEINIANS ?

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

f' = c'/L'

Crucial questions:

c' = ?

L' = ?

Newton's emission theory of light (the speed of falling light varies just as the speed of ordinary falling objects):

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

L' = c'/f' = L

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..."

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."

Einstein's general relativity (the speed of falling light varies twice as fast as the speed of ordinary falling objects):

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

L' = c'/f' L

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."

The increase in wavelength (L'L) the superacceleration predicted by general relativity implies is obviously absurd, which means that the Pound-Rebka experiment has actually confirmed Newton and refuted Einstein.

Today's Einsteinians teach:

c' = c

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

This interpretation suffers from two fatal drawbacks:

1. It has nothing to do with Einstein's general relativity.

2. The wavelength shift, from L to L'=L/(1+gh/c^2), is an ad hoc fabrication whose only function is to reconcile c'=c to f'=f(1+gh/c^2).

Pentcho Valev

That the speed of photons falling in a gravitational field varies like the speed of ordinary falling objects (as predicted by Newton's emission theory of light) is so obvious that many Einsteinians cannot help but admit it:

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."

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."

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. Déjà, 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."

On the other hand, the fact that the emission theory is so obviously correct (and Einstein's relativity so obviously wrong) forces Einsteiniana's priests to adopt extraordinary camouflage. Most of them teach that the speed of light is constant in a gravitational field, knowing that the acceleration of photons predicted by Einstein's relativity is twice the acceleration of ordinary falling objects:

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."

http://helios.gsfc.nasa.gov/qa_sp_gr.html
Dr. Eric Christian: "Is light affected by gravity? If so, how can the speed of light be constant? Wouldn't the light coming off of the Sun be slower than the light we make here? If not, why doesn't light escape a black hole? Yes, light is affected by gravity, but not in its speed. General Relativity (our best guess as to how the Universe works) gives two effects of gravity on light. It can bend light (which includes effects such as gravitational lensing), and it can change the energy of light. But it changes the energy by shifting the frequency of the light (gravitational redshift) not by changing light speed. Gravity bends light by warping space so that what the light beam sees as "straight" is not straight to an outside observer. The speed of light is still constant."

The champion is Steve Carlip who admits that Einstein's variable speed of light "is perfectly valid and makes good physical sense" but teaches that after Einstein the speed of light in a gravitational field somehow became constant (and is going to remain so forever):

http://www.desy.de/user/projects/Phy..._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

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."

http://www.desy.de/user/projects/Phy..._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. (...) In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers."

Clever Einsteinians know that, if a stationary (relative to the source of gravity) observer measures the speed of light to be different from c, then, in accordance with the equivalence principle, in gravitation-free space, some moving observer also measures the speed of light to be different from c. In other words, if the speed of light "varies with position" in a gravitational field, then it varies with the speed of the observer in gravitation-free space.

The equivalence of "speed of light varies with position in gravitational field" and "speed of light varies with speed of observer in gravitation-free space" is relatively easy to see so excessive brainwashing is needed if Einsteinians wish to minimize the danger and safely sing "Divine Einstein" and "Yes we all believe in relativity, relativity, relativity". Recently it has been realized that Steven Carlip's article "Is The Speed of Light Constant?" referred to above, although being a paradigm of successful brainwashing, could still be improved. Don Koks, an even more skilful brainwasher than Steven Carlip, perfected it in the following way:

http://math.ucr.edu/home/baez/physic..._of_light.html
Don Koks: "That the speed of light depends on position when measured by a non-inertial observer is a fact... (...) So consider the question: "Can we say that light confined to the vicinity of the ceiling of this room is travelling faster than light confined to the vicinity of the floor?". For simplicity, let's take Earth as not rotating, because that complicates the question! The answer is then that (1) an observer stationed on the ceiling measures the light on the ceiling to be travelling with speed c, (2) an observer stationed on the floor measures the light on the floor to be travelling at c, but (3) within the bounds of how well the speed can be defined (discussed below, in the General Relativity section), a "global" observer can say that ceiling light does travel faster than floor light. (...) If an observer is sitting up at the ceiling of this room and another is sitting on the floor, and they each have their own identical factory-set clocks and rulers, the ceiling observer measuring light in his vicinity will measure c, and so will the floor observer. But if I now ask these observers to set their clocks and rulers up so that they agree with me on distances and simultaneity - which can be done, although it's not an obvious thing - then things change. I collate their measurements and find that in this "global" uniformly accelerated frame, ceiling light travels faster than floor light... (...) When light is far away, its speed becomes ill-defined. But it's not a great idea to say that in this situation "light everywhere has speed c", because that phrase can give the impression that we can always make measurements of distant speeds, with those measurements yielding a value of c. But no, we generally can't make those measurements. And the stronger gravity is, the more ill-defined a continuum of observers becomes, and so the more ill-defined it becomes to have any good definition of speed. Still, we can say that light in the presence of gravity does have a position-dependent "pseudo speed". In that sense, we could say that the "ceiling" speed of light in the presence of gravity is higher than the "floor" speed of light. Einstein talked about the speed of light changing in his new theory. In his 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 [Einstein means speed here] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers. In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the not-quite-well-defined "speed" of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers."

Pentcho Valev

For years, I have been quoting this video in support of Newton's emission theory of light according to which the speed of falling light varies like the speed of ordinary falling 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."

Now I see I have been misled by the words quoted above and have failed to notice that, in the calculations, the lecturer actually reaches the opposite conclusion: UNLIKE the speed of falling mechanical objects, the speed of falling light DECREASES. (I should have paid more attention to the signs of the variables.)

The concept that light undergoes DECELERATION as it falls in a gravitational field is rather popular (I have often heard of it), although it does not seem to be officially taught. Usually, Einsteinians declare that the (measured) speed of light is CONSTANT in a gravitational field and leave it at that. Could the two concepts (1: light DECELERATES; 2: the measured speed is CONSTANT), despite their apparent incompatibility, be related? Consider, again, the following scenario:

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

f' = c'/L'

Crucial questions:

c' = ?

L' = ?

It can be shown that the following argument is valid:

Premise 1: There is gravitational time dilation.

Premise 2: Light DECELERATES as it falls in a gravitational field.

Conclusion: The answer to the "crucial" questions is:

c' = c

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

This answer suffers from two fatal drawbacks:

1. It has nothing to do with Einstein's general relativity.

2. The wavelength shift, from L to L'=L/(1+gh/c^2), is an ad hoc fabrication without any physical meaning.

Pentcho Valev