FALLING LIGHT IN THE WORLDS OF NEWTON AND EINSTEIN

[Pentcho Valev]

In the world of Newton, photons fall like ordinary falling bodies. This means that, if the top of a tower of height h emits light downwards, the photons will have acceleration g and will reach the ground with speed:

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

This prediction is obviously consistent with the frequency increase f'=f(1+gh/c^2) measured by Pound and Rebka (f is the initial frequency as measured at the top).

In the world of Einstein (that is, according to Einstein's relativity), the acceleration of the falling photons is not g but, rather, (-2g). In other words, photons decelerate (their speed decreases) as they fall:

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

If one expects Einsteinians to be unable to adjust this to the frequency increase f'=f(1+gh/c^2) measured in the Pound-Rebka experiment, one would be wrong. Introducing gravitational time dilation changes the formula - an observer on the ground will measure the speed of the photons to be:

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

This formula is still incompatible with the Pound-Rebka experiment but Einsteinians don't stop here. They assume, without any justification, that the wavelength varies in the following way:

λ' = λ/(1 + gh/c^2)

where λ is the initial wavelength (as measured at the top). So the speed of the photons and the frequency, as measured by the observer on the ground, become:

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

In the text above by "Einsteinians" I mean clever people that are long dead. Today's Einsteinians are silly and unable to understand how the negative acceleration (-2g) leads to the conclusion that the (measured) speed of light is constant in a gravitational field (c'=c). So they are usually silent about (-2g) and just teach c'=c in various silly ways:

http://www.amazon.com/Why-Does-mc2-Should-Care/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://www.oapt.ca/newsletter/2004-02%20Newsletter%20Searchable.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-Time-Stephen-Hawking/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://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."

http://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/speed_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

[Pentcho Valev]

If the speed of falling photons varies like the speed of ordinary falling bodies (as predicted by Newton's emission theory of light), then, when the top of a tower of height h emits light downwards, the photons will have acceleration g and will reach the ground with speed (as measured by an observer on the ground):

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

This prediction is obviously consistent with the frequency increase

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

measured by Pound and Rebka (f is the initial frequency as measured at the top). Sometimes Einsteinians do explain the Pound-Rebka experiment in terms of variable speed of light as predicted by Newton's emission theory of light:

http://www.einstein-online.info/spotlights/redshift_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/phys419/sp2013/Lectures/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."

It would be very risky to state that the Newtonian formula

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

is false, then to show the allegedly correct formula (given by Einstein's relativity), and finally to explain why the "correct" Einsteinian formula, just like the "false" Newtonian one, is consistent with the frequency increase measured by Pound and Rebka:

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

Einsteinians would not take the risk - they would not even think in that direction:

http://ebooks.adelaide.edu.au/o/orwell/george/o79n/chapter2.9.html
Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."

Pentcho Valev

[Pentcho Valev]

Does the gravitational redshift arise from gravitational time dilation (clocks at different heights tick at different rates), or does it arise from the fact that the speed of falling photons varies like the speed of ordinary falling objects, as predicted by Newton's emission theory of light and confirmed by the Pound-Rebka experiment? See a discussion here:

https://www.youtube.com/watch?v=ce24uorjGj0
Movie vs. science: Neil deGrasse Tyson on "Interstellar"

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