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THE ESSENCE OF GENERAL RELATIVITY



 
 
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  #1  
Old November 4th 13, 09:34 AM posted to sci.astro
Pentcho Valev
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Default THE ESSENCE OF GENERAL RELATIVITY

The top of a tower of height h emits light downwards. According to Newton's emission theory of light, light falls with the same acceleration as ordinary matter. That is, when the emitted light reaches the observer on the ground, its speed relative to him is:

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

Pound and Rebka showed that the observer on the ground measures the frequency to be:

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

where f is the initial frequency (as measured by the emitter) and L is the wavelength.

Clearly the equation c'=c(1+gh/c^2) given by the emission theory is consistent with the equation f'=f(1+gh/c^2) confirmed by the Pound-Rebka experiment:

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..."

The essence of general relativity is the replacement of the Newtonian equation c'=c(1+gh/c^2) with the equation c'=c(1+2gh/c^2) predicting that 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."

Pentcho Valev
  #2  
Old November 4th 13, 11:22 PM posted to sci.astro
Pentcho Valev
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Default THE ESSENCE OF GENERAL RELATIVITY

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."

This is the whole essence of general relativity; "in this sense, at least" introduces a loophole allowing Carlip, in times of trouble, to deny any double acceleration and start singing his favorite song about a speed of light which was variable in Einstein's time (and this interpretation is perfectly valid and makes good physical sense) but then gloriously became constant and will never be variable again:

http://math.ucr.edu/home/baez/physic..._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
  #3  
Old November 5th 13, 11:49 PM posted to sci.astro
Pentcho Valev
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Default THE ESSENCE OF GENERAL RELATIVITY

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]

Equation (3.39) gives the variation of the speed of light with the gravitational potential predicted by Newton's emission theory of light.

Equation (6.28) gives the variation of the speed of light with the gravitational potential predicted by Einstein's general relativity. The factor 2 on the potential term is the essence of general relativity. This factor makes the general relativity's prediction incompatible with the frequency variation f(r)=(1+phi(r)/c^2)f confirmed by the Pound-Rebka experiment.

Pentcho Valev
  #4  
Old November 7th 13, 09:33 PM posted to sci.astro
Pentcho Valev
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Default THE ESSENCE OF GENERAL RELATIVITY

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."

That is, just like the speed of any material object, the speed of light increases as light is falling in a gravitational field and decreases if the light is travelling away from the gravitational field. The relevant equation given by Newton's emission theory of light is:

c' = c(1±gh/c^2)

and the frequency shift measured by Pound and Rebka unequivocally confirmed the emission theory's prediction:

f' = f(1±gh/c^2)

An important implication is that the gravitational redshift of the light coming to the Earth from distant astronomical objects is due to the simple fact that the speed of that light (relative to the Earth) is decreased.

Clever Einsteinians know that, according to general relativity, the speed of light varies twice as fast as the speed of ordinary matter in a gravitational field: c'=c(1±2gh/c^2). This variation is, obviously, incompatible with the frequency shift measured by Pound and Rebka. Silly Einsteinians know nothing and teach that the speed of light gloriously remains constant in a gravitational field (c'=c), Divine Einstein, yes we all believe in relativity, relativity, relativity.

Both clever and silly Einsteinians regularly set to work to exercise themselves in crimestop. They present themselves with propositions - "the Pound-Rebka experiment gloriously confirmed Divine Albert's Divine Theory", "the light coming to the Earth from distant astronomical objects always has the same constant speed c relative to the Earth" - and train themselves in not seeing or not understanding the arguments that contradict the propositions:

http://ebooks.adelaide.edu.au/o/orwe...hapter3.4.html
"He set to work to exercise himself in crimestop. He presented himself with propositions - "the Party says the earth is flat", "the party says that ice is heavier than water" - and trained himself in not seeing or not understanding the arguments that contradicted them. It was not easy. It needed great powers of reasoning and improvisation. The arithmetical problems raised, for instance, by such a statement as "two and two make five" were beyond his intellectual grasp. It needed also a sort of athleticism of mind, an ability at one moment to make the most delicate use of logic and at the next to be unconscious of the crudest logical errors. Stupidity was as necessary as intelligence, and as difficult to attain."

Pentcho Valev
 




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