Variable Speed Of Light In General Relativity

[Paradigm Shift]

In his book (Relativity) published in 1920 Einstein said that in General Relativity the speed of light is affected by gravity and therefore isn't a constant:

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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; it's results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light) - Relativity, Albert Einstein, page 64

What this means is that the speed of light that we measure with our telescopes is constant because the light is affected by our gravitational field. By the time light reaches our telescopes it enters into our gravitational field and gives us it's constant speed. We don't know the speed of light outside our gravitational field. For those who disbelieve the variable speed of light in General Relativity, taught by Einstein, here's a paper published in 2015 demonstrating a variable speed of light model consistent with General Relativity.

http://arxiv.org/pdf/1503.06763.pdf

Abstract

It is a little known fact that while he was developing his theory of general relativity, Einstein's initial idea was a variable speed of light. Indeed space-time curvature can be mimicked by a speed of light c(r) that depends on the distribution of masses. Einstein's 1911 theory was considerably improved by Robert Dicke in 1957, but only recently has the equivalence of the variable speed of light approach to the conventional formalism been demonstrated. Using Green's functions, we show that Einstein's 1911 idea can be expressed in an analytic form, similar to the Poisson equation. Using heuristic arguments, we derive a simple formula that directly relates curvature w to the local speed of light. In contrast to the conventional formulation, this allows for a Machian interpretation of general relativity and the gravitational constant G. Gravity, though described by local equations, has it's origin in all other masses in the universe.

 

[PAllen]

You should know a few things:

1) The title and content of the paper do not show an equivalence between this proposed theory and general relativity. The title claims an improvement in an early theory of Einstein's (NOT general relativity), and that is what the content of the paper actually shows. The content of the paper proposes as open questions how different the predictions of this theory may be from general relativity. Thus, the sentence in the abstract is highly misleading.

2) This paper has not been published in any peer reviewed journal, thus its reliability is suspect.

3) The discussion from Einstein (1920) that you present, while not wrong, would be cast a bit differently nowadays. We would say that what Einstein is referring to is coordinate speed of light, which is not very significant physically precisely because coordinates are arbitrary in GR. The locally measured speed of light remains c in general relativity. Further, the relative speed of light and any material body, even over great distance, remains c in the only way this can be given meaning in general relativity (parallel transport the 4-velocity vectors to the same place and compare them; independent of path, this always comes out c for the velocity of light relative to a material body). Finally, modern derivations of light bending do not rely on a coordinate dependent variable speed of light. Instead they compute the null geodesics in the space-time geometry. There is no varying speed of light involved in such a computation of light bending.

 

[Paradigm Shift]

P Allan,

You said: 1) The title and content of the paper do not show an equivalence between this proposed theory and general relativity. The title claims an improvement in an early theory of Einstein's (NOT general relativity), and that is what the content of the paper actually shows. The content of the paper proposes as open questions how different the predictions of this theory may be from general relativity. Thus, the sentence in the abstract is highly misleading.The early (1911) idea of Einstein was his variable speed of light. We see that he never got rid of it for it is repeated in the 1920 publication "Relativity". The Abstract gives the reference to where the demonstration of the equivalence of the variable speed of light approach to the conventional formalism. Here it is:

A Spatially-VSL Gravity Model with 1-PN Limit of GRT

http://link.springer.com/article/10.1007/s10701-008-9210-8

 

[PAllen]

P Allan,

You said:1) The title and content of the paper do not show an equivalence between this proposed theory and general relativity. The title claims an improvement in an early theory of Einstein's (NOT general relativity), and that is what the content of the paper actually shows. The content of the paper proposes as open questions how different the predictions of this theory may be from general relativity. Thus, the sentence in the abstract is highly misleading.The early (1911) idea of Einstein was his variable speed of light. We see that he never got rid of it for it is repeated in the 1920 publication "Relativity". The Abstract gives the reference to where the demonstration of the equivalence of the variable speed of light approach to the conventional formalism. Here it is:

A Spatially-VSL Gravity Model with 1-PN Limit of GRT

http://link.springer.com/article/10.1007/s10701-008-9210-8

The form of variable speed of light referred to in 1920 is very different from the 1911 theory. In the 1911 theory, the variable speed of light was a fundamental quantity. In general relativity, the metric from field equations was fundamental, and variable speed of light was coordinate dependent derived result of limited significance (that is no longer even used in modern treatments of general relativity).

That article also DOES NOT claim equivalence. It shows that matching predictions for one special case, and (in general) for weak gravity. Please stop misrepresenting what papers claim. This is very bad practice.

 

[Paradigm Shift]

P Allan,

It is included in Einstein's General relativity whether you use it today or not. Einstein clearly states that in General Relativity the speed of light is a variable. There's no way around it. The speed of light that we measure from distant galaxies has to come through our gravitational field and according to Einstein's General Relativity this will affect it's speed. We don't know the speed of light outside our gravitational field regardless of what you think the above paper says. The authors of the abstract disagree with your reading as does Wikipedia.

 

[PAllen]

P Allan,

It is included in Einstein's General relativity whether you use it today or not. Einstein clearly states that in General Relativity the speed of light is a variable. There's no way around it. The speed of light that we measure from distant galaxies has to come through our gravitational field and according to Einstein's General Relativity this will affect it's speed. We don't know the speed of light outside our gravitational field regardless of what you think the above paper says. The authors of the abstract disagree with your reading as does Wikipedia.

Well, then the authors of the paper can't read. "1-PN Limit of GRT" means extreme weak field limit of GR, not remotely equivalence to GR. In analogy with Taylor series, it means agreement to the first term of the expansion. What wikipedia says is irrelevant (plus you don't indicate what wikipedia entry you refer to - there is wide variation in quality in wikipedia).

As for a correct appreciation of what Einstein said in 1920, my initial post says all that is relevant. There is nothing more to respond to.

 

[Orodruin]

The OP was accurately addressed in post #2. Thread closed.