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If no, why not or how can we be so sure?

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If no, why not or how can we be so sure?

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jtbell

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The constancy of the speed of light has been tested a lot, along with the related concept of "Lorentz invariance." So far, experiments support them with high precision. See section three of the following FAQ:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

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As jtbell correctly notes, the most direct way to interpret this question is to think of it as a question about the current state of the art in testing Lorentz invariance.

There are other possibilities.

Loop quantum gravity predicts that the vacuum is dispersive, so the speed of light isn't constant even in a single frame: http://arxiv.org/abs/0908.1832

The photon could turn out to have a nonvanishing rest mass:

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters , 1998, 80, 1826-1829, http://silver.neep.wisc.edu/~lakes/mu.html

If this is the case, then there are no implications for the foundations of relativity, but gauge theory would be in trouble.

There are other scenarios motivated by quantum gravity, e.g., doubly-special relativity: http://en.wikipedia.org/wiki/Doubly-special_relativity If doubly-special relativity is right, then there is no violation of Lorentz invariance, but there is a higher symmetry as well.

You can also search for Lorentz violation in the gravity sector rather than the photon sector: http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.4 [Broken] (subsection 2.4.3)

There are other possibilities.

Loop quantum gravity predicts that the vacuum is dispersive, so the speed of light isn't constant even in a single frame: http://arxiv.org/abs/0908.1832

The photon could turn out to have a nonvanishing rest mass:

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters , 1998, 80, 1826-1829, http://silver.neep.wisc.edu/~lakes/mu.html

If this is the case, then there are no implications for the foundations of relativity, but gauge theory would be in trouble.

There are other scenarios motivated by quantum gravity, e.g., doubly-special relativity: http://en.wikipedia.org/wiki/Doubly-special_relativity If doubly-special relativity is right, then there is no violation of Lorentz invariance, but there is a higher symmetry as well.

You can also search for Lorentz violation in the gravity sector rather than the photon sector: http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html#Section2.4 [Broken] (subsection 2.4.3)

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A more up to date reference: http://arxiv.org/abs/0908.1832

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