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Part 1: It’s been said that dark matter makes up about 26 % of the universe. The restart of LHC would be dealing with the existence of dark matter also. Consider a situation that the results are positive, i.e there is dark matter? Would it demands any revisions for theories which currently we use? For example, Special Relativity, in which Einstein establishes that velocity of light in vacuum (will it be still valid to use the word vacuum? Well I am not quite certain) is a constant(=3x$10^8 ms^{-1}$, I hope this fact doesn’t need any revision other than redefining “vacuum”) and is the highest attainable velocity.

$$c=1/(ε_0μ_0)^{1/2}$$

Where the symbols have their usual meaning. Then $ε_0$&$μ_0$ are the values of permittivity and permeability of free space (as we say today) should be the values for dark matter?

The question: Do we have to revise any theory? If yes, what would be its aftereffects? And are we capable of revising them and coming up with more accurate theories?

Part 2: Consider a situation where we have absolute vacuum (i.e. nothing including dark matter is present), what would be the values of $ε_0$&$μ_0$? From their definition, I think they should be zero, which in turn shows that radiation has an infinite velocity in absolute vacuum, is it possible?

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    $\begingroup$ A subtle point. The universal speed limit $c$ is a concept separate in principle from light. You can infer the existence of $c$ from Galilean relativity with the assumption of absolute time relaxed and derive all of SR in this way without referring to light at all. Experimentally we find that the speed of light transforms in the same way as the universal speed limit $c$, and of course light featured importantly historically in Einstein's treatment of relativity.Although unlikely, $C=1/\sqrt{\epsilon_0,\,\mu_0}$ could change in presence of DM without the value of $c$ changing .... $\endgroup$ – WetSavannaAnimal Apr 8 '15 at 0:49
  • $\begingroup$ ...-this would imply nonzero photon rest mass though, so it would complicate other things. See my answer to "what's so special about the speed of light" $\endgroup$ – WetSavannaAnimal Apr 8 '15 at 0:51
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The permittivity and permeability of free space are non-zero in 'absolute vacuum' and they will be unaffected by dark matter which interacts extremely weakly (if at all) with the EM force. We might need to modify gravity to account for dark matter (hopefully not) but that's all.

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  • $\begingroup$ Why it is so? permittivity and permiability are the properties of matter, aren't they? $\endgroup$ – RogUE Apr 7 '15 at 23:33
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    $\begingroup$ @RogUE $\epsilon_0$ and $\mu_0$ are properties of vacuum. Matter can modify them, giving rise to relative permittivity and permeability factors. $\endgroup$ – lemon Apr 7 '15 at 23:38
  • $\begingroup$ We might need to modify gravity to account for dark matter, what does that mean? $\endgroup$ – RogUE Apr 7 '15 at 23:45
  • $\begingroup$ Well we don't know what dark matter is. One theory is that our understanding of gravity is wrong and that it behaves differently at the scale of galaxies. This has given rise to a bunch of so-called 'modified gravity' theories. As far as I can tell though, most experts doubt that this is the case. $\endgroup$ – lemon Apr 7 '15 at 23:58
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On average the density of dark matter in the universe is about the same as two hydrogen atoms per cubic metre. That's about 0.00000000000000000000001% of the density of air (a factor of $10^{-25}$). So even if it did interact with light, the effect of the relative permittivity and permeability would be negligable.

But dark matter doesn't interact strongly with light - if it did it wouldn't be dark! For example a popular model of dark matter is particles that only interact via the weak and gravitational forces, and light only interacts strongly via the electromagnetic force.

Dark matter does interact with light via the gravitational force. We see this in lensing experiments such as the Bullet Cluster. However we describe this interaction as being due to the curvature of spacetime rather than due to any change in its dielectric properties.

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