# Maxwell's Equation and Special Relativity

1. Jan 17, 2010

### sergei flamel

I've got a couple of question about Maxwell's Equation and its relation to Special Relativity.

1. Why do we think that free space has permittivity and permeability? For me, due to quantum effects free space should have permittivity and permeability, but how did Maxwell accept that the free space has permittivity and permeability? What did he based the idea of "permittivity and permeability" on? Well, I could think that they are just experimental results, but how did he explain the "permittivity and permeability of free space" to himself without any clue on quantum field theory?

2. So, in the presence of permittivity and permeability of free space, we know "the speed of light" can be written in terms of those quantities. However, if there were no permittivity and permeability, them c -> infinity. So, by accepting that the free space has permittivity and permeability, a finite speed of light emerges naturally. Thus, I dont see why it is surprising to see that Maxwell's Equations are consistent with Special Relativity. Of course it would be consistant because it assumes that even in the free space, the speed of light cannot be infinity. ( Ok, I know relativity is much more than that, but accepting that the speed of light is finite in free space is too much for 1861 )

3. I, personally think that "the speed of light" should be much more unique than just the speed of a photon. For instance, gravitational waves also travels with speed of light and they dont have such electromagnetic properties. So, obviously we cannot impose those "permittivity and permeability" things on gravitational waves. So, could I safely assume that, inside a fluid, gravitational waves travels faster than light? Than what happens to relativity? How should I write Lorentz Transformations in this case? Do I need a relativity which keeps two speeds constant instead of one?

Thanks for the answers :-)

Last edited: Jan 17, 2010
2. Jan 17, 2010

### clem

Free space does NOT have permittivity epsilonzero and permeability muzero.
The QED "vacuum polarization" is a kind of p and p, but that is a higher order quantum effect.
Maxwell DID NOT accept that the free space has permittivity and permeability.
Maxwell only accepted c, and in fact devised an experiment to measure c even before he showed it was the speed of light. c was originally introduced as the relation between magnetic and electrical phenomena.
The constants epsilonzero and muzero were introduced in a clumsy attempt to correlate the units of physics with units that engineers like. They have nothing to do with properties of free space. In fact muzero/4pi is just a pure power of ten relating mks to cgs units, and the ampere to the original absolute ampere.

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