On Friday, October 13, 2017 at 7:26:24 PM UTC-5,
numbernu...@gmail.com wrote:
> RE: Fresnel--Michelson's experiment
> "The undulatory theory of light assumes the existence of a medium called the ether,
Maxwell's theory does not assume there to be an underlying medium, but rather REQUIRES it. For without it, there'd be nothing left to determine in which frame of reference a set of isotropic constitutive relations (D = epsilon E, B = mu H) hold. These relations are not invariant under the Galilean transformation, nor even under the Poincare' transformation (except for the special case where epsilon mu = 1/c^2).
This made it necessary, after Maxwell over the course of the 19th century, to make a distinction between the "stationary" theory (the one where the constitutive relations are isotropic) versus other frames where they are not. In other frames, the laws would become:
D = epsilon (E + G x B), B = mu (H - G x D)
where G is the velocity associated with that frame. You don't see it clearly in Maxwell's presentation because (1) he made the G x B term part of his E field (i.e. what Maxwell calls E does NOT coincide what we now refer to as E) and (2) he made the mistake of failing to note the -G x D term (partly because he kept confusing B and H from the 1850's onward) -- a correction Thompson later made. Or Thomas, I forgot his name.
Maxwell's E and B were defined in terms of the potentials A and phi by
E_Maxwell = -del phi - dA/dt + G x B, B = del x A
where today we would define them by
E = -del phi - dA/dt, B = del x A
So Maxwell's constitutive law D = epsilon E_Maxwell is equivalent to our D = epsilon (E + G x B).
The -G x D correction was later experimentally verified, at the turn of the 20th century, by a husband and wife team.
The relativistic versions of these relations were published independently by Einstein and Laub in 1908 and Minkowski in 1908 (the latter being the first place 4D Minkowski geometry was used) and in contemporary form they would read:
D + alpha G x H = epsilon (E + G x B)
B - alpha G x E = mu (B - G x D)
where alpha = 1/c^2. The sole distinction between the relativistic and non-relativistic forms of electromagnetic theory rest with the value of alpha, which for non-relativistic theory would be 0.
The only condition under which these equations are INDEPENDENT of G are where epsilon mu = alpha. In that case, one can describe the underlying medium as a vacuum because it is invariant under a "boost", as well as being homogeneous, isotropic and stationary (the 4 defining qualities of what comprise a vacuum; i.e. a vacuum is any medium that is invariant under the full set of kinematic transforms: boosts, spatial and temporal translations and rotations).