ptamirez@yahoo.co.uk wrote:
>I don't understand: On the one hand with special relativity Einstein
>got rid of the aether - the medium which electromagnetic waves use to
>travel and which can be used as an absolute reference system. On the
>other hand in quantum field theory quantum fields are invented which
>fill all space and which are the "medium" for particle waves. Isn't
>this reinventing the aether? In what way is this 'aether' bettern than
>the one Einstein got rid?[/color]
This reply, in full (below), originally intended for someone else, is
eminently suitable here.
Some of what follows is discussed in greater depth in the "Yang-Mills
Equations in Maxwell Form" article in http://federation.g3z.com/Physics
where more detailed cited from Maxwell's treatise are provided.
The reply to follow:
> Bilge said: The causal structure of spacetime is determined by the
> geometry.
>
> I'm getting confused. What really is an ether?[/color]
Aether.
The causal structure of spacetime is determined by the constitutive
relations of the electromagnetic field. For Minkowski spacetime they
are:
D = epsilon_0 E; B = mu_0 H.
For Galilean spacetime they would be (to use Maxwell's "G"):
D = epsilon_0 (E + G x B); B = mu_0 (H - G x D)
where "G" would indicate the velocity relative to a certain
distinguished frame where wave propagation is of equal velocity in all
directions.
> What is your understanding of ether?[/color]
A lot of it is historical revisionism and mythology built up by people
who never read the originals (much less, transcribed and copy-edited
them, as I have done).
Maxwell never talked about any "aether". Instead, the central premise
of his theory was that the vacuum was a dielectric capable of
charge-screening, vacuum polarization, with a non-trivial relation
between (D,H) and (B,E) holding, particularly, in the close vicinity of
point-like and line-like sources. He believed that infinities in the
classical field theory are avoided because the vacuum polarizes near
such sources, thus leading to a distinction between "bare" and
"dressed" charges (which, in turn, he briefly discussed in Chapter 1).
All of this eventually came to be adopted as the central features
(after the 1940'/s) of what came to be known as renormalization theory.
His relations were the Galilean invariant ones above (as far as any
relations were set out explicitly); not the Lorentz relations.
It's because Lorentz relations were found to hold in all frames, that
you no longer see the "G" in the alphabet soup comprising Maxwell's
nomenclature (A, B, C = total current = J + dD/dt, D, E, F = force
density, (G), H, I = magnetization, J).
The biggest misconception cast, in the way of historical revisionism,
was that relativity did away with an *otherwise equivalent* "aether"
theory. What it did away with is NOT equivalent -- it did away with the
"G" and the Galilean invariant relations posed above, which Maxwell
originally surmised. The difference between the Lorentz and Galilean
relations *is* the difference between Minkowski and Galilean spacetime.
And the instant you write down (D = epsilon_0 E; B = mu_0 H), you're in
Relativity, not Galilean physics.
So, Relativity began (whether its participants realized it or not) as
soon as the G was dropped and (what are today known as) Maxwell's
equations were first written down .. after Maxwell died.
... which gets back to the original point: the constitutive relations
determine the causal structure of spacetime; in particular,
distinguishing causal structure of Galilean spacetime from that of the
Minkowski spacetime; distinguishing Galilean relativity from Poincare
relativity.
The punchline comes at the very end ... in the presence of point-like
sources, *no* linear relations can hold between the (D,H) and (B,E)
fields. For a singularity in the sources (rho, J) mean a singularity in
(D,H) via the relations (div D = rho; curl H - dD/dt = J). In the
presence of a linear relation that would entail a singularity in (E,B),
which would make the force law (F = rho E + ...) ill-defined --
contradiction. Therefore, a linear (D,H) vs. (E,B) breaks down near
point sources.
Given the foregoing, about constitutive relations reflecting the causal
structure that nature already puts there, this is then a clear
indication that the causal structure, itself, breaks down near
point-like sources and is being reflected as such by the break down of
the linear relations between (D,H) and (B,E).
