Re: General Theory of Relativity

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Brian Whatcott's expressed surprise:
> At 00:48 12/12/98 -0500, J. Epstein wrote:
> > ....
> > Maxwell's equations are not invariant to the Galilean transformation
> > because they explicitly contain a velocity, while Newton's laws are
> > invariant, because they contain only acceleration.
> >
> > J. Epstein
>
> This is a most interesting, even contrary position.
> One often sees the opposing assertion: that Newton has a preferred
> coordinate system. I would like to see this position debated, if it
> is not yet completely accepted.

There's is not much to debate here.  Jerry is completely correct.
Newton's laws of mechanics *are* invariant under Galilean
transformations.  Newton may have believed in Absolute Space, but his
equations of mechanics do not betray a preference for any inertial
frame over another as far as defining a state of absolute rest goes.
Also it is the very *non*invariance of Maxwell's equations under those
same Galilean transformations (and the demonstrated existence of free
propagating electromagnetic waves) that led 19th century physicists to
suppose the existence of the Luminiferous Ether which both defined a
preferred absolute rest frame *and* provided a propagation medium for
those newfangled electromagnetic Hertzian waves as well as for visible
light.  In such a scheme Maxwell's equations (in their normal form) were
taken to hold *as is* in an inertial frame that was at rest w.r.t. the
Ether.  But for any other frame moving w.r.t. the Ether there were extra
(hydrodynamic-like) streaming terms generated (by the Galilean
transformation that transformed from the Ether-at-rest frame to the
Ether-moving frame) in Maxwell's equations which depended on the
velocity of the Ether 'wind' in that frame which included the effects of
that 'wind' which (among other things) caused the velocity of
electromagnetic waves to depend on the relative orientation of the wave
motion w.r.t. the Ether 'wind'.

This situation troubled Einstein in that he philosophically preferred for
there to be no preferred rest frame in nature, and wanted *both* the
equations of electromagnetism *and* mechanics to be invariant under the
coordinate transformations that transformed between the various inertial
frames.  Since he already knew that Maxwell's electromagnetism were
invariant under Lorentz transformations he reasoned that it must be those
Lorentz transformations, rather than the Galilean transformations that
really define how to transform between various inertial frames in nature.
Since Newton's laws of mechanics (other than N1) were not invariant under
Lorentz transformations he modified those laws so they *would* be so-
invariant.  The result was his special theory of relativity.  Needless to
say the experimental null result of the Michaelson-Morley experiment
indicated that either the Earth was always at rest w.r.t. the Ether or
that the bare Maxwell's equations *without* those streaming terms seem to
hold also in moving frames.  The latter option was almost universally
(except for, maybe, a few diehard geocentrists) considered to be the
case.  This experimental result was nearly conclusive evidence that
Lorentz transformations really are the correct ones to use between
inertial frames, and it also had the other effect of banishing the Ether,
since every inertial frame acts as if it is at rest w.r.t. the Ether.

David Bowman
dbowman@georgetowncollege.edu