Re: Speed Of Light Slowing Down.

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

Regarding Justin's question:

> Isn't it not that the speed of light is not changing but that it is
> the same for all observers regardless of their reference frame?
> These seem like two different postulates to me.

It may seem that way, but it's not.  Requiring that c have the same
value in all inertial frames automatically makes it a universal
constant (i.e. a constant everywhere in space, in every direction,
in all states of uniform motion, for all time).

The group of all mutually inertial frames (i.e. the Poincare' Group)
is specified by 10 parameters.  These parameters include one which
shifts the origin in time, 3 which shifts the origin in space, 3
which reorient the coordinate axes, and 3 which specify a boost
velocity.  The requirement that c be invariant under the operation of
*arbitrary* elements of this group (i.e. all of them) has the effect
that it forces c to be a global constant of nature.  For instance
suppose c had a particular dependence on time c(t) in some inertial
frame of reference.  Now apply a transforamtion that shifts the
origin in time by an arbitrary amount a.  In the new frame the
functional dependence is now c(t+a). but since c is invariant (by
hypothesis) under the transformation we must have c(t) = c(t+a) in
order for the laws of nature to have the same form in both frames.
But since a is a completely arbitrary transformation parameter which
can take on any and all real values we see that our function c(t) is
required to be independent of its time argument i.e. constant in its
time dependence.  A similar argument holds for the other parameters
of the Poincare' group, and the upshot is that the value of c cannot
have *any* directional dependence, any time dependence, any spatial
dependence, or any dependence on the velocity of the inertial frame.
IOW c is a universal constant of nature.

David Bowman