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Re: Speed Of Light Slowing Down.



All interesting comments. But, the problem IMHO is that since propagation
speed is equal to

1 / [sqrt( mu-zero x epsilon-zero)]

If one starts messing with the speed of light, then one must also recon with
changes in other fundamental constants. That is, the basic forces of nature
must change also.

Oren Quist, SDSU


-----Original Message-----
From: David Bowman [mailto:dbowman@TIGER.GEORGETOWNCOLLEGE.EDU]
Sent: Wednesday, December 11, 2002 4:49 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Speed Of Light Slowing Down.

Regarding Jim Green's questions:

Why would E=mc^2 be "under challenge" if c were changing?

The theory from which it is derived is completely based on the
idea that c is not changing. If the hypotheses of a theory are
not satisfied we can have no confidence in the decuctions from
that theory.

Where in SR is it required that c be the maximum possible velocity
of a system?

First of all, c is not the maximum speed in nature in general. There
are some phenomena that have aspects of them involving motion faster
than c. All such motions are for phenomena that are *acausal*. The
kind of things for which c bounds the speed of motion is the
propagation of *causally informative influences* from one place to
another. This means (among other things) that no particle can travel
locally w.r.t. another particle faster than c. It also means that no
extended field can have its value respond at some place to a change
in its value at some other place faster than c. It means that energy
can't flow faster than c either (e.g. for EM waves in a dispersive
medium the quotient of the Poynting vector over the EM energy density
must everywhere have a magnitude that is never greater than c
anywhere). In short, it means that a 'cause' here can't influence
any 'effect' there any faster than by an influence going from the
'cause' to the 'effect' at a speed c.

The reason that SR requires c be the speed limit for causal
influences is that it directly follows from the fundamental
postulates of SR. The first postulate of SR is that the
mathematical form of the laws of nature is the same in all inertial
reference frames. A second postulate is that there is no such thing
as instantaneous interaction at a distance. IOW, two different
things in two different locations cannot interact (across the finite
spatial distance between them) instantaneously with each other. A
consequence of these postulates is that in nature there must be an
upper bound to the speed of causation. A second consequence of this
is that this speed limit must be the same in all inertial frames.
This means that this speed limit is a universal constant. We, by
convention, give the label c to the actual value of this universal
constant. The above two postulates are sufficient to determine the
way time and space intervals transform among each other in going
from one inertial frame to another (i.e. Lorentz transformations)
and to determine how the various relativistic effects spacetime
effects occur, e.g. lack of absolute simultaneity for spacelike
separated events, time dilation, length contraction, etc..

BTW, these postulates are *not* sufficient to determine the laws of
classical (or quantum) dynamics (equations of motion, relationship
between energy and momentum, E_0 = m*c^2, etc.), though. To get
the relativistic laws of classical mechanics (including
E_0 = m*c^2) we need to add a third postulate that essentially says
that nature obeys Hamilton's Principle of least action. To get the
corresponding quantum laws of nature we replace Hamilton's
Principle with Feynman's (or something equivalent to it) principle
that the amplitude for any process is the path integral sum over
all dynamical histories of the complex exponential of the action
(in units of h-bar) for the process.

Why couldn't Jon Luc travel faster than c?

If he did he probably would be carrying a verboten causally
informative influence (i.e he would probably produce some effect
somewhere faster than c).

The Enterprise clearly did -- I
know because I was a Scientific Officer aboard for a few months.

I suppose this is not a problem if the motion of the Enterprise
doesn't carry any information, and if its travels produce no
measurable effects anywhere.

David Bowman