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Re: Energy



Regarding:
>the suggestion of simultaneity -
>in the memorable phrase, there is a relativity of simultaneity.

At 08:13 AM 9/21/01 -0400, David Bowman wrote:

There is no need to fear.
...
What is being discussed here is what happens across a surface of
separation between 2 *adjacent* regions. This surface has *zero* thickness.
...
everything in our discussion [is] spatially close enough so that any
causal propagation delay is arbitrarily close to zero. I think this
allows the use of the term 'simultaneous' in the above context.

Exactly. The usual sentence that one should keep in mind is
"breakdown of simultaneity at a distance."
Here we have no distance, and therefore no problem talking about simultaneity.

>Propagation rate must enter if there is to be a flow, I would think.

Good point. We certainly can evaluate this (and ought to do so to
verify the claim I made above).

The statement
change(stuff inside boundary) = - flow(stuff outward across boundary)
can be restated as
zero = change(stuff inside boundary) (equation 1)
+ flow(stuff outward across boundary)
and in the latter form the LHS (zero) is obviously relativisically
invariant. The RHS, if it were nonzero, would contain relativistic "gamma"
factors, but since it is zero these factors are completely
inconsequential. (For extra credit, anybody who is sufficiently interested
can verify that the two terms on the RHS contain the _same_ gamma factor,
and explain why.)

This is one of the most fundamental laws of physics. If it were not
relativistically kosher, somebody would have blown the whistle before now.

=================

The conservation law doesn't even care about the speed of
propagation. Equation (1) applies to photons (which carry energy at the
speed of light) and it also applies to phonons (which carry energy at the
speed of sound). The wave equation takes the same form in both cases,
differing only in the value of "c" that is used. And the conservation law
takes the same form in both cases, quite independent of c.