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Re: Energy



/snip/
I am uncomfortable with the suggestion of simultaneity -
in the memorable phrase, there is a relativity of simultaneity.

At 08:13 9/21/01 -0400, David Bowman wrote:
There is no need to fear.

There are many things that I fear, but mathematically tenable
definitions of physics units do not figure among them.

But to strike fear in the heart of any reasonably rigorous educator,
as I believe David to be, I will now proceed to mangle the pristine
description he gave, while retaining some unrecognizable fragment
of the sentiment, possibly so as to ridicule it?

I start with a vector of mass flow rate spatially extended along a
riparian boundary.
I specify a local mass density at some point in an infinity of
locations in the flux.
The quotient represents a volumetric flow rate which would ordinarily
be expressed in terms of volume per time.
I take a particle of volume so small that it has no spatial extension,
and proclaim that when this particle passes a bounding surface,
no time has elapsed.
Did I get the general idea? :-)

Brian, more in joy than in earnest.


The lack of absolute simultaneity in
relativity is not relevant here because it applies only to spacelike
separated events, i.e. events that are farther apart in space than
the time separation between them. What is being discussed here is
what happens across a surface of separation between 2 *adjacent*
regions. This surface has *zero* thickness. The *continuity* of the
energy density and the energy flux density fields allows us to keep
everything in our discussion 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.

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). If we locally take the energy flux
current density vector j_u and divide it by the local energy density
u the quotient (point by point in space) is the velocity field for
the energy flow rate. In all cases the value for the magnitude of
this vector field is everywhere safely bounded above by c (assuming
of course that for now we are discussing only *classical* energies,
densities, and currents here and are not dealing with quantum
operator-valued distributions on Fock space in the Heisenberg
picture as we note that the causality of quantum fluctuations is
problematic).

David Bowman
David_Bowman@georgetowncollege.edu
brian whatcott <inet@intellisys.net> Altus OK
Eureka!