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Re: Energy



Regarding Brian Whatcott's discomfort:

... flow means that any positive change in a given
region is balanced by a simultaneous negative change in an adjacent
region. My brief description of the word is that it means " move
smoothly and continuously".

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

There is no need to fear. 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

-----Original Message-----
From: brian whatcott [mailto:inet@INTELLISYS.NET]
Sent: Thursday, September 20, 2001 9:38 PM
To: PHYS-L@lists.nau.edu
Subject: Re: Energy


At 09:40 9/21/01 +1000, Brian McInnes wrote inter alia:
... flow means that any positive change in a given
region is balanced by a simultaneous negative change in an adjacent
region.
My brief description of the word is that it means " move smoothly and
continuously".
/snip/
Brian McInnes


I am uncomfortable with the suggestion of simultaneity -
in the memorable phrase, there is a relativity of simultaneity.
Propagation rate must enter if there is to be a flow, I would think.


brian whatcott <inet@intellisys.net> Altus OK
Eureka!