Re: Conserving Q ? (long)

[Bob Sciamanda <trebor@VELOCITY.NET>]

Hi David,
I agree that your 4 dimensional, covariant interpretation is
mathematically more elegant.  However, in this 4 dimensional view the
terms "cause" and "source" have an at least diluted meaning, since
nothing "happens"; events are simply statically embedded in space-time.
Perhaps in that view, the questions of "cause" and "source" should not
even arise, since nothing "happens".  This may be the conceptual view
proper to God, but as an aid to human conceptualization I have to favor
the view of spatially located stuff and fields evolving in time.

I do thank you for a clear exposition of this view which has always
bothered me.

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Wednesday, November 25, 1998 7:55 AM
Subject: Re: Conserving Q ? (long)


> . . .
> One could also (as I often prefer to do for conceptual purposes) put the
> time derivative terms in with the curl terms leaving the true source
terms
> on the RHSs of these equations completely absent.  The composite
> expressions involving the mixed curls and the partial time derivatives
> along with the other Maxwell equations (involving the divergences of E &
> B) are themselves just the various components of the exterior derivative
> (generalized curl) and 4-divergence of the EM field strength tensor when
> they are written in the relativistically covariant notation of 4-tensors
> and forms on Minkowski spacetime (where time has been demoted from a
> global parameter to another coordinate direction in spacetime).  As such
> these, now homogeneous, equations do *not need* (or have in regions free
> of real charges and real currents) any source terms.  The propagating
> wave-like motions do not require such source terms since the propagating
> nature of the solutions of the equations is supplied by the (hyperbolic)
> effects of the indefinite signature of the metric for spacetime.
>
> David Bowman
> dbowman@georgetowncollege.edu