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Re: Energy



Virtual pair creation is often described (particularly in lower level
courses) as a temporary non-conservation of energy situation, allowed by
virtue of Delta E Delta t uncertaintly relationships. Which is why I was
asking for your take on those situations.

Joel

-----Original Message-----
From: John S. Denker [mailto:jsd@MONMOUTH.COM]
Sent: Friday, September 21, 2001 10:00 AM
To: PHYS-L@lists.nau.edu
Subject: Re: Energy


At 09:29 AM 9/21/01 -0500, RAUBER, JOEL wrote:
how do you view virtual particle pair creation and the usual
Delta E *
Delta t statement regarding such matters?

I'm not 100% sure what Delta E * Delta t statement Joel is
alluding to, so
here is the best answer I can give:

1) In general: I consider all Delta E * Delta t statements
to be highly
suspect.

I know where Delta p * Delta x comes from, because p and x
are dynamically
conjugate variables. There is no corresponding conjugacy relationship
between E and t. There are some analogies based on
dimensional analysis
and whatnot, but "analogy" is a long way from "proof".

2) The usual virtual-pair scenario starts with nothing (zero
energy) and
creates a pair with positive rest-mass energy and negative
kinetic energy
(for a total of zero). So this scenario is consistent with,
and indeed is
a fine illustration of, a rigorous local conservation of energy.

3) If you have in mind some other experimental setup, if you
describe it we
can discuss what limitations, if any, the laws of nature impose on the
accuracy (Delta E) with which the energy can be measured.