Re: Energy

["John S. Denker" <jsd@MONMOUTH.COM>]

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.