Re: virtual particles preferred frame?

[John Denker <jsd@MONMOUTH.COM>]

At 06:46 PM 11/6/99 -0600, Glenn A. Carlson wrote:
> I'm sorry, but John's comments re "why the virtual particles don't
> propagate very far" and "Because they have zero total energy.  They've
> got negative kinetic energy
> which just cancels their rest-mass energy" strike me as a misread of
> the theory of virtual particles.

I stand by what I wrote.

> Virtual particles don't go very far because they cannot exist longer
> than a time interval defined by the uncertainty principle; not because
> they have "imaginary momentum."  E.g., creation of a virtual
> electron-positron pair violates conservation of energy by an amount at
> least 2mc^2 (m=electron mass=positron mass) which is a very positive
> amount, but which is allowed only for a time interval delta-t =
> h-bar/2mc^2.  Hence, the electron or positron can move at most a
> distance c*delta-t = h-bar/2mc from their point of creation; any
> farther is prohibited by the uncertainty principle.  "Advanced Quantum
> Mechanics," Sakurai, p. 138.

Ahemmm.  If you work out the consequences of having the negative kinetic
energy and imaginary momentum that I describe, you find that the
probability falls off exponentially over a distance h-bar/mc -- about the
same length-scale that Sakurai gives.

Remarks:

1) This serves to illustrate the point I've been making in another thread,
namely that the equations of physics do not usually imply causation in the
usual sense.  When somebody says "this is why XXXX" it should usually be
read as shorthand for "this is one way of explaining XXXX" or perhaps "this
fact is sufficient to correctly predict XXXX".  If two lines of reasoning
lead to the same conclusion, it is hardly grounds for saying one of them is
a "misread" of the physics.

2) The argument I gave is more rigorous than the one Sakurai gives, in
various ways:
  a) Strictly speaking, the energy-time uncertainty principle that Sakurai
invokes is not a law of physics.  It is only a heuristic.
  b) Sakurai claims only an upper bound on the distance, because the speed
might not always be exactly c.  My argument gives the actual dependence of
probability versus distance, not just a bound.
  c) Sakurai's upper bound is not even a rigorous bound.  There is a
nonzero probability that the bound will be exceeded.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com