Re: conundrum regarding propagation of virtual particles

From: Igor Khavkine (k_igor_k_at_lycos.com)
Date: 10/24/04 

Date: Sun, 24 Oct 2004 14:04:14 +0000 (UTC)

On Fri, 22 Oct 2004 17:31:39 +0000, vernonner3voltazim wrote:

>
> Feynman's "sum over histories" method of explaining certain
> quantum-mechanical interactions works nice, and a lot of people think it
> may be an accurate interpretation of Reality. On the other hand, Feynman
> once suggested that anti-particles were merely ordinary particles that
> happened to be travelling backward in Time, relative to us, and that math,
> too, works nice. But few think it is an accurate interpretation of
> Reality; it is just a useful tool.

This should tell you something about Reality or perhaps about people's
interpretations of it. Or both.

> One thing about the sum-over-histories model is that it assumes virtual
> photons travelling between electric charges can do so at every possible
> speed from zero up to infinity. Well, if this model is so good, shouldn't
> it work for other Forces than Electromagnetism?

As far as physicists are concerned, the usual operator and Feynman's
formulations of quantum mechanics are equivalent. So yes, it does work for
other things besides electromagnetism.

> Consider the Strong Nuclear Force. The virtual pions that carry quarks
> and gluons between protons and neutrons in the nucleus have a fair amount
> of mass. The Uncertainty Principle allows them to borrow that energy for
> just enough time to cross the nucleus. To be more specific, this
> borrowing is VERY STRICTLY TIME-LIMITED. As a result (as described by
> Yukawa well before Feynman's trick came along), the pions can only
> propagate so far, and indeed the Strong Force has a very sharp cut-off
> with respect to its range of action.
>
> My point here is that if we applied the sum-over- histories method to
> virtual pions and the Strong Force, then some of those pions should be
> able to go infinitely fast and consequently the Strong Force would have a
> much greater range than is observed. This indicates that probably we
> cannot apply (in terms of "interpretative meaning") the sum-over-histories
> method to that aspect of the Strong Force. It MAY also indicate that
> while sum-over-histories is a good tool, it is not a valid interpretation
> even for the Electromagnetic Force, to say that all those virtual photons
> are taking all possible paths (space-like and time-like).

You are forgetting cancellation in Feynman's "sum over histories". The
amplitudes given to pions that travel very far is such that their sum is
negligible once all paths are taken into account.

> Which brings me to ask whether or not there is SOME OTHER technique that
> works just fine to explain QED without sum-over-histories, and only
> involves virtual photons that propagate only at light-speed. Is there?
> Thanks in advance!

What you refer to as "techniques" are simply ways of visualizing the
actual calculations. The visualization is not strictly necessary. In fact
the same calculation can be visualized in several different ways, some
involve virtual particles, some involve sums over histories, some involve
neither. There's been a couple of recent threads about virtual particles
here. Check out the news group archives for further discussion.

Igor

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