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From: gwyn@brl-tgr.ARPA (Doug Gwyn )
Newsgroups: net.physics
Subject: Re: Collison with ONE particle?
Message-ID: <788@brl-tgr.ARPA>
Date: Mon, 19-Aug-85 01:02:51 EDT
Article-I.D.: brl-tgr.788
Posted: Mon Aug 19 01:02:51 1985
Date-Received: Sun, 25-Aug-85 13:51:32 EDT
References: <494@sri-arpa> <496@sri-arpa.ARPA> <1702@hao.UUCP>
Organization: Ballistic Research Lab
Lines: 65

> > 	This sounds like an idea attributed to Feynman and Wheeler.
> > 	The idea is that a positron can be considered an electron
> > 	going backward in time.  If one thinks solely in terms of
> > 	particle collisions in space-time, it becomes possible to
> > 	propose that there is only one electron/positron trajectory
> > 	zigzagging back and forth in time to produce all the
> > 	electrons and positrons that we observe.

> I was curious about how you describe a collision between two identical
> particles using only one particle in a space-time continuum (in which every
> space-time point is assumed to be unique).

This is Feynman's theory, not mine!  In any case, nothing
prohibits a point of space-time from hosting more than one
particle concurrently.  There is no problem with the "same" particle
appearing twice at the same event, since each of its appearances is
a different point on its infinite zig-zag worldline.  Presumably
all the concurrent appearances are just the returns from positrons
(backward-traveling electron) bouncing off events in the past.

A space-time diagram helps one understand this theory.  The collision
between an electron and a positron would look something like:

        \ photons /
         \       /
          \     /
^          \   /
|           \ /
|            o
            / \
time       /   \
          /     \
         /       \
electron/         \positron

        distance -->

Now, you can think of the electron and positron converging on "o"
or you can think of the electron bouncing backward in time and
being interpreted as a positron "after" (farther along its wordline)
the bounce.

In the following diagram, I have shown the "same" electron
participating in more than one collision at the same time:

        \ photons / \         /
         \       /   \       /
          \     /     \     /
^          \   /       \   /
|           \ /         \ /
|            o same time o
            / \         / \
time       /   \       /   \
          /     \     /     \     /
         /       \   /       \   /
electron/         \ /         \ /same electron
                   o           o

        distance -->


Feynman really was looking for a way to assign physical meaning to
the advanced solution of the wave equation as well as the
conventionally accepted retarded solution.  If you follow that
idea far enough, this theory is what you come up with.