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From: sra@oddjob.UUCP (Scott R. Anderson)
Newsgroups: net.physics
Subject: Re: White Holes?
Message-ID: <937@oddjob.UUCP>
Date: Fri, 23-Aug-85 12:28:38 EDT
Article-I.D.: oddjob.937
Posted: Fri Aug 23 12:28:38 1985
Date-Received: Sun, 25-Aug-85 05:26:22 EDT
References: <3656@decwrl.UUCP> <166@prometheus.UUCP> <490@talcott.UUCP>
Reply-To: sra@oddjob.UUCP (Scott R. Anderson)
Organization: University of Chicago, Department of Physics
Lines: 48
Summary: 

In article <166@prometheus.UUCP>, pmk@prometheus.UUCP (Paul M Koloc) writes:

>> Two things tell us that the universe isn't continuous.  First, the "big bang",
>> and second, the constant "h bar" or even the fact that particles are not 
>> points. 

And in another article,

>> Particles aren't points.  They have a "delta function"
>> over a discrete distribution width in space, and if there is an 
>> symmetry then there is a "delta function distribution" in time as well.

So far as we know, the "fundamental" particles (quarks, leptons, etc.) ARE
points.  Experiments have yet to determine any finite extent for these
particles.  I believe that the current upper limit on the radius of the
electron is 10^(-18) meters or 0.001 fermi.

Such particles are described by wave functions, which under appropriate
conditions (i.e. the particle is at point x) are delta functions.  A
delta function has no width, as it is non-zero only at x.  This is how
one describes a point particle quantum-mechanically.

In article <490@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes:
>
>Time is, of course, treated as a real variable in QM, and you
>can't just go from differential equations in time to difference
>equations and still have a working QT (at least I have never seen
>such a theory... it would definitely be interesting, though).
>....
>Your remark about QM and discreteness of space strikes me
>as even odder. If you know of a way of representing QM on
>a lattice, I would like to hear about it.

This is done on a regular basis in field theories, although only as
a calculation technique.  The procedure uses the path integral
formulation of QM and discretizes space-time onto a lattice with
some lattice spacing 'a'.  After everything is all said and done, 
the limit a -> 0 is taken.

Lurking nearby, however, is the question of the distinguishability of
small a (e.g. Planck Length) from a = 0.  At this point, we can't tell
the difference because the energies required are so enormous.  If space
were discretized, though, there would be some probability of "Umklapp"
processes occurring, in which a particle could change it's momentum for
no apparent reason.

				Scott Anderson
				ihnp4!oddjob!kaos!sra