Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/5/84; site prometheus.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!gamma!epsilon!zeta!sabre!petrus!bellcore!decvax!genrad!panda!talcott!harvard!seismo!lll-crg!gymble!umcp-cs!prometheus!pmk
From: pmk@prometheus.UUCP (Paul M Koloc)
Newsgroups: net.physics
Subject: Re: Re: White Holes?
Message-ID: <171@prometheus.UUCP>
Date: Sun, 25-Aug-85 09:38:42 EDT
Article-I.D.: promethe.171
Posted: Sun Aug 25 09:38:42 1985
Date-Received: Wed, 28-Aug-85 02:11:05 EDT
References: <3656@decwrl.UUCP> <166@prometheus.UUCP> <490@talcott.UUCP> <937@oddjob.UUCP>
Organization: Prometheus II Ltd., College Park, MD
Lines: 55

> In articles <166@prometheus.UUCP>, pmk@prometheus.UUCP (Paul M Koloc) writes:
>>> Two things tell us that the universe isn't continuous.  First, "big bang",
>>> Particles aren't points.  They have a "delta function"
> 
> Scott Anderson  (ihnp4!oddjob!kaos!sra)  <3656@decwrl.UUCP> answers:
> 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.

If you had said kilometers.  Actually, electron radius is ~ e^2/(m*c^2)
which comes to about 3 * 10^(-15) meters.  Still infinitely larger than
a point radius. --"e" is charge; "m" is electron mass; and "c" is light 
speed. They are represented as points, for convenience. 

> 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.

I think "point" in quantum mechanics means "smudge".  And certainly, you
are right provided your mesh isn't too fine.  Now reads:
                    "only at (smudge) 'x'".

> In article <490@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes:
> >. ..Your (Koloc) 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.  

Thanks for the help.  Consequently, a --> 0 approximates a --> "smudge x"
It usually is considered to be the other way around!

> 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.

It does "change" and the reason is its lack of infinite "information 
density"; so it "jiggles" a little in "momentum space".  Wish I could 
claim that as an excuse to get out of paying off a speeding ticket.

       -   -   NOTE: MAIL PATH MAY DIFFER FROM HEADER  -   -
+-------------------------------------------------------+--------+
| Paul M. Koloc, President: (301) 445-1075              | FUSION |
| Prometheus II Ltd., College Park, MD 20740-0222       |  this  |
|  ..umcp-cs!seismo!prometheus!pmk.UUCP                 | decade |
+-------------------------------------------------------+--------+