From: platt@watson.ibm.com (Daniel E. Platt)
Subject: Re: Compelling Mysteries (II)
Date: Tue, 10 Nov 1992 21:57:10 GMT
Disclaimer: This posting represents the poster's views, not necessarily those of IBM
Organization: IBM T.J. Watson Research Center
Keywords: compelling, mysteries, partridges and pear trees

In article <1992Nov10.183620.483@sei.cmu.edu>, firth@sei.cmu.edu (Robert Firth) writes:
|> Well, thudding in company with Mr Bass, here are a few of my 'mysteries'
|> 
|> (a) We had atoms, then subatomic particles, then quarks.  Is there an
|> ultimate structure of matter, or will we find more and more fine structure
|> for ever?

Depends on if the energy in the universe is finite, or was finite at
the 'start.'  That will tend to apply a lower bound to how small things
can get.

|> 
|> (b) Why has almost every theory of 'small stuff' since Newton thrown up
|> these wretched infinities?  We have them in gravitation, electrostatics,
|> classical electrodynamics, and all over quantum physics.  Is this the
|> consequence of a single bogus assumption, and is that assumption indeed
|> the assumption that spacetime is continuous?

Generally seems to have something to do with trying to get a Green function,
and that has to do with the shape of things that yield a Gauss' law behavior...
at least in gravitation, electrostatics, classical electrodynamics.  Yet, for
appropriately distributed stuff, many of those seem to go away, or end up being
finite afterall.  In quantum field theory, it all comes back again... even
vacuum fluctuations seem to diverge.  But then, that can be subtracted as being
background energy using Wick's theorem (or am I all confused? I vaguely remember
that time-ordering can be used to remove this, and Wick's theorem deals with
getting the time-ordering right... but at the least, I'm betraying the time its
been since I've looke at this kind of material).  Even then,
there will be singularities that pop out... fields may be renormalizable,
which implies the singularities are such that interactions are big enough
to change the basic (naive) scaling behavior of physical quantities.  This
can be turned around to talk about what experiments actually measure (vertex
functions) via a Callen-Symanzik approach.  Then there are fields whose 
singularities cannot be dealt with.  (I'm probably saying all of this poorly...
everytime I try to talk about this, I embarrass myself.)

Some of these singluarities are really bad; some of them aren't so profoundly bad.

|> 
|> (c) Are there magnetic monopoles?  More importantly, is there a way to
|> decide this other than by hunting for monopoles - some simpler experiment
|> that will disprove one model or the other?
|> 

Jackson talks a bit about this in his Electrodynamics... sort of a fun
article.  There are connections, but apparently not enough of one.

|> (d) How sure are we that, in the microcosm, gravitational mass is the
|> same as inertial mass?  How could we ever test this, anyway?

The impact of this question reaches back to question (a)... how much
do you believe about modern cosmology -- especially with the missing
mass problem(s)...  It all goes back to being able to tell the
difference between being in an accellerating frame or being in
a gravitational field.  Gravitational red shift should be one way
to start to get a test, and that's been tested.

|> 
|> (e) Do antiparticles really travel backwards in time?  I mean, could you
|> use the spin state of a positron to send one bit of information into the
|> past?

The propogators look like they go backwards; the cross-sections for events
are all calculated in the forward direction.  Even so, there's symmetries
for the + roots and - roots that come from Klein-Gordon and Dirac fields.
The treatment of those roots, and the concommitant creation and destruction
operators for each of the field components, leads to the interpretation of
antiparticles as being time-reversed when you try to draw interactions in
the form of Feynmann diagrams.  I'm not sure I believe it means anything --
especially since there are some interactions that seem to violate time
reversal invariance.

|> 
|> Well, enough for one day.
|> 

Ditto...

Dan
-- 
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Daniel E. Platt                                      platt@watson.ibm.com
The views expressed here do not necessarily reflect those of my employer.
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