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From: stern@bnl.UUCP (Eric Stern)
Newsgroups: net.physics
Subject: Re: Light as the boundary between energy and matter
Message-ID: <399@bnl.UUCP>
Date: Fri, 30-Mar-84 21:35:15 EST
Article-I.D.: bnl.399
Posted: Fri Mar 30 21:35:15 1984
Date-Received: Sun, 1-Apr-84 08:30:02 EST
References: <939@ihuxm.UUCP>
Organization: SUNY StonyBrook
Lines: 73


   Let me try to give my interpretation of the standard views
on the issues raised in a previous article(939@ihuxm.UUCP).

   In that article, the question was raised about the difficulty
of classifying things.  My view is that when there is such a
problem, it means that the categories into which you are
trying to classify objects, are the wrong ones.  The example
given in the article, the archaeopteryx, is not clearly a reptile
or a bird.  I would say that "reptile" and "bird" are arbitrary
categories imposed on the continuous permutation of characteristics
exhibited by species.

   Fortunately, in physics the situation is far simpler.  The
phycisist in classifying objects has the goal of reducing a
complex object into a combination of finite and hopefully small
number of subunits.  There we have the hope that suitable
categories can be found to classify things.  In physics the
trend has been to unify dichotomous concepts such as matter
and energy, or particles and waves.  We now believe that
all matter and energy can be represented by fields, and
furthermore, that there is no difference between matter and
energy.  I should explain fields a little bit.  A field is
a mathematical construct that has a value depending on position
in space and time, and also on the quantum numbers of the
entity it represents.  The type of field also determines the
way in which that field interacts with other fields.  These
fields satisfy a minimum action condition which specifies
the propagation of the field in space and time.  These are
quantum fields though, so the field only specifies a probability
for any particular behavior.

   How do things look like both particles and waves?  The answer
is that the fields that represent particles are wave packets.
These packets are made up of a superposition of pure waves in
such a manner that the amplitude of the field is non-zero only
in a localized portion of space.  The field amplitude squared
respresents the probability that the particle exists at that
point.  So by making a localized field we have constructed
something that has the local property normally associated with
particles but made out of waves.  For events with a scale larger
than the size of the wave packet, the field behaves like a particle.
It is only when you look at distances smaller than the wave packet
size, that the wave nature becomes evident.

   Energy is a quantum number associated with a field.  The
minimum energy that a field can have in vacuum is its mass.
Fields also have momentum and the relation between the field
energy and momentum is the same as the relation between a
particle's energy and momentum, namely E**2 = P**2 + M**2 where
M is now the mass of the field and of the particle it represents.
I am going to use the term particle and field interchangably
in the next few sentences, with the understanding that the
field represents the particle.  In particle reactions, a particle's
energy may be used to create other particles (matter) or a particle's
mass may turn into energy of another particle.  The usual examples
are particle production and decay, for instance a proton
colliding with another proton may produce pions, and a particle
may decay at rest producing other particles at large energies,
but with a total mass less that that of the original particle.
Here, a propery normally associated with matter (mass) is being
converted into energy and vice-versa.

   Since matter and energy are being interconverted, the idea
that matter and energy are separate concepts breaks down, and
we are forced to broaden our categories to include the idea of
matter and energy as one concept thus unifying another dichotomy.

				Eric G. Stern
				SUNY StonyBrook

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