Newsgroups: sci.physics
Subject: Re: Size of neutrino
From: mcirvin@husc8.harvard.edu (Mcirvin)
Date: 15 Sep 92 18:59:43 GMT
 <1992Sep15.064618.6423@midway.uchicago.edu> <1992Sep15.143024.20764@CSD-NewsHost.Stanford.EDU>

pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:

>In article <1992Sep15.064618.6423@midway.uchicago.edu> mfm0@midway.uchicago.edu writes:
[about the size of fundamental fermions, including electrons and
 neutrinos]
>>I seem to remember a upper bound on the size of an electron,
>>a statement like "we know that an electron is smaller than
>>10^-x cm in diameter.

>Then you have the corresponding lower bound on its momentum.  There is
>no a priori reason I know of to place any lower bound on the momentum
>of an electron.

You're thinking of the other definition of the size of a particle.
Confusion between these two concepts has bedeviled all sci.physics
discussion about the "size of photons."  Particle people generally
mean one thing and quantum-optics people another.

What a particle physicist means by the size of a particle is the
distance over which its field can interact with other fields.  The
electron has a tiny size, zero as far as anyone knows, by this
definition.  The electron field operator at a given point only
acts as a source for the electromagnetic field, for instance, *at
that point*, and electromagnetic effects propagate to and from there.
On the other hand, since a proton or a pion or an atom has a certain
size, the effects of the particle's field are smeared out:  the
proton field operator at a certain point can serve as a source for
other fields a short distance away, since we're still "inside the
proton" there.  In this sense, in standard particle physics, all
fundamental particles are infinitely small.  Whenever experimental
data show that some sort of nonlocal effect is present in the 
interactions of fields, physicists start thinking about the particles
in question being made up of constituents.  No such effects have
been seen for the electron, so there's just an upper bound on the
size.  In this sense the photon is a point particle too, in the
standard model. 

What you're thinking of is different-- it's more like what a physicist
working on quantum optics means by the "size of a photon," namely the
uncertainty in position.  In this sense a particle in a plane wave
state is infinitely *large*.  Putting an upper bound on this will
indeed put a lower bound on the uncertainty in momentum.  But this
is not the sense in which there is an upper bound on the electron
size.
 
>Or does the phase velocity / group velocity distinction somehow enter
>into the story in order to distinguish "size" from "uncertainty in
>position"? 

The real distinction between the two concepts of size is that
one refers to *interactions*, and in particular to the extent to
which the interaction Hamiltonian depends on fields evaluated at
the same point; whereas the other refers to uncertainty in position.

You could argue, as some did recently, that the locality of
interactions is distinct from the true size of the particles,
but the question is really academic, since a particle without
interactions is an undetectable one.
 
>Are fermions such as electrons any more "concrete" than
>bosons such as photons, in regard to the size question?

Not really; it's more a matter of which kind of size is being
talked about by the people who work with the particles.

>I rather doubt
>it but I'm in the process of trying to grasp this stuff myself just now
>and I still feel shaky about getting an electron out of Dirac's
>equation.

You're in good company, then.  That's a sticky matter.

>-- 
>======================================================| God found the positive
>Vaughan Pratt   pratt@cs.Stanford.EDU   415-494-2545  | integers, zero was
>======================================================| there when He arrived.
-- 
Matt McIrvin, Cambridge, Massachusetts, USA 
Newsgroups: sci.physics