From: bhv@areaplg2.corp.mot.com (Bronis Vidugiris)
Subject: Re: Why are elementary particles small?
Organization: Motorola, CCR&D, CORP, Schaumburg, IL
Date: Wed, 6 Jan 1993 10:49:04 GMT

In article <MATT.93Jan3200346@physics2.berkeley.edu> matt@physics.berkeley.edu writes:

)This is, unfortunately, a confusion of two different senses of what
)"the size of a particle" means.
)
)The first is: quantum-mechanically, we can describe the position of a
)particle by a wave function.  We could, then, say that the size of the
)particle is the size of the wave packet that describes its position.
)
)The second meaning is a somewhat more intrinsic one: when we write a
)wave function for a particle, are we writing about the spatial
)distribution of a point object, or an extended object?  One way to
)understand this distinction is to think about interactions; an
)interaction between point particles is local, but an interaction
)between extended objects (e.g., protons) involves points separated by
)spacelike intervals.
)
)When particle physicists talk about the sizes of particles, they
)usually have the second idea in mind, just because it is more
)intrinsic; after all, you can write an arbitrarily large wave packet
)for any particle. 
)
)And as far as we can tell today, photons do appear to be point
)particles.  (As do the other gauge bosons, the gluon, W, and Z.)

A few related points on the 'size' of photon wavepackets.

In 'Quantum Reality', Nick Herbert points out that the 'size' and 'shape' of
the  wavepackets of photons from distant stars is a thin 'fuzzy' disk
which varies from a *minimum* of about 3ft (don't recall the exact figure) in
diameter to a maximum larger than the entire solar system.  This 'size' can
actually be experimentally measured using the idea of a 'self-interference
distance'.  Herbert cites "The Intensity Interferometer", Robert Hanbury
Brown, New York: Halstead Press (1974) for a more complete reference.
Several stars were actually measured with this device in order to determine
their angular size (and hence their physical diameter, given that the
distance to the star can be determined by parallax measurements or other
means).  'Sizes' up to a limit of several hundred feet (the diameter of the
apparatus) were actually measured.

If photons from a distant star can be thought of as 'fuzzy disks',
spectrally pure photons from a laser can be thought of as long fairly
thin lines.  This again comes from a 'self-interference' concept - the
self-coherent length of a laser is a useful concept when preparing holograms,
and depends on the spectral purity of the source.  I believe that there
is a limit on the spectral purity of a laser set by the length of its
resonant cavity - the 'long photon' has to fit inside the resonant cavity
of the laser, so you can't get a self-coherent length longer than the
resonant cavity size.  [This also suggests that if you 'cut' the 'long'
photons somehow, say an apparatus which confines the photon to a length
shorter than its previous self-coherent length, you also destroy the
spectral purity of the photon/beam.  I believe that this would be borne
out in practice using the Heisenberg principle of measuring location ->
uncertain angular momentum -> uncertain energy.]

Thus the 'size' of a photon defined in this way isn't really a property
of the photon itself, or its energy, but of the details of how it is
'prepared'.

The ideas of self interference are really more suited to a beam than a
particle, IMO, and more readily understood in that context.  However,
the idea that light is a particle as well as a wave more-or-less forces us to
view each individual particle as having 'self-interference' length
property, even if it doesn't make a lot of sense, as these interference
patterns do not disappear even when only one photon is present in an
apparatus at a time.
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