From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Size of neutrino
Organization: Computer Science Department,  Stanford University.
Date: Wed, 16 Sep 1992 01:15:11 GMT

In article <mcirvin.716583583@husc8> mcirvin@husc8.harvard.edu (Mcirvin) writes:
>pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>You're thinking of the other definition of the size of a particle.
>What a particle physicist means by the size of a particle is the
>distance over which its field can interact with other fields.  The
>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.

Ah, excellent.  Thanks.

>In this sense a particle in a plane wave state is infinitely *large*.

Only in two dimensions, namely in that plane.  A week or so ago I asked
(in the context of describing the hundred-foot-wide photons collected
at the Narrabri stellar interferometer) how big these photons were in
the direction normal to the plane, but no one answered.  (To be exact,
I asked how thick a photon from a distant star was.)  I still can't
think how the thickness would vary if at all as it traveled away from
the star.  Nor can I see what the shape of the wave packet should be
for a single photon.

So again: can anyone tell me how *thick* a photon is (quantum
optically)?

>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.
>...
>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.

For the second concept, does the physicist in quantum optics really
*mean* this, or is this better described as an indirect way of
determining a directly observable property?  Doesn't the Narrabri
stellar interferometer directly observe photon diameter?  This is how I
recall Hanbury-Brown describing the principle to us in Physics 4 in
1966.

In the same message asking about thickness of photons, I also asked
whether the photons existed in transit or only at transmission and
receipt.  I gave this some more thought, but was unable to come up with
any reason for preferring the former view over the latter.

But then with that viewpoint I found myself wondering why the stellar
interferometer was described in terms of photon size at all.  Well,
actually the whole setup is easily understood classically.  The two
antennas form the 2 slits of a conventional 2-slit setup.
Monochromatic light from a point source creates a diffraction pattern,
nothing quantal about that.  As you move this point around the surface
of a larger source, say your star, the pattern moves around too.  The
cumulative effect for the source as a whole is then the convolution of
the pattern with the shape of the source.  But this is the exact same
description of what happens when you defocus a lens.  Therefore as the
source widens the diffraction pattern drifts out of focus until it
disappears.  This happens when the width of the image of the star is on
the order of half the spacing of the fringes.

OR you can hold the star fixed and move the slits apart, as done at
Narrabri.  Now the fringe spacing decreases; when it shrinks to the
order of twice the diameter of the image of the star it disappears.

Since this explanation doesn't depend on photons, why is the Narrabri
instrument explained in terms of them?  For pedogical value when
explaining quantum mechanics, or for some more substantive reason?

The idea for the stellar interferometer, exactly as described above,
goes back to Fizeau in 1868.  Stefan built one in 1874, measured the
separation of a double star, then tried but failed to measure the
diameter of a single star.  In 1890 Michelson used one to measure the
diameters of Jupiter's satellites.  In 1920 Michelson and Pease built a
much larger one and measured the angular diameter of Betelgeuse to be
.047", for which they had to move the slits ten feet apart.  (As a
check that the fringes hadn't disappeared for some other reason they
pointed it at a smaller star and the fringes returned.)  [C.J. Smith,
Optics, Edward Arnold, 1960.]

So all the Narrabri interferometer would seem to be is just a yet
larger stellar interferometer.  And yet when people talk about using
photon diameter to estimate stellar diameter they always cite the
Narrabri instrument as the prima facie example of this phenomenon.  Why
do they cite only this massive latter-day instrument rather than
Stefan's original instrument based on Fizeau's idea?  This sounds very
misleading.  I was sure as heck misled, I thought, gee, here's a
really neat application of quantum mechanics in astronomy, and it sounds
like some other people on this list may have been misled too.

This must surely have been pointed out by someone at the time photons
and Narrabri were first juxtaposed, but I'm not aware of it.  Am I just
confused?  Does anyone want to defend the photon explanation of
Narrabri as somehow differentiating it from Stefan's setup?

This in no way is meant to contradict the claim that photon diameter
really is being measured directly.  It certainly is, but Stefan was the
first person to measure the diameter of a photon, in 1874, not bad for
someone who'd never even heard of photons.

-- 
======================================================| God found the positive
Vaughan Pratt   pratt@cs.Stanford.EDU   415-494-2545  | integers, zero was
======================================================| there when He arrived.
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