Re: Is light a wave or a particle?

From: Aleksandr Timofeev (a_n_timofeev_at_my-deja.com)
Date: 10/13/04 

Date: 13 Oct 2004 02:20:09 -0700

Timo Nieminen <timo@physics.uq.edu.au> wrote in message news:<Pine.LNX.4.50.0410111333500.8960-100000@localhost>...

[snip]
 
> By the way, have you been able to come up with any cheap interferometric
> experiment to check whether your theory of light or classical
> electromagnetic theory describes real-world light more accurately? Or are
> you just going to continue to offer your overpriced inconclusive rocket
> experiment (basically just a repeat of de Sitter!)? I would have expected
> that you would be eager to propose an experiment that (1) might actually
> be carried out, and (2) might actually test things one way or another!
>
> Have you been able to come up with any quantitative relations for
> photon energy, frequency, momentum, wavelength and speed in your theory? I
> would have expected that you would be eager to provide such, so as to
> facilitate comparison between your theory and experiment. Are you scared
> your theory might fail experimental test?

In regard to your request

"any quantitative relations for photon energy, frequency,
momentum, wavelength and speed "

, no decision has been made officially by John Baez:

"Education is a process of telling a carefully chosen sequence of lies
in which the amount of deliberate deception gradually tends towards zero.
There is a limit to how much truth someone can absorb all at once without
their brain turning to jelly!" John Baez

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http://groups.google.com/groups?selm=78g1c2%24vfe%241%40pravda.ucr.edu

From: baez@galaxy.ucr.edu (john baez)
Subject: Re: photon wave-functions?
Date: 1999/01/27
Message-ID: <78g1c2$vfe$1@pravda.ucr.edu>#1/1
Approved: mmcirvin@world.std.com (sci.physics.research)
Sender: mmcirvin@world.std.com (Matthew J McIrvin)
Organization: University of California, Riverside
Newsgroups: sci.physics.research

In article <78d7ds$q6v@news.dtc.hp.com>,
(Greg Weeks) <weeks@orpheus.dtc.hp.com> wrote:
>In the discussion single-photon wavetrains, it seems to be generally
>assumed that the photon has a wave-function. Even in free field theory, I
>don't believe this is true.

Education is a process of telling a carefully chosen sequence of lies
in which the amount of deliberate deception gradually tends towards zero.
There is a limit to how much truth someone can absorb all at once without
their brain turning to jelly!

Oz - or whoever originally asked the question - seems to be wondering
something like "what's the shape of the wavefunction of a photon of a
given energy?" Of course they're not phrasing it that way, but that's
my desperate attempt to translate it into something I can understand.

Now you're right, it's a bit of a pity that they chose a *photon* as
the particle to ask about in this question. Massless particles are a
nuisance because the Newton-Wigner localization breaks down. Gauge
bosons are a nuisance because it's harder to separate out the physical
degrees of freedom in a gauge theory. So even *ignoring* the extra
subtleties when we take interactions into account and drop the pleasant
fictions of free field theory and Fock space, we have some serious
issues to deal with in a complete answer to this question!

But if someone asks the question "what's the shape of the wavefunction
of a photon of a given energy?" and you start talking to them about
Newton-Wigner localization, gauge-invariance, and Fock space, their
brain is going to turn to jelly! They're going to walk away in a daze
having learned nothing. They'll probably be shocked that such a simple
question elicited such a complicated bunch of mumbo-jumbo. They may
become politicians and cut funding for physics.

So you have to tell them something helpful even if it's oversimplified.

First and foremost, it seems to me, you have to disabuse of them of the
assumption that the wavefunction of a particle has some fixed "wavetrain
with finitely many wiggles" shape that depends solely on the energy of the
particle. When one starts out learning physics, one tends to think of
a particle as a little tennis ball or something, perhaps with some wiggly
waves thrown in for good measure. The idea that it's just a "field mode"
doesn't come easily! Usually one absorbs this slowly and painfully by
solving Schrodinger's equation with all sorts of different boundary conditions
and potentials, learning all sorts of different orthonormal bases for the
space of states, and eventually realizing that the choice of basis is just
a matter of convenience. The idea that a particle is just a solution of a
partial differential equation and that there are *lots* of solutions having
the same expectation value of energy, or even the same eigenvalue - that
doesn't come easily! So, somehow you have to broach these issues.

Thus I'm reluctant to talk about the issues you're raising now. They're
too fancy for this conversation. I'll just whisper to you the approach
I'm implicitly taking towards this question:

>What, then, is a photon's wave-function?

I'm taking it to be a solution of Maxwell's equations, either described
using the vector potential in some fixed gauge, or perhaps even better
for the present purposes, using the electric and magnetic fields. I bet
people who do quantum optics do something like this when they talk about
the wavefunction of a photon, and I don't think it's so bad, despite the
objections you note.
====================================================================

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