I'm no field theorist, just a knuckle-dragging experimentalist, but it
seems to me there is one "obvious case" -- photon self-interactions.

Classically, the linear Maxwell equations require that electromagnetic
waves pass through one another without effect.  However, in QED, loop
diagrams such as
                                 g *       * g
                                    *_____*
                                    |  e  | e
                                  e |_____|
                                    *  e  *
                                 g *       * g

give photon-photon couplings, and hence two electromagnetic waves in
vacuum which intersect _can_ affect one another in ways contrary to
classical electrodynamics.  Since this effect only appears in a
quantized theory (which I thought had been demonstrated with
ultra-high power lasers, though I can't find a reference), it seems to
me that it requires the in-transit EM field to be quantized, or
"particulate", if you want to use that term.

                                                -- Mike Kelsey
--
[ My opinions are not endorsed by SLAC, Caltech, or the US government ]
 "I've seen things you people wouldn't believe.  Attack ships on fire
  off the shoulder of Orion. I've watched C-beams glitter in the dark
  near the Tannhauser Gate.   All these moments will be lost in time,
  like tears in rain."                                    -- Roy Baty

I'm not yet convinced that there is any obvious case in which it is
necessary to use a particle model to describe electromagnetic radiation
in transit.  Of course, since emission of photons is a quantized
process, disturbances to the field will normally themselves be at least
approximately quantized, and for waves (at least below the energy needed
to create electron/positron pairs) it is only through interference
effects that the transmitted and received disturbances can avoid being
one to one equivalents.  I don't count the Compton effect as proof
because it involves a quantized interaction, but I think that some
experiments relating to "empty waves" might convince me.

I'm basically just taking a "devil's advocate" position against the
particle model of waves, because I get the impression that it has not
really been shown to be necessary so far, and that using terminology
which assumes a particle model may possibly be placing unnecessary
constraints on our mental tools for understanding quantum theory.

Jonathan Scott
jonathan_sc...@vnet.ibm.com  or  jsc...@winvmc.vnet.ibm.com

              ********************
                    *     *
                    *     *
               *******************
for photons but you will find a similar diagram for gluons. The reason
is mentioned above. This sort of diagrams are called self
interactions.

But you are right. Photon-photon scattering (the one which you drew)
is predicted only by QFT. Its a fourth order QFT effect. There is no
classical prediction of Photon-Photon Scattering to my knowledge
(although I would welcome if anyone provides evidence to the
contrary). But anyway such photon-photon scattering diagrams (the
first diagram which you drew) is called VACCUM POLARISATION. Its not
SELF INTERACTION. VACCUM POLARISATION  and SELF INTERACTIONS are
completely different.  

Anyway as one final note : I donot have any objections to the views
you expressed. In fact I agree with them whole heartedly. I just
wanted to point out that self interaction is different from self
energy. Photons donot self interact. Photons being gauge bosons in QED
and QED being an Abelian theory there is no self interactions of
Photons. Gluons on the other hand being gauge bosons of QCD (which is a
non abelian theory) have self interactions. The self interactions of
Gluons are in a way responsible for the aymptotic freedom in
QCD. Without asymptotic freedom QCD would be not very practical as no
perturbative calculations could be done.

No dispute about that; I was loose with my terminology.  Loop diagrams of
the form I considered are vacuum polarizations, in exactly the same way as
modifications to the single-photon propagator by e+e- virtual pairs.  I'm
a bit ticked off by your vituperativeness; the other theorists involved
in this discussion recognized and understood what I meant, and corrected
me less violently.

|> Yes actually you can Compton backscatter two laser beams and get
|> the effects of photon-photon collision. This is a quite well
|> established practice and it is being done for a number of years
|> now.

I'm confused by this.  I thought that Compton backscattering was when you
collided a laser (for example) with an electron beam, not two lasers.
For example, that's how the polarization of the beams at the SLC is
measured: on the far side of the IP, a circularly polarized laser (using
a series of Pockells cells) interacts with the outgoing e- beam, and the
intensity of the scattered beam is measured, with both the electron and
laser polarizations being varied randomly and independently.

The expreiment you describe would be exactly the sort of thing I was
concerned with -- photon-photon interactions through higher-order
diagrams.  Since it's an O(a^4) process, and all anyone else in this
thread has mentioned have been null upper-limit results -- I wouldn't
expect it to be a "well-established practice."  Am I missing something?

                                                -- Mike Kelsey
--
[ My opinions are not endorsed by SLAC, Caltech, or the US government ]
 "I've seen things you people wouldn't believe.  Attack ships on fire
  off the shoulder of Orion. I've watched C-beams glitter in the dark
  near the Tannhauser Gate.   All these moments will be lost in time,
  like tears in rain."                                    -- Roy Baty

I've thought about this a bit more, and you _can_ sensibly use the term
"self-interaction," from the viewpoint of an effective theory, rather than
the underlying Lagrangian.  Let me argue by analogy to something I am a
bit more familiar with.

In the standard model, there are no direct flavor-changing neutral currents.
That is, both the photon and the Z^0 couple to particle-anti-particle pairs
only (Z0 -> e+ mu- or c u are absolutely forbidden).  However, a Penguin
diagram, such as b -> W+* (u,c,t)* -> s, is a higher-order process which
gives the "external appearance" of a flavor-changing neutral current, and
in fact you can build an effective field theory where the W-t loop is
collapsed into a vertex with an effective coupling constant for the flavor
change.

Similarly, it seems to me that you can take the box diagram(s) for the
gamma gamma -> (stuff) -> gamma gamma interaction, and subsume them into
an effective four-photon vertex with some phenomenological coupling
constant.  In such an effective field theory, this would indeed be a
photon "self-interaction," and only when you looked "inside the vertex"
would you see the underlying photon-fermion interactions that generate it.

                                                -- Mike Kelsey
--
[ My opinions are not endorsed by SLAC, Caltech, or the US government ]
 "I've seen things you people wouldn't believe.  Attack ships on fire
  off the shoulder of Orion. I've watched C-beams glitter in the dark
  near the Tannhauser Gate.   All these moments will be lost in time,
  like tears in rain."                                    -- Roy Baty

I would however like to thank the other person who provided some
references on photon-phton collisions.

Just in passing, following the general refutation of the poor old photon 'in flight', I guess any interaction could be considered as operating at the photon (ie quantised) level. Seems to me that any EM interaction (even with another EM) will be regard
d as a quantised interaction, which of course it is. Should perhaps be in philosophy 'how to see the unobservable'.

--
-------------------------------
'Bye, Oz    
"I am always doing things I can't do, that's how I get to do them": Picasso

Whilst it is indisputably true that the photon does not exist in an
inertial universe (or is it the other way round?) I don't really think
that there is any evidence against considering it could see the
universe this way, simply taking relativistic views to the limit. One
can after all propose this for inertial particles to any arbitary
degree of accuracy as they approach C. Argueable anyway. What I am NOT
saying is that a photon 'is' a particle, it could equally be (probably
is) a wave propogating at C.

Now a light 'wave' (ex Mr Maxwell, but probably dated) propogates at C
IN ALL DIRECTIONS, the 'direction' of the photon or light beam being
the sum of all paths, in other words it's observable universe is only a
subset of the inertial universe due to mirrors/lenses/planets etc etc.
Within its universe, that universe has zero size. It is therefore
everywhere simulaneously in its universe, hence no problem with it
going through both slits simultaneously (cos its going in all
directions simultaneously). Please note that in this world view the
frequency of the wave is 'merely' the representation of its energy in
the inertial frame of reference.

There may be good arguments against this! (Particularly as it hasn't
really been adequately thought out).

Now we need to take on the wave aspect of inertial particles. I really
don't have enough knowledge any more to extend this adequately. My
knowledge of Feynman's technique is regettably 'popular' (which shows
my age). However could I ask if the summing over all possible paths is
regarded as the ACTUAL representation of the particle, or just a
convenient mathematical technique. I ask this because for quite a time
that was the view taken of relatavistic analyses, and also quantum
mechanical ones, whilst now these are regarded as real.

I hope you can find the energy to continue the discussion.

--
-------------------------------
'Bye, Oz    
"I am always doing things I can't do, that's how I get to do them": Picasso