Re: wave and light

From: zigoteau (zigoteau_at_yahoo.com)
Date: 09/18/04 

Date: 18 Sep 2004 05:32:21 -0700

srp@microtec.net (Andr? Michaud) wrote in message news:<562f286c.0409170908.11410809@posting.google.com>...

Hi, André,

> Your post got me to thinking of the hypothetical physical structure
> of a maxwell pure EM wave "if it really could exist".

Of course EM waves exist. Light is an EM wave.
 
> Maxwell's original theory (before the idea of photons was conceived
> of) has traditionally been dealt with strictly from the mathematical
> point of view offered by plane wave treatment, which resulted, obviously,
> in the space geometry that mandatorily must underlie it to perpetually
> remain obscured.

Obviously?
 
> Space being three-dimensional, it seems to me that treatment by plane
> wave analogy can only be a mathematical approximation that easily
> obscures the fact that physically, an actual electromagnetic wave,
> if they could exist as Maxwell defined them) could only be in spherical
> expansion in vacuum from its point of origin, assuming unbounded
> isotropic expansion in deep space; Maxwell's equations describing
> the electromagnetic interaction only once the wave already is in full
> swing and has begun to propagate.

This all seems OK, eve if the way you express it suggests you don't
know how to analyze it.

> Consequently, if electromagnetic waves such as Maxwell imagined really
> existed, the geometry of their propagation would of necessity be much
> more similar to the spherical expansion of sound waves in the air than
> to the propagation of waves on a plane liquid surface, but it then
> becomes somewhat difficult to accept the idea that the intensity of
> the initial energy of the wave could be maintained at all points of
> the wave front.

Well of course, real light beams usually become weaker with distance,
although using a lens you can get the intensity to increase for a bit.

> Obviously, he found no way to mathematize the wave at its source,
> most probably due to the insurmountable problem caused by the assumed
> infinite energy that is associated with all such a punctual electromagnetic
> event in his theory.

Maxwell lived a long time ago, and various aspects of the analysis
have become easier with new methods.

> That's where photons came into the picture to solve the problem of
> maintaining the energy at all points of the so-called wavefront.

No. Your statement here suggests that you don't know any quantum field
theory. Maxwell's equations are still the basis for modern quantum
optics.

> Plane wave treatment does that, as for physical counterpart,
> only photons come to mind, and not continuous spherically
> expanding wave.

Mathematically-perfect plane waves cannot be implemented. However it
is possible to implement beams of light whose behavior can be
understood in terms of the ideal mathematic objects. It is possible to
do even better and treat a real light beam as if it were the sum of an
infinite number of ideal plane waves.

> > A traveling EM wave consists of coherently arranged
> > photons, and while it might be empirically impossible
> > to define a wave front of zero photon energy density,
> > Old Man knows of no theoretical limitations against
> > doing so.
>
> Since the photon concept (discrete EM events individually moving at c)
> cannot truly be reconciled with the continuous wave idea (I don't
> see how, anyway), I can't comment on this.

It sounds as if you have been confused by quantum mechanics. There are
a lot of people in this situation. I'm not sure if I can totally go
along with Old Man's statement.

The word 'photon' describes the particle-like aspects of light.
However there is nothing in the quantum field theory of light with the
individuality suggested by the word. In modern quantum optics,
'photon' is used almost synonymously with 'electromagnetic field'. The
particle aspects are apparent when the field is observed. A silver
halide grain turns to silver, or an electron-hole pair is created in a
block of silicon, and you can say that a photon has been absorbed, but
you would not have been able to predict from the theory which grain,
or where the e-h pair would materialize.

The EM field in any system has modes. You can say "Mode A has 5
photons in it, and mode B has 6 photons". You can never have a
fractional number of photons. However you can't say where the
individual photons in each mode are at any one time, and you certainly
can't label them and say, "There's the 3rd photon of mode A". If the
system was definitely in mode A at the beginning of the experiment and
definitely in mode B at the end, you can say that there's one more
photon in the system, but you can't say for certain when it arrived,
because in the middle of the experiment the system is in a
superposition state.
 
> I can find logic either in continuous EM wave treatement (Maxwell's
> initial idea) or in discrete EM particles treatment, but I connot
> reconcile both.

(1) Maxwell's equations are at the basis of quantum optics
(2) with the added complication of quantization

Are you familiar with second quantization notation?

> > Furthermore, it seems that having a wave front of
> > maximal intensity involves a discontinuity in the field,

> It does only if we try to incorporate the photon idea in
> wave treatement.

> > whereas a wave front of zero intensity involves, at
> > most, a discontinuity in the field gradient.
 
I definitely do not go along with Old Man there. A field discontinuity
is inconsistent with Maxwell's equations. In quantum optics, the field
at a point is an operator, which can be attached to a distribution of
possible values of the classical field. There is no way you can attach
any operational meaning to the word 'discontinuity'.

On the positive side, quantum optics is a good deal easier to master
than quantum electrodynamics, the quantum field theory of electrons
and photons together. If you're serious about learning, I haven't seen
any textbook good enough to take you from the classical concepts to
the quantum ones. I think it's essential to have a teacher. I hope you
can find one.
 
  
Cheers,

Zigoteau.

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