Re: POLARIZATION

[Leigh Palmer <palmer@sfu.ca>]

> At 15:39 6/15/98 -0700,Leigh wrote:
>
> > Please point out for the slower of those among us: what are you
> > arguing, and where is the argument? I surely don't see it. What
> > is the proposition? What are the assumptions?
>
> It will help if I here reproduce the question which I attempt to answer:
>
> ------------------------------------------------------------
> At 12:13 6/13/98 -0700, [James McLean] wrote:
> ...
> > If linear polarization can be described as a superposition of circular
> > polarization, and vice versa, how can one be more 'basic' than the other?
> >
> > --James McLean
>
> " Here's a weak, quantum argument:
>
> " A linear wave has twice the amplitude of its two component helical waves.
> " A helical wave has the same amplitude as its component linear waves.
> " In the limit, smaller helical waves are permitted than linear waves. QED
> ------------------------------------------------------------
>
>
> This is a 'reductio' argument for the least possible magnitude of two
> components of an electromagnetic wave which can yet synthesize a wave
> of a combined type.

Surely you realize that the "magnitude" of an electromagnetic wave
is quantity with which has not been generally recognized in the
physics community. Perhaps you should rethink what you say above.
In the development you suggest above there is no limit to the
degree to which one may make "smaller" waves. It is not  a quantum
argument at all.

This analysis is seriously flawed, principally because of a common
conceptual error. If one wishes to think about photons (and I will
usually be the last to adopt a photon model to explain physical
phenomena) then one must recognize that the components of a photon
are not themselves photons. "Components" refers to the terms in a
linear combination of wave functions. These are mathematical
entities; they are not physical ingredients which one may combine
to form composite systems. The photon itself is an indivisible
quantum, yet its wave function can readily be expressed as a
linear combination of wave functions.

> I say here that if two helical waves can have smaller amplitude than
> the least amplitude of a linearly polarized wave, then ipso facto the
> helical waves may be said to be more basic or fundamental than linearly
> polarized waves.
> One concludes that some equivalent of circular polarization exists at the
> quantum level, and one supposes this to be a 'spin' property.
>
> I see that not only is this 'weak' but difficult to follow as well?

I can't follow it; perhaps someone else can.

> > [Leigh]
> > I don't know what photopolarization is, either. Should I?
>
> I would have thought that a radio amateur (as Leigh has sometimes
> described himself) might also remark that the polarization of an
> electric dipole at radio frequencies is to be thought of as a
> statistical effect; for the quantum energy available at these low
> frequencies implies that very many photons would be associated with
> even the few watts emitted as plane polarized waves by say a cell-phone.
>
>  An electrochemist, by contrast, might tend to associate polarization
> with polarography than polarimetry; he would be alerted by the "photo-"
> prefix, I had hoped?

I'm still not enlightened. Perhaps reference to some source I
might have on my bookshelf would help.

> > *A* photon picture is entirely adequate to model polarization
> > phenomena. *No* model explains all electrodynamic phenomena
> > except in an *ad hoc* manner.
> >
> > Leigh
> Leigh seems to have let passed unnoticed my recent assertion that his
> "adequate photon picture" appears to have lead him into error in
> connection with the putative lack of angular momentum or spin of a
> single photon, "transmitted or not" as he recently asserted.
> I will take this opportunity to replay this interesting thread
> as a rebuttal:
>
> -------------------------------------------------------------------
> At 17:35 6/11/98 -0700, Leigh answered this question as follows:
>
> > > So can one account for the phenomenon (of polarization) in terms of the
> > > interactions of spinning photons with the polarizer?
> [Leigh]
> > If one considers the interaction of a circularly polarized
> > photon with a (dissipative) linear polarizer, then its
> > angular momentum is absorbed by the polarizer whether it
> > is transmitted or not.
>
> [Me - bw]
> " This statement appears to be completely in error, if by circular
> " polarization of a single photon one is referring to its spin.
> " A photon has spin or it is not a photon.
> " I expect Leigh had some other meaning in mind.
> -------------------------------------------------------------------------
>
> I attempted in my introductory text to make clearer the "quantum argument"
> which I employed as a basis for the claim that helical polarization is
> a more fundamental property than linear polarization.
> This represented my answer to James McLean's question: which polarization
> type is more basic.
>
> I suppose that helical polarization is likely to be a manifestation of
> the 'spin' value associated with a photon because it is not usually held
> that an individual photon may exhibit properties such as polarization,
> considered as a seperate parameter.
>
> Having attempted to expand my position, I can ask if now Leigh would
> favor us in turn with his explanation for the surprising statement that
> a photon can lose its angular momentum and survive?

OK. We adopt a photon model. (More on this later.)

Isystem = circularly polarized photon + ideal linear polarizer.
Polarizer is initially at rest; photon is propagating in direction
normal to polarizer. Photon has been prepared by dilution from a
beam of circularly polarized light and possesses nonzero linear
and angular momentum.

Interaction occurs.

Final states of system possible, both equally probable:

Fsystem1 = polarizer moving with initial linear and angular
momentum of photon. The photon has been absorbed by the polarizer.

Fsystem2 = polarizer moving with initial angular momentum of
photon, linearly polarized photon moving with undiminished linear
momentum.

The usual idealizations apply to these interactions.

Now I ask the question: what is the value of adopting a photon
model to explain this very simple wave phenomenon? It is not
difficult to do so, but where is the conceptual payoff? In what
way is this picture superior to the conventional picture? Is
there some inherently quantum mechanical aspect to the
phenomenon? In my opinion the gratuitous introduction of photons
encourages conceptual errors. Photons are a fine way to treat
the photoelectric effect; they don't help anyone to understand
polarizetion.

I apologize for not answering your previous posting of this
question, Brian. I was trying to remain consistent in my policy
of ignoring threads that were initially cross-posted to both
groups for no good reason (the POLARIZATION thread started that
way). I had changed the subject line to be helpful, but for some
reason you changed it back.

Others may not object to gratuitous cross-posting; I do. I don't
require that others share my feelings, but I reserve the right
to ignore such crosspostings.

Leigh