Re: POLARIZATION

[brian whatcott <inet@intellisys.net>]

[John]
> > > The *rms* amplitude (i.e., the only one that "really matters") of 
> > > a transverse wave is always sqrt(2) times larger than that of its 
> > > two equal amplitude component waves whether the wave is linear and 
> > > the components helical or vice-versa.  This is a simple 
> > > mathematical result and it (reassuringly) agrees with the dictum 
> > > of conservation of energy since the intensity of a wave is 
> > > proportional to the mean square amplitude.
> > >
> > > John
[bw]
> > It is certainly not difficult to frame an elementary rebuttal to 
> > this curious post....

[John]
> It's easy to "rebut" an argument by constructing strawmen.  A second
> reading of my post, however, will surely reveal that I was referring to
> two cases and two cases only: 
>
> 1  A linearly polarized wave constructed from two equal magnitude
>   circularly polarized ("helical") waves 
>
> 2  A circularly polarized wave constructed from two equal magnitude
>   linearly polarized waves

I ask for John's forgiveness in dismissing his argument by taking his
proposition as free-standing, when in fact he was precisely and 
exactly discussing the two component wave that I had in mind, as I can 
now see by reviewing his two case definitions.
 This is a much more telling position.

 I take John's point as just that argues that a photon of given 
frequency carries a given energy; that if two photons considered as 
waves are superposed, their rms combined amplitude would be 
expected to grow by a factor of root(2) so that their combined energy,
which can be measured as an intensity proportional to amplitude squared, 
is in fact doubled.

I now ask John to evaluate the thrust of my argument, which 
I shall restate here in a form closer to John's conceptual arrangement.
By applying a letter prefix to each proposition, I hope John will be 
able to indicate at which point in the text I diverge from the facts.

A) Given two helical waves of mirror phase rotations, a resultant 
linear wave of peak amplitude larger than either of the component 
waves is produced.

B) Given two linear waves of orthogonal polarization and zero phase
difference, a linear wave of peak amplitude larger than either 
component wave is produced.

C) Given two linear waves of orthogonal polarization and pi/2 phase
difference, a helical wave of peak amplitude IDENTICAL to its 
components is produced.

D) Case A gives a peak amplitude of twice that of the component waves.

E) Case B gives a peak amplitude of root(2) of that of the component 
waves.

F) Case C gives a peak amplitude the same as that of its components.


G) I shall suppose that John in fact agrees with all six of these 
propositions. I built my case on the basis of propositions A) and C)
by noting that a synthesized linear wave has greater peak amplitude (D)
than the synthesized helical wave (F)

H) Ah yes! I think I see that John sets this aside by noting the rms 
amplitudes may be the same for all cases.

I) If cases A) thru C) do in fact carry the same aggregate energy
then the 'weak' argument I put forward is easily refuted.

J) If case A) can be constructed from components as small as one 
photon each, but case C) can only be constructed from components of 
higher energy, my assertion is not disproved.

K) We would then be left with the question: is helical polarization
a facet of the spin property of the photon?

L) Either polarization is a facet of photon spin, or if not there is 
a NEW property of a photon which would be called polarization.

> ... a linearly polarized wave of
> zero amplitude may be constructed from two (opposite parity) circularly
> polarized waves of equal amplitude if and only if those amplitudes are
> zero as well.  The same holds for constructing zero amplitude circularly
> polarized waves from two (orthogonal) linearly polarized waves. 
>
> John

Agreed!

(May I also ask if John supports Leigh's assertion that a photon 
may be stripped of momentum and survive?)

Sincerely
Brian Whatcott     Altus OK