Re: phase in quantum optics

From: Edward Green (spamspamspam3_at_netzero.com)
Date: 10/03/04 

Date: 3 Oct 2004 10:54:18 -0700

John Denker <jsd@av8n.com> wrote in message news:<cjo1mk$pjg$0$216.39.142.124@theriver.com>...

> Edward Green wrote:
>
> > Semantic questions, but worth clearing up, I think.
>
> Quite so.

Thank you for your detailed response.
 
> > Ok. Then what do we call the instantaneous value of the thing which
> > is oscillating between +/- the amplitude, for short?
>
> If you want a term that works for all sorts of waves, not
> just the specific cases enumerated below, you can call it
> "the ordinate".

Very good -- "ordinate" it is then (though I can't say I've heard this
outside of HS mathematics)!

> Often though, people use case-specific
> names for the ordinate:

Of course, I should have thought of that.
 
> 1) For an electronic signal in a coaxial cable, the ordinate might
> be "the voltage".
>
> 2) For a sound wave in air, the ordinate might be "the pressure".
>
> 3) For mechanical wave on a piano string, the ordinate might be
> "the displacement".
>
> 4) For the important case of an electromagnetic wave, we have
> our choice of misnomers. Folks tend to call it "the field"
> which is short for "the electromagnetic field" which is even
> shorter for "the local value of the electromagnetic field"
> ... where the word "local" calls attention the fact that we
> are talking about the value of the field evaluated at a point,
> not the entire field which is by definition a function of
> position. (Locally we have a vector space; globally we
> have a vector field.)
>
> 5) Similarly for QM, folks tend to call it "the wavefunction"
> which is short for "the local value of the wavefunction".
> This terminology is valid for classical waves, too.

I've noticed recently, for what it's worth, how much of the
terminology of quantum mechanics is really an exact and appropriate
application of classical terms, which, in the minds of students and
students of students, take on an association through unfamiliarity:
the "wavefunction", as you say, is really an example of a broader
class of objects called wavefunctions, the "state vector" really is a
vector in a vector space and the "expectation value" really is an
expected value or mean of a random variable. But it is almost
impossible not to receive the initial impression these are special
terms coined for that mysterious entity called "quantum mechanics".

> > For what it's worth, I notice that both "amplitude" (your sense) and
> > phase are concepts which lose meaning for all but a simple plane wave,
> > whereas "instantaneous amplitude", whatever we call it, does not.
>
> That's a valid point, but not the only way of looking at it.
>
> An alternative is to Fourier-analyze the non-simple wave,
> whereupon each of the Fourier components has its own
> amplitude and phase.

True. For what little else it's worth, I recently caught myself, or
rather was caught, conflating "phase" and ordinate or field strength,
as I should have called it, when I blithely suggested looking at
surfaces of constant phase in two crossed EM plane waves, as if that
meant something.

I don't think I remembered to raise another small point in my reply:
you made the standard comments about only relative phase being
physically meaningful. I was going to ask what the limits of this
idea were: classically the absolute phase often seems to have physical
meaning -- consider a travelling transverse sine wave on a string...

I now realize the same semantic difficulty resurfaces, since I might
plausibly mean by phase a constant "phi" in sin(kx-wt+phi), which is
dependent on coordinates, and the value of the argument of sin() at a
particular locus on the travelling wave, with does not. I meant
classically the latter, instantaneous, phase at least often seems to
have an absolute meaning -- provided we are talking about pure sine
waves.

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