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[Phys-l] wave/particle duality, or not



I suspect that 10% of what I'm about to say is not quite right,
but I'm not sure which 10%. Challenges are welcome.

On 12/14/2008 06:57 AM, chuck britton wrote:

ok, it's coherence vs incoherence. I think that I can appreciate
this dichotomy.

I know I'm jumping into the middle of a discussion, but I'm
not convinced that coherence/incoherence is "the" dichotomy.
There's a lot of dichotomies in the world.
-- wave versus particle
-- male versus female
-- classical versus quantum mechanical
-- animal versus plant
-- coherent versus incoherent
-- chocolate versus vanilla

... and there are usually *not* close analogies between
one dichotomy and another. I offer a carefully-crafted
pedagogical analogy below, but even it has limitations.

But, as a dedicated pedagog who wants to bring as much understanding
as I can to the 'great unwashed' -
must I put aside the wave/particle words when dealing with true
beginners?

I would never say anybody "must" do anything. But I'm not
convinced that unwashed beginners care about wave/particle
duality.

Why would people who don't have any detailed notion of what
a wave is or what a particle is care about the "conflict"
between waves and particles? I reckon they only worry about
it if/when they've been told to worry about it. As for me,
I've got better things to worry about.

IMHO the nightmare scenario is to spend a day explaining what
a wave is, spend another day explaining what a particle is,
and then spend a third day explaining why the previous two
days were all wrong. It seems like a waste of three days.

Can't I use the analogy of
wave => incoherent and
particle => coherent

That seems mostly backwards to me, if it means anything at
all. Particles behave sorta like incoherent waves. But
backward or forwards, I don't buy it. There are coherent
classical waves and incoherent classical waves.

Example: The EM wave coming from a radio station is coherent,
and is classical by a huuuuge margin.

Example: The light coming from an ordinary incandescent
bulb is a classical wave, but is incoherent for all practical
purposes.

as a warm-up exercise?

We agree that seeking a warm-up exercise is smart strategy.

or is there too much evil lurking in the words wave and particle for
this to be acceptible?)

My strategy for students, and everybody else too, is to
avoid getting sucked into wave/particle discussions. I
don't want to discuss whether it's evil or not; I just
don't want to discuss it.

IMHO the better strategy is to discuss something else instead.

One good candidate for a warm-up exercise is _photon polarization_.
That is, rather than fussing with wave/particle duality we can
talk about linear/circular duality.

Photons can be linearly polarized (XY) or they can be circularly
polarized (LR) and various other things besides. The photon can
be linearly polarized OR it can be circularly polarized but not
both at the same time. Sometimes you can convert one to the
other and/or you can project one onto the other, but you can't
ride both horses at the same time.

Students can also appreciate that there's a lot of unpolarized
light in the world. Linearly polarized and circularly polarized
are just names we give to certain extreme cases.

I hope the alert reader has noticed that the previous two
paragraphs are a parable. You can substitute "wave" for
linearly polarized and "particle" for circularly polarized
and much of what I just said remains true.

The analogy is not 100% perfect, but it fairly deep and
almost quantitative. See gory details below.

The difference is that photon polarization is much easier
to understand (compared to wave/particle duality), more
relevant and practical, et cetera.

Polarized light experiments are easy and cheap and safe for
kids to do hands-on.

The theory is cloyingly simple; 2x2 matrices. Or if they
have never heard of matrices, just write it as two linear
equations in two unknowns; if you line it up properly and
write the variables small and the coefficients big, it looks
like a matrix whether you call it that or not.

If you want the gory details: I have a vivid mental
image of the phase space of a harmonic oscillator. This
space is spanned by the two dynamically conjugate variables.
For a mechanical oscillator, position is conjugate to
momentum. For an electrical LC oscillator, charge in the
capacitor is dynamically conjugate to flux in the inductor.
Or you could write things in a very symmetric way using
the two phasor components; the in-phase component is
conjugate to the quadrature component. You can measure
one phase or the other as precisely as you wish, but you
can't measure both at the same time ... which is where
we make contact with circular polarization and linear
polarization. It's just a change of basis. It's a
_linear_ transformation. It's reversible. Buzzwords
include canonical transformation, contact transformation,
Bogoliubov transformation.

Now there is a different sort of transformation that
switches from the voltage representation to the photon
number representation. This, for better or worse, is
a _nonlinear_ transformation. It is not reversible.
In phase space, states of constant photon number are,
approximately, _rings_ of constant Vx^2 + Vy^2. This
is worth mentioning because photons are _particles_.
So playing with linear transformations won't tell you
everything you need to know about particles versus
waves, But it will tell you a lot of good stuff,
and will lay the foundation for later (if necessary)
consideration of particles versus waves.

All this can be quantified using the formalism of
_second quantization_. The particle number operator
(a†a) is different from, but not wildly different from
the voltage operator (a† + a).

I say again: (a†a) is different from (a† + a), but not wildly
different.

===================

Back in the 1940s and 1950s, they taught classical mechanics
in undergrad school and then taught quantum mechanics in grad
school, if at all.

But we are smarter than that now.

In the 1960s, Feynman taught QM to college sophomores.

Nowadays, we teach QM to college freshmen and to high-schoolers,
and teach classical mechanics later if at all.

In quantum mechanics, there is no wave/particle duality. You
can say *everything* is a wave and a particle or both or neither.
I say neither. As far as I can tell, the big fuss about
wave/particle duality only comes up if you try to explain QM
in terms of classical mechanics. So, as Henny Youngman said,
don't do that.

The real world is quantum mechanical. Classical mechanics is
just a name we give to certain limiting cases. If/when you
find yourself *not* in one of those limiting cases, don't worry
about it, and don't try to explain it in classical terms.
Let QM be QM.