Re: [Phys-L] Spins First

[John Denker <jsd@av8n.com>]

On 06/09/2014 12:24 PM, David Craig wrote:

> I’m interested in people’s attitudes toward and experience with the 
> “spins first” approach to teaching the junior-senior level quantum 
> mechanics course, which seems to be gaining in popularity in some 
> intriguing new textbooks (e.g. Mark Beck’s).

It's not entirely a new idea.  Some 50+ years ago there
appeared a large red book that spends a lot of time on
two-state systems before extending that to countably-many
states (on a lattice).  The Schrödinger equation doesn't
get mentioned until chapter 16 (out of 21).  The whole
thing is online, free for all:
   http://www.feynmanlectures.caltech.edu/III_toc.html

I strongly recommend re-reading that every so often.
It's a masterpiece.

> I am suspicious whether this is doing the good it purports to for
> the following reason: spin is typically initially perceived by
> students as mysterious and arbitrary.

We agree that physics ought to be connected to the
real world.

So spend a few minutes reviewing photon polarization.
They "should" have seen that in third grade science, 
and again in middle school, yet again in high school,
and a third time in college physics.

When I was about 6 years old, my father gave me the
lenses from a broken pair of polaroid sunglasses, plus
a small piece of window glass wrapped in cellophane
tape (which is birefringent).  The piece of glass got
cracked -- maybe accidentally, maybe not, I don't
remember -- which made it even more interesting, because 
the stresses in the glass are also birefringent.  The 
tape kept the pieces of broken glass together.

I'm not sure that "spin first" is the optimal way to
frame the idea.  I see the core idea as "two-state
and few-state systems first".  Photon polarization is 
a two-state system.  Spin 1/2 is another.  The tight-
binding model of the (H2)+ ion is another.

> I get it: teach the distinctive features of quantum mechanics and
> attendant mathematics in the mathematically simple setting of a
> finite dimensional Hilbert space.

Photon polarization counts as a finite-dimensional 
Hilbert space.  So does (H2)+.  So does tight binding
on a finite lattice.

> It’s weird and arbitrary anyway.

Everything's weird if you don't understand it.  And spin
isn't arbitrary;  it is necessary to account for the
observed facts.  If you know of a simpler and/or better 
way to account for the facts, please explain!

> It’s “spin”, but there’s nothing spinning?   And you can’t change it? 

Be careful there.  One of the notorious ambiguities in
scientific terminology concerns "spin".  Sometimes it
refers to the eigenvalue of the S^2 operator, and 
sometimes to the eigenvalue of the Sz component.  It
is not hard to trick experts into using the word with
two different meanings /in the same sentence/.  This
is the sort of thing that drives students crazy.

The S^2 value for an elementary particle cannot be
changed, but the Sz value certainly can.  The classical
behavior of a macroscopic spinning object can be readily
understood in terms of quantum-mechanical spin+orbit
angular momentum.  Furthermore, for a composite object,
even the S^2 value can be changed.  Example:  ortho-
hydrogen versus para-hydrogen.

Also:  For a vehement refutation of the idea that "nothing 
is spinning", see
  http://motls.blogspot.com/2012/12/the-electron-is-spinning-after-all.html