Re: ENERGY WITH Q

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:49 AM 10/26/01 -0700, John Mallinckrodt wrote:
> I do like the spin glass example because, as you say, it is easy
> to calculate the absolute entropy.  But I don't yet see why that
> absolute value is *important*, that is, why one could not add an
> arbitrary constant to it without changing any measurable
> thermodynamic results.

Here's a simpler version of my previous argument.

  1) Consider low-energy proton-proton scattering at right angles.  If the
spin label is the only label that matters, there will be _zero_ scattering
amplitude for right-angle scattering when both spins are polarized |up>,
because those are indistinguishable fermions.  When one spin is |up> and
one spin is |down>, then they are distinguishable, and there will be
perfectly ordinary right-angle scattering.  Zillions of experiments confirm
this result.

  2) Now hypothesize that in addition to the spin label (which contributes
one bit per proton of entropy) there is another 17 bits per proton of
"secret entropy" that we hitherto didn't know about;  we just stuck that in
there because somebody wanted to shift the zero-point of the entropy scale.
 But this means there are now 2^17 _distinguishable_ types of proton, even
when the proton is in the |up> state.  Zillions of experiments refute this
hypothesis, including the measurements of spin waves in spin-polarized
hydrogen.

(I did the spin-polarized hydrogen experiment myself.  We saw beautiful
spin waves.  They would not have existed if the atoms had had "secret"
quantum numbers we didn't know about.  The effect was not just measurable,
it was spectacular.)

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

Let me tell you a little story that may put this in context.  I took a
modern-physics course from Charlie Peck.  Good guy.  Won lots of
best-teacher awards.  He derived for us an expression for the entropy in
!!classical!! thermodynamics.  There was an arbitrary constant in the
expression.  He said "We have to give a name to this arbitrary constant, so
let's arbitarily call it hbar".  That made us laugh pretty hard.  I still
smile when I remember the incident.

Let me explain the joke:  For the thermodynamics of a continuous system,
you can count states by dividing phase space into cells of size "hbar" and
seeing how many cells are occupied.  In !!classical!! thermodynamics there
is no way of knowing how big hbar is;  it is just an arbitary scale factor.
 Choosing a new value of hbar shifts the zero of entropy.

But "classical thermodynamics" is a contradiction in terms.  There is no
completely self-consistent classical thermodynamics.  We know the value of
Planck's constant.  The zero of the entropy-scale is not arbitrary, because
the value of hbar is not arbitrary, and anybody who tells you otherwise is
pulling your leg.