Re: [Phys-L] [SPAM] Re: heat content

[John Denker <jsd@av8n.com>]

On 02/16/2014 06:03 PM, Anthony Lapinski wrote:
> I always heard that at absolute zero, molecules have minimum (not zero)
> motion. However, there is misinformation about this online. So what
> happens at 0 K -- do molecules have motion or not?

Absolutely they do have motion, even at absolute zero.

The fact that a hydrogen atom has nonzero size is most
easily explained in terms of the zero-point motion of
the electron.

I strongly recommend the following exercise:  you can
estimate the Bohr radius using little more than dimensional
analysis plus electrostatics plus the most basic quantum
mechanical idea, namely p = ℏ k.  Treat the atom as a 
particle in a box.
  KE =  p^2 / 2m  for a particle in a box of size 2 a0
  PE = − qq / r   for a separation r on the order of a0.

If this takes more than half a sheet of paper you're doing
it wrong.

Bottom line:  If we didn't have any KE in the lowest 
particle-in-a-box state we wouldn't have atoms.  This 
would be a bad thing.  It is well known that atoms are 
required to make physicists.

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

As another angle on the same idea:  As I wrote in the
cryptography forum yesterday:  There is no such thing 
as purely zero-point fluctuations as distinct from purely 
thermal fluctuations;  those are just two asymptotes on 
the *same* graph:
  http://www.av8n.com/physics/oscillator.htm


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

On 02/16/2014 06:09 PM, Chuck Britton wrote:

> > As I understand it - Zero Point Energy is motion without 
> > Entropy. 

That's true.

> > (totally ordered)

Gaack!  I wouldn't have said that.  Please do not confuse 
entropy with disorder.

 *) Entropy is a property of the macrostate.  It is defined
  as the ensemble average of the surprisal.

 *) Disorder, to the extent it can be defined at all, is
  a property of the microstate.
    http://www.av8n.com/physics/thermo/entropy.html#sec-s-vs-disorder

In the present case, the zero-point fluctuations *are* random.
They are disorderly ... even they they are associated with
zero entropy.

This is related to the fact that despite what you've been
taught all along, energy is not quantized.  Planck's constant
doesn't even have /dimensions/ of energy.  It is better to
think of ℏ as the _quantum of action_ i.e. the quantum of
area in phase space ... and even then, it is more a unit
of measurement than a strictly quantized quantity.

A zero-entropy state is spread out over one unit of area in
phase space ... not zero units.  If you want the picture that
goes with this, along with some more discussion, please see
  http://www.av8n.com/physics/coherent-states.htm