[Phys-L] zero-point motion at the introductory level

[John Denker <jsd@av8n.com>]

On 02/18/2014 08:29 AM, Anthony Lapinski wrote:
> What do I tell kids about motion and absolute zero? What's 
> appropriate?

Tell them that zero-point motion is motion.  Show them
the picture, as discussed below.

> They know that temperature is a measure of the average KE of the
> molecules in an object. To them, absolute zero would imply no
> motion.

Like all of classical physics, that is an approximation to
the true physics, i.e. quantum mechanics.

Show them the picture:
  http://www.av8n.com/physics/oscillator.htm

If you take the high-temperature behavior and extrapolate it
to zero temperature, you might expect zero RMS motion ... but
extrapolation is always risky, and in this case it gets the
wrong answer.

At low temperature, the behavior departs from the high-temperature
asymptote.

At the next level of detail, show them this picture:
  http://www.av8n.com/physics/coherent-states.htm#fig-glauber-movie

At high temperature, there is a narrow spike going around 
in a huge circle, and the width of the spike is not relevant,
not noticeable.  However, when the temperature gets low enough
and/or if you look really carefully, the width of the spike 
gets to be an appreciable part of the story.  Here is a picture 
of an oscillator only slightly above the ground state: 
  http://www.av8n.com/physics/coherent-states.htm#fig-glauber-movie-tiny

Classically, you don't care about the width of the spike, and
you might have approximated it as zero, but it's not really
zero.  Even at high temperature the width is not zero;  it's 
just not particularly noticeable.

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

Have them fire up a spreadsheet and plot

       E = .5 * coth(.5/T)

with 100 points, starting from T=1e-6 and going up by
delta_T=0.02 units per point.

Then zoom out by setting delta_T=0.2

Then zoom out by setting delta_T=2 or 3.

The high-temperature behavior looks classical to an
excellent approximation ... but it's not the whole 
story.  It's fairly easy to see how people could get 
fooled for a few hundred years.

This is an example of the /correspondence principle/
at work.  The modern theory agrees with the classical
result in all situations that had previously been checked,
but makes a new prediction in a new part of the world.

Another lesson is:  Don't make overly-bold extrapolations.
Don't over-generalize from limited data.

Sometimes the first thing you learn (E = mgh) isn't the
whole story.  Sometimes it's just an approximation.  It
might be an exceedingly good approximation over a limited
range, but there's more to the story (E = GmM/r).