Re: intermolecular forces

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

At 12:54 PM 2/20/01 -0500, Richard Bowman wrote:

> I simply go back to Schrodinger's equation and remember that for
> atoms (and molecules, at some level of approximation) we solve the energy
> equation for the behavior of an electron in the presense of the Coulombic
> (electrostatic) potential.

That's fine, but everybody please note that this involves electrostatics
AND Schrödinger's equation.  A classical approximation using only
electrostatics would be hopelessly wrong.

> And whether we talk about (what chemists call) Leonard-Jones potentials
> or van der Waals forces or whatever model, we are still modeling the
> electrostatic interactions between particles.

Well, vdW models only the electrostatic interactions, and to the extent
that it ignores identical-particle effects it is wrong.  Meanwhile, L-J
makes a really crude ad-hoc attempt to model the interparticle
effects.  This is so ad-hoc that one could claim it is modelling
practically anything.  It could be modelling little green men who push on
the electrons with a 1/r^12 potential.

Also, both of these models produce purely classical potentials.  Both of
them predict that an added deuterium atom will interact with a gas of
spin-aligned hydrogen in the same way as an added hydrogen atom -- and this
is just dead wrong.
   For details on this, see
  http://mailgate.nau.edu/cgi-bin/wa?A2=ind0102&L=phys-l&F=&S=&P=52285

In any case, the notion that "just" modeling the electrostatic potential
leads to a correct description of nature is, IMHO, implausible and
certainly unproven by the arguments given above.


> John also wrote today:
> > Similarly, to return to the uncharged gas in a piston that I mentioned at
> > 09:16 AM 2/11/01 -0500, you could argue that "normally" the gas particles
> > interact with the piston via electrostatic forces at impact.  But what
> > happens if I coat the surface of the piston with some hypothetical material
> > that repels the gas via some magnetic interaction, or some nuclear
> > interaction, or whatever?  The measured pressure is unchanged.  The
> > pressure does not depend on the nature of the interaction.  It only depends
> > on the kinetic energy via the quantum statistics.
>
> But in fact this is what I referred to as the "hard sphere"
> approximation.

1) That's not what most people mean by the hard sphere approximation.

2) If you think that hard-sphere gases are worth mentioning, you must
concede that non-hard non-sphere gases also exist.  I am free to talk about
the latter.  I say again that my remarks apply perfectly well to non-hard
non-spherical particles.  Indeed, one of my main points is that I make no
assumptions about the shape of the interaction potential.

>  At its basic level, all such interactions are in fact not
> totally elastic.

I suppose that's true, but it has no bearing on the points I was making.

> I may be applying too fine a distinction to this discussion, but I thought
> that was what Tucker Hiatt was asking about when he questioned whether
> there were only four basic forces in our universe or not.

1) As I said before, there are three main fields, the way most experts count:
  Gravitational
  Electroweak
  Strong
... but the details of the count are not important.

2) As I said before, calling these "force" fields is a gross misnomer.

3) Of course these fields give rise to forces, and to potentials, but to
describe the world solely in terms of these is a huge mistake.  These
fields only have meaning when they are plugged into the laws of motion
(e.g. the Schrödinger equation) and those laws bring other things to the
table, notably kinetic energy and identical-particle effects.

So, perhaps we can converge on the following pair of statements:
 -- The fields listed in item (1) plus the usual zoo of particles,
    if plugged into suitable quantum equations of motion, give a
    pretty complete description of nature as we know it.
 -- The fields listed in item (1), if plugged into classical equations
    such as F=ma, do not give anything approaching a complete description
    of the interactions between particles.  This can be patched up by
    supplementing the classical description with various pseudo-fields
    e.g. the "molecular fields" I described in the note cited above,
    and this often results in a very serviceable description.