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[Phys-l] symmetry of the force (was: irregular bodies)



Richard Tarara wrote:
... since the forces in question are actually electrical forces
(repulsion between electron clouds that get too close I'm guessing...

Yes, the Coulomb energy is the dominant contribution to the
potential energy, to a more-than-good-enough approximation.

or do
we have to use QM here?), then we could proceed from there.

We do need QM; see below.

.... there should be a good cancelation of all components in the
plane of the surfaces leaving only the perpendicular components--the normal
force.

Now of course there are NO perfectly flat surfaces .....

We agree that the Coulomb interaction (i.e. electrostatic force) is
purely radial in direction; there is no tangential component.

However, that is less meaningful than it might appear.

The trick is that you have to use the Coulomb interaction
*in the equation of motion* and the equation of motion is highly
nontrivial. In an atom, the Coulomb energy is not the only energy;
it is dominant over other forms of potential energy, but it is
nowhere near dominant over the *kinetic* energy.

To make this entirely concrete, consider the vibrational spectroscopy
of molecules. Overwhelming observational (and theoretical) evidence
shows that there is such a thing as a chemical bond, and such bonds
are directional. That is, they resist tangential bending forces.

If you wish, you can consider this an example of _broken symmetry_,
since the solution to the equation of motion is less symmetric
than the equation itself.

Bottom line: Observation indicates that tangential forces are as
common as sand on the beach. This is perfectly consistent with
detailed theory.