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Re: Re IONS/metals pedagogy



Any scheme to make a stable system out of only Coulomb forces must answer
to Earnshaw! We need a conceptual bridge to QM's defiance of Earnshaw.

You may have noticed that in my earlier "proof" of Earnshaw I specified
that the test point be in empty space (cuz there Div (E) =0 ). Now
consider an electron smeared out into a sphere (radius prox 1 Angstrom),
constituting a continuum of charge. A proton would enjoy a stable
equilibrium position at the center of that sphere. (This is roughly the
Shroedinger picture of the Hydrogen atom ground state). The classical
problem of course is what keeps the electron parts from flying apart?

If we simply assert that parts of the electron do not exert forces on
each other - they settle into the state dictated by the proton - electron
potential - then we can allow this as a stable configuration. Earnshaw
is circumvented.

If we consider multi-electron systems, things get much more sticky -
certainly the "clouds" of different electrons will interact. But the
door is open - by smearing electric charge into a continuum, so that
there is charge "everywhere", Earnshaw is in trouble and electrostatic
equilibrium has a chance. Is this the needed conceptual bridge?

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor