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Re: problems with classical physics



Regarding:

What are some of the problems (or unresolved issues) with classical physics
....

Although I don't think the effects below provided much motivation to
pursue quantum theory and to junk classical theory, nevertheless, it is
true that in a universe governed by classical (non-quantum) physics, (not
only would there be no such thing as atoms) there would be *no
equilibrium bulk magnetism* effects (even assuming we could still somehow
have bulk matter made of electrically charged particles which somehow
stabilized themselves and was globally electrically neutral). What I mean
by equilibrium bulk magnetism effects are the phenomena of para-, dia-,
ferro-, ferri-, antiferro-, etc. -magnetism in macroscopic samples of
matter in thermal equilibrium.

Also, all physical *entropies would be infinite* since in any finite
region of phase space, no matter how small, there are a continuously
infinite number of microscopic states in classical mechanics. It
requires an infinite amount of information to specify the microscopic
state of a classical particle since each position and momentum
coordinate requires the precision of an infinite number of significant
figures to determine the microstate exactly. If we took the correct
statistical mechanical expression for a system's entropy and subtracted
off an appropriate infinite constant behaving like ~ ln(1/h-bar) we
could get finite expressions for classical entropies, but then the
minimal entropy of a system would no longer be zero; it would be
negative infinity (to which the system's entropy would diverge when
the temperature approached absolute zero). The third law of thermo
would be violated.

If the universe was nonrelativistic (where c --> infinity) then the total
energy of any finite mass object would diverge to infinity since every
massive object would have an infinite rest energy. Also, every massless
object would have an infinite kinetic energy when it had a finite
momentum (and it would always move infinitely fast at any finite
momentum). In order to make such a world make sense we would have to
subtract off from the system's energy an infinite constant (m*c^2) when
the system had a finite mass. We would also probably have to ban
massless particles as well so all kinetic energies remained finite at
finite momenta. Particle transmutations would have to be verboten in the
interest of energy conservation (since they would cause infinite changes
in the subtracted rest energies between the reactants and the products).

If the nonrelativistic limit 1/c^2 --> 0 were taken consistently
(for both mechanics and for electromagnetism) then all magnetic effects
and magnetic fields would vanish since magnetic effects are a kind of
relativistic effect. Electromagnetism would degenerate to a form of
electrostatics where charged particles only interacted instantanously
via their Coulomb forces and instantaneously carried their Coulomb field
around with them as they moved. The electric field itself would become
a non-dynamical mathematical artifact of the instantaneous Coulomb
forces acting at a distance. There would be no electromagnetic waves.

Since the fine structure constant (the perturbation parameter of QED)
behaves like e^2/(h-bar*c) we see that this quantity would become
indeterminant if both h*bar vanished and c diverged to infinity. If only
either one of these two limits was taken we would be bound get some
degenerate behavior for charged particles in an electric field, and there
would be problems with their spin-induced magnetic dipole moment (unless
the elementary quantum of charge was also simultaneously taken to an
appropriate limit to keep the fine structure constant finite).

All in all it may somehow seem to be a little easier to imagine a
nonrelativistic world with instantaneous interaction at a distance where
1/c^2 is zero, than a classical non-quantum world where h-bar is really
zero. (In the latter case, how would there even be any discrete
elementary particles at all that could be used to build a non-vacuum
universe? Would matter be continuously divisible?) A world where both of
these parameters were zero would be probably quite weird, and sterile.

David Bowman
David_Bowman@georgetowncollege.edu