Re: higher mass -> more zero-point energy? or zero-point energy is constant??

In the quantum mechanical harmonic oscillator, for which the classical
analog is a point mass m attached to an ideal massless Hooke's Law
spring with force constant k, the zero-point energy is 1/2 of Planck's
reduced constant (h-bar) times the angular frequency of oscillation
(omega) above the bottom of the parabolic potential well.
Classically, omega is the square root of k/m.  So as the mass
increases in this model, the zero-point energy decreases.
 http://en.wikipedia.org/wiki/Zero-point_energy

and
 http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator

For massless fields, like the electromagnetic field, there is a
contribution to the vacuum energy of 1/2 h-bar omega for every photon
frequency omega at each point in space.  This leads to an infinite
energy which is treated differently in quantum field theory and in
general relativity, which are still not unified in physics.
 http://math.ucr.edu/home/baez/vacuum.html

and
 http://en.wikipedia.org/wiki/Vacuum_catastrophe

For massive fields, like the electron field, the quantum excitations
are virtual particle-antiparticle pairs.  The contribution to the
vacuum energy is still infinite as in the case of massless fields.
The difference is that the lowest energy excited mode of the vacuum
is now twice the mass of the particle times the speed of light squared
(when the virtual particle pair is created at rest) instead of an
arbitrarily small frequency photon with energy close to zero.
 http://en.wikipedia.org/wiki/Virtual_particle


--Randall J. Scalise
 http://www.physics.smu.edu/scalise