On Jun 21, 2007, at 4:32 AM, Paul J. Werbos, Dr. wrote:
At 11:18 PM 6/20/2007, RAY HUDSON wrote:
I was going to respond to this as well, but how could I do better than Creon has done? He has captured all of the thoughts I was going to offer from an engineering perspective… and then some! The most interesting to me (not surprising given my flight controls bias) is the gyroscopic effect of a spinning mass where rotation provides a “stiffness” that permits attitude maintenance with respect to some inertial reference. Ergo, rotation leads to stability, and stability is a result of converting the otherwise chaotic effects in the universe into something orderly (and therefore easier to perceive).
Stability is indeed the central issue here.
In order to get past the description of particles as perfect points (with infinite energy of self-repulsion
due to charge being all in one point), the obvious alternative is to describe them
as stable "lumps" of force... "solitons," in physics-talk.
You know I have solved this problem in the frame work of Bohm's objective nonlocal pilot wave-Hidden Variable (HV) ontological picture of quantum theory. CFD (Counter Factual Definiteness) is absent here completely - it's a rather obscure notion to begin with in the Copenhagen type interpretations with literal "collapse" for particle theory. See my book Super Cosmos. My solution came out of my debate with Hal Puthoff on Ken Shoulders's "charge clusters."
OK imagine a hollow thin spherical shell of electric charge e of rest mass m that is rotating with spin J of radius a. We use Galilean relativity i.e. v/c << 1, though we can use 1905 SR later with the gamma factor.
The unstable self-Coulomb repulsive potential energy is ~ +e^2/r. We are in the rotating non-inertial rest frame of the charged shell. Therefore, the effective rotational potential energy is ~ +J^2/mr^2.
This total classical potential is unstable repulsive. OK zero point energy comes to rescue! That's what Lorentz, Abraham & Becker and Poincare did not have back ~ 1900. We have an inner core of negative zero point energy ZPE density ~ /\zpf with positive quantum pressure. This will strongly gravitate according to Einstein's 1916 GR. It is the attractive glue for stability. Furthermore the effective Sakharov ZPE induced gravity is so strong that the electron looks like a "point particle" to Ibison's AFO from the extreme micro-space warping! Same for quarks of course explaining deep inelastic electron scattering off protons etc.
The total potential energy is now (mod some dimensionless coefficients ~ 1)
U(charged shell)= -mc^2/\zpfr^2 + e^2/r + J^2/mr^2
The net force is
F = - dU/dr = 2mc^2/\zpfr + e^2/r^2 + 2J^2/mr^2
F = 0 in dynamic equilibrium in the rotating frame
Therefore, we have to find the roots of a quartic polynomial
Homework problem: Find the roots!
2mc^2/\zpfr + e^2/r^2 + 2J^2/mr^3 = 0
/\zpfr^4 + e^2r/2mc^2 + 2J^2/2m^2c^2 = 0
(/\zpf)r^4 + (classical electron radius)r + (Compton wave length)^2 = 0
Fine structure constant = (classical electron radius)/(Compton wave length) ~ 1/137 at low energy
Note with these sign conventions /\zpf > 0 means negative ZPE pressure, stability requires /\zpf < 0 i.e. positive ZPE exotic vacuum pressure.
Stability of this dynamic equilibrium from elementary calculus of max & min is
y = f(x)
dy/dx = 0 critical point
d^2y/dx^2 > 0
is a minimum, hence
d^2U/dr^2 > 0
no problem, there are stable solutions for /\zpf < 0
Check that as a homework problem.
But stability is not so easy to achieve. All known stable solitons require "topological charge" of some kind.
(See Makhankov et al, The Skyrme Model, or Rajaraman, Solitons and Instantons.)
They end up having to have rotation... i.e. spin coupled to isospin.
This is the start of a very important story -- but only the start.
Best of luck to us all,
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein