Sunday, June 13, 2004

On Jun 13, 2004, at 5:21 PM, Jack Sarfatti wrote:

Things are getting pretty exciting Ken!

On Jun 13, 2004, at 3:52 PM, Ken Shoulders wrote:


Just got back from a trip and tried to download your corrections to the paper but could not reach your URL with the link given. Please get it to me somehow.


I have not made the corrections yet. Actually they are not really corrections. What's up there now, is OK. I have just redone it in a more elegant way. In what's now on there now at

I compute the stability of a non-rotating EVO using the total potential self-energies from the uniform interior zero point fluctuating core "glue" of the EVO and its self-Coulomb repulsive energy spherical thin shell distribution.

What I did recently - reproduced below is only for N = 1 (single electron), but I include its rotation, which Hal cannot do in PV BTW, and I calculate NOT the total potential self-energies, but the potential-self energies per unit test mass. In this case, since it is a self-energy, the test particle and the source particle are one and the same. Also, since we NEVER need go to the unphysical point particle limit, everything is always finite!

I get a 4th order polynomial equation

2c^2/\zpfr^4 - e^2r/m - 2J^2/m^2 = 0

In dimensionless form the EVO stability condition is:

2/\zpfr^2 - (e^2/mc^2)(1/r) - 2(J/mc)^2 (1/r)^2 = 0

2(Zero Point Exotic Vacuum Core Induced Curvature)r^2 - (Classical Particle Electron Radius)/r - 2(Compton Quantum Wave Length)^2/r^2 = 0

However, physically the real on-mass-shell BARE electron sans its ionized plasma cloud of virtual electron-positron pairs, virtual photons, virtual W bosons etc has r = e^2/mc^2, therefore, our stability polynomial is

2/\zpf(e^2/mc^2)^2 - 1 - 2/(alpha)^2 = 0

Where alpha is the fine structure constant ~ 1/137

Therefore, the single electron is stabilized in this toy model when

/\zpf = (mc^2/e^2)^2(1 + (2/alpha)^2) ~ (274)^2(10^-13 cm)^-2 ~ (Electron Compton Wavelength)^-2


/\zpf ~ ~ (10^-11 cm)^-2

which is a nice result of this toy model. In other words the zero point energy induced radius of curvature is of the order of the virtual electron-positron plasma cloud "soliton" ~ 10^-11 cm dressing the bare spatially-extended electron 10^-13 cm across, which should perhaps show J. P. Vigier's "cold fusion" i.e. his "tight atomic states" below that predicted for the hydrogen atom with a "point electron."


Before I got

Back to our thin spherical shell electron model. I neglect factors of pi etc.

Assume a uniform zero point energy density ~ /\zpf "core" inside the electron charge thin spherical shell.

The effective zero point induced self-gravity potential energy per unit test mass is then

V(ZPF) ~ c^2/\zpfr^2

Note that potential energy per unit test mass has dimensions (velocity)^2. The simple harmonic oscillator r^2 dependence is same as drilling a hole through the center of the Earth and dropping a bowling ball down through it. The electrical potential energy per unit test mass is

V(electric self-energy) = U(electric self-energy)/m ~ +e^2/mr

The total potential energy per unit test mass is then

V(total) = V(ZPF) + V(electric self-energy) = + c^2/\zpfr^2 + e^2/mr

Note that /\zpf can be zero, positive or negative.

Here, of course, the test mass = source mass, i.e. self-energy.

Suppose the electron is rotating with angular momentum J, the centrifugal potential energy per unit test mass in the rotating frame is then

V(rotation) ~ J^2/m^2r^2


V(total) = + c^2/\zpfr^2 + e^2/mr + J^2/m^2r^2

A necessary condition for stability is that the total force per unit test mass vanish!

i.e. critical point

dV(total)/dr = 0

2c^2/\zpfr - e^2/mr^2 - 2J^2/m^2r^3 = 0

Notice that /\zpf > 0 is required in this particular model! This means a dark energy core not a dark matter core! This counter-intuitive result is because we assume a uniform volume core of zero point energy density and a thin shell of charge at the periphery. Also we made an approximation in the V(rotation) term. The sign of /\zpf is highly model-dependent.

If V(total) is plotted we can see that there is a minimum "well of stability" only when all the potential energy terms are positive because the positive electric and centrifugal energies decrease as r increases, whilst the zero point energy induced strong gravity energy increases as r increases from the assumption of its uniform distribution in space.

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