See Hal Puthoff's remarks at bottom:
I don't think it works well for 2 electrons. You need, in simplest model, N >> 1 electrons close-packed to form a sphere of area N(h/mc)^2 of radius r* ~ N^1/2(h/mc). Both Hal and I seem to agree on that point but for very different reasons.
Does this formula fit your data?
h/mc ~ 10^-11 cm
N = 10^12 gives charge cluster radius ~ 10^-5 cm. Is this in the ball park? For a more exact formula see below. This is only very crude.
I deduce a dark energy ZPF density ~ /\zpf that would bind the shell of electrons that way.
I have not read Hal's paper carefully enough yet to really see how he gets it. I will eventually.
The KEY IDEA is as follows:
1. The repulsive electro-static self energy per unit electron mass for the N poly-electron cluster is
V(Coulomb Self-Energy) ~ N^2e^2/mr > 0
where the N electrons are arranged in a mono-layer thin spherical shell of thickness h/mc ~ 10^-11 cm
i.e. Euclidean area of the shell is
A = 4pir^2 = N(h/mc)^2
r ~ N^1/2(h/mc) = Schwarzschild radial coordinate if large space warp from G* ~ 10^40G at short-range.
That is, N on-mass-shell bare electrons each of radius e^2/mc^2 ~ 10^-13 cm in a soup of virtual plasma of virtual photons and virtual electron-positron pairs - the latter partially condensed as a vacuum condensate!
OK Hal Puthoff sticks in a Casimir force. I don't really care what it's exact formula is. It plays a minor secondary role.
The Casimir potential energy per unit electron mass will be of the form
V(Casimir) ~ C(hc/mr)N(h/mcr)^2
Where C is a dimensionless coefficient that can be positive or negative, but is positive for our Casimir Type 1 shell model.
Note that V(Casimir) scales only as N because it depends on the surface area of the N poly-electron thin shell. This is a boundary effect!
Ignoring rotational and vibrational modes - to be added later. All we have next is the GR correction term that Hal leaves out completely.
V(Dark Energy) = c^2/\zpfr^2 a 3D Harmonic Oscillator Potential like a ball in a tunnel through center of Earth
Note that /\zpf > 0 i.e. an anti-gravity repulsive "dark energy" exotic vacuum core that COUNTER-INTUITIVELY BINDS the N electrons into a metastable BOUNDARY WALL THIN POLY-ELECTRON SHELL making the QED Casimir force in the first place that Hal sticks in ad-hoc!
Adding all three potential energies Coulomb, Casimir & General Relativity with PW Anderson's "More is Different"
V(total) = BN^2(e^2/mr) + CN(hc/mr)(h/mcr)^2 + c^2/\zpfr^2
B is also a dimensionless coefficient
The critical point for dynamical equilibrium is
dV(total)/dr = 0
i.e. the total acceleration must vanish in metastable equilibrium where r --> r*
-BN^2(e^2/mr*^2) - 3CN(hc/mr*^2)(h/mcr*)^2 + 2c^2/\zpfr* = 0
So I do not care about Casimir force, which when N >> 1 is obviously a small perturbation!
We now have a more accurate formula for r*, or rather, if you want to keep
r* = N^1/2(h/mc) then you can compute /\zpf.
We also have the stability constraint:
d^V(total)/dr^2 > 0
When this constraint is violated WE HAVE WHAT IS BEGINNING TO SUGGEST A BOMB!
A COLD FUSION BOMB RELEASING DARK ENERGY!
Or better maybe a COLD FUSION REACTOR?
Hal Puthoff wrote:
In a message dated 8/27/2004 8:44:19 PM Central Daylight Time, firstname.lastname@example.org writes:
"The inward ZPF radiation pressure is given by the left-hand-side of
the third equation in this section, and is not a function of r."
(Jack) is false because his cutoff frequency is itself c/r where r is the
radius of the thin shell of the N-polyelectron charge cluster in
"Wrong again. The cutoff frequency is hard-wired fixed at the electron's compton frequency (read the sentence following the fourth equation), and therefore is not a function of r; the c/r relationship to the cutoff frequency in the fourth equation that led to your false statement is a consequence, not a determiner, of pressure balances, and thus simply provides the shell value radius r = a.
(Please forward this to the bcc list that you sent your incorrect statement to, concerning my rebuttal).
I say Hal is wrong here. I am still using Casimir Type I model that Hal is not able to get to work. Hal is using Type II model in his remark above, which is physically inconsistent. You cannot take the cutoff at the Compton wavelength. That is a self-contradiction. Hal's Type II model is no good at all. I will argue this in detail another time. I am using Type I which works perfectly once one puts in Einstein's gravity correction MISSING FROM HAL'S MODEL!
PS You can see the basic inconsistency in Hal's Type II. The Casimir pressure is from missing modes induced by the boundaries of scale L, therefore the cut-off frequency must be at c/L. That is, the cut-off is a macro-boundary effect not a micro-quantum effect. But in any case, in the real physics you can ignore the Casimir pressure to first order when N >> 1!
On Aug 28, 2004, at 2:06 PM, Ken Shoulders wrote:
If you get time, please look at the following word picture and see if you can put some numbers to it. The aim of this exercise is to see if a form of energy gain results from this simple loop of operations.
There is a loop of action that arbitrarily starts with electron emission from a cathode using field emission or tunneling.
It is assumed for this example that only two electrons are emitted using an applied field of about 3 x 107 volts per centimeter. As often seen in tunneling electron microscopy, a single atom site can supply this emission. This can be achieved practically by applying nearly any voltage, depending on the spacing between cathode to anode, down to about 1 volt. Obviously, the lower the voltage, the lower the applied energy.
Furthermore, it is assumed that the two electrons obey the electron binding rule seen experimentally and are bound together with a spacing of about 1 atomic diameter, in direct violation of simply applied Coulomb repulsion laws.
Upon applying some presently unknown level of excitation, the pair of electrons exceeds the trapping energy level and fly apart with the force specified by Coulomb force yielding a potentially available energy output.
The electrons rejoin the normal current flow path in the anode to complete the energy loop and are returned to the cathode through the power supply to be emitted again at a later time.
The question is: What is the numerical energy level at each step in the process.
It is assumed that the energy threshold required for dishevelment of the electron pair is about the same as it would be for a large group of electrons bound together by the same process. However, the total energy required per pair of electrons would be less for the large group due to a cascading action from a single input trigger point at threshold energy level. This runaway breakdown process itself would be sufficient evidence to show energy gain of the sort described in chemical reactions but this may or may not be the type desired in this calculation.