In a message dated 8/29/2004 1:24:31 PM Central Daylight Time, email@example.com writes:
Hal's Type II model is Rube Goldberg. He takes a short-wavelength cutoff at h/mc which is adhoc.
Hal: "Not so. Read Weisskopf. Read Bethe. Read Callen and Welton. Compton frequency is taken to be the cutoff for electron interaction with the vacuum fluctuations."
Jack: Of course I have read Weisskopf & Bethe papers on the Lamb shift with the high frequency virtual photon cutoff at h/2mc. I fail to see how choosing that particular cutoff helps your case with EVOS?
You seem to be saying, correct me if I am wrong, that the POSITIVE virtual photon ZPF energy density is
u(virtual photon) ~ hc(h/mc)^-4 ~ 10^-27 10^10 (10-11)-4 ~ (10^-17)(10^44) ~ 10^27 ergs/cc
You next say that the POSITIVE virtual photon pressure is
P(virtual photon) ~ (1/3)u(virtual photon)
That's a very BIG PRESSURE of course apart from the fact that w = -1 not +1/3 for all virtual quanta of all species.
You have ZERO VACUUM COHERENCE here in the sense that I mean it.
OK, a typical EVO has an electron shell of radius a ~ 10^-5 - 10^-6 cm says Ken Shoulders.
Now you and I both agree that
N^1/2(h/mc) ~ a
Let's take a ~ 10^-5 cm, h/mc ~ 10^-11 cm
Therefore N ~ 10^12 electrons close-packed to make a thin spherical shell 100 nanometers across that is 10^-4 nanometers thick. Right? Yes? No? Are we on the same page here?
The electrostatic self energy is
U(self-energy) ~ +(Ne)^2/a ~ N^2(1/137)hc/a ~ (10^24)(10^-2)(10^-27)(10^10)(10^5) ~ (10^39)(10-29) ~ 10^10 ergs ~ 1 kilojoule.
Now what virtual photon modes are allowed outside the spherical shell, and what modes inside the shell are allowed according to you?
The radial outward electrostatic force F is therefore
10^10 ergs/10^-5 cm ~ 10^15 dynes
Your EXTRAORDINARY claim is that dP(virtual photon) cancels this radial outward force of ONE THOUSAND TRILLION DYNES!
If the only virtual photon modes allowed inside the N-electron shell have wavelengths less than a = 10^-5 cm, then the additional modes outside the shell giving the excess pressure dP(virtual photon) integrate out to energy density
~ hc/a^4 ~ (10-6)^4hc(h/mc)^-4 ~ (10^-24)(10^27) ergs/cc ~ 10^3 ergs per cc.
Because the inside of the N-electron shell has all the virtual photon ZPF modes the outside has except for the INFRARED long wave ones than cannot fit inside the shell. This is very small Hal. Where does your cutoff at h/mc even enter into the dP = P(Outside) - P(Inside) > 0 computation? Please explain this mystery.
Suppose we make your false assumption that w = +1/3 so that
dP ~ 10^3 ergs per cc directed radially inward from the extra OUTSIDE INFRARED LONG WAVE modes.
The inward virtual photon radial force is then ~ 10^3(10^-11)^2 ~ 10^-18 dynes that opposes the electrostatic outward radial force of 10^15 dynes. Therefore, Hal your prediction is TOO WEAK BY 33 POWERS OF TEN!
As I said, the Casimir force is irrelevant to this problem!
OK, if I have done the numbers above WRONG, show us all how to do it right according to your idea!
Hal: "This is not cosmology, Jack. This is not general relativity. This is quantum physics."
Jack: You are being polemical and hand-waving with transparent sophistry not addressing yourself to the real problem here. You have confused the limits of the large scale FRW metric with the Einstein field equations themselves that hold at all scales - down to at least 10^-33 cm unless G gets large at small scales.
Hal: "The math is there. The references are there. Until you're up to speed on the relevant quantum calculations there is nothing more I can help you with with regard to understanding my posting at http://arxiv.org/abs/physics/0408114"
Jack: Tell that to Cliff Will, Matt Visser and Bill Unruh! ;-)