Zero Point Energy
I am not misusing cosmology. Your w = +1/3 model of the EVO requires that we live in a sea of random zero point energy with /\zpf ~ (mc/h)^2. It is you who do not understand the restriction that cosmology places on your model. Also you do not understand that even a uniform field of zero point energy density must bend spacetime because of the equivalence principle. Your argument that only differences in zero point energy density are physical contradicts Einstein's theory of General Relativity. Hal your argument below is surface looking blindly at the formalism without any deep physical intuition on what that formalism really means IMHO.
On Sep 22, 2005, at 12:15 PM, Puthoff@aol.com wrote:
Jack, you have many times invited me to critique your theoretical approach as you have mine. OK, I then provide the following for your consideration.
First, yes, it is true that, as you and Ibison have agreed upon (as do I, BTW) an "empty" universe filled only with a cubic-frequency ZPE that is Lorentz invariant and has no cutoff has an equation of state w = -1 for the very good reasons stated in Peacock, p. 26 ff., and as restated in very clear terms by Michael. We have no disagreement there.
OK. But you did use w = +1/3 in that EVO paper right? I mean you have a positive ZPE density with a positive ZPE pressure outside your shell of charge with zero ZPE inside. Yes?
When it comes to applying ZPE concepts to Casimir Effect calculations, however, the vacuum territory is radically restructured. The introduction of specifically-placed plate boundaries with materials-dependent cutoffs means that we no longer have a w = -1, Lorentz-invariant vacuum structure, but rather a frame-dependent vacuum structure defined by the placement and materials of the Casimir plates.
I am not talking about that. You have used w = +1/3 outside the shell of charge in the space of the entire universe.
The details, explicitly stated in GR vacuum stress-energy terms as you wish to do, are provided in B. S. DeWitt, "Quantum Field Theory in Curved Spacetime," Phys. Reports, vol. 19, pp. 295-357 (1975). In setting up the problem of a ZPE-filled vacuum into which plates are to be inserted, regularization of the now-required frame-dependent stress tensor at the beginning setup yields T^(uv) = (3/\^4/pi^2) x diag [1, 1/3, 1/3, 1/3], where /\ here is a high-energy cutoff (not the cosmological constant). As stated by DeWitt, "This has exactly the same form as the stress tensor of a photon gas at rest (zero total 3-momentum) in the chosen frame." That is, w = + 1/3.
This makes no sense at all. What stress tensor are you talking about? The stress tensor of the matter of the plates? What do you mean by a "photon gas"? If you mean real photons then they obey hf = hck and of course w = +1/3 for things like black-body radiation. What does that have to do with the ZPF? There is something very wrong with what you say here. The error may be DeWitt's not yours. What you seem to say is something like this, start with Einstein's equation
Guv = KTuv(Matter)
Do some kind of quantum regularization on classical Tuv(Matter) to get T*uv(Matter)
But that is irrelevant to what I am talking about.
I start with VACUUM in which classical Tuv(Matter) = 0
The quantum vacuum has
Guv + /\zpfguv = 0
where the stress-energy density of the vacuum ZPF is
tuv(ZPF) = K^-1/\zpfguv with w = -1
Now if you stick in the plates as well then you get
Guv + /\zpfguv = KTuv(PLATES)
Regularize the RHS and according to you one allegedly gets something like
Tuv(Plates) -> T*uv(Plates + QF)
where the QF part has w = +1/3 like a real photon gas (e.g. black body rad) and the Plates have w = 0.
I use "QF" from quantum fluctuations induced by inserting plates so as not to confused them with the ZPF that is there even when there are no plates.
This makes some sense because of the Unruh-Hawking Effect. That is your w = 0 PLATES fixed in a gravity field are in a LNIF off geodesic, therefore they will see LNIF black body radiation with w = +1/3 from the equivalence principle but of very low temperature.
But that is irrelevant, because DeWitt is talking about a completely different term than I am talking about! DeWitt is talking about Tuv(Plates) in a non-geodesic LNIF in which YES I agree there will be a TINY w = +1/3 component artifact of inserting the plates.
I am talking about the different term /\zpfguv. Also
/\zpfguv >> Regularized Tuv(Plates)
in your EVO model, if you did it correctly.
So, in general
Guv + /\zpf(vacuum)guv = KT*(LNIF Plates + Hawking-Unruh Radiation)
/\zpf(vacuum)guv is w = -1
KT*(Plates + Hawking-Unruh Radiation)
has both a w = 0 classical Plate component and the w = +1/3 LNIF Hawking-Unruh black body radiation component.
Both of these terms are SMALL compared to /\zpfguv (in the interior of the shell of charge in my model and in the exterior of the shell in your model.
Then, when the parallel conductors are introduced, "the vacuum between is no longer the vacuum of uncluttered Minkowski space" and calculation leads to the result
T^(uv) = (3/\^4/pi^2) x diag [1, 1/3, 1/3, 1/3] + (pi^2 h-bar c/720 d^4) X diag [-1, 1, 1, -3], where d is the spacing between the plates. This leads to a net pressure that can be written T^33 = - pi h c/480 d^4. (Note use of h, not h-bar, here.)
Yes for QED Casimir force that is irrelevant to my point about the direct bending of space-time by any residual zero point energy density that is not absorbed into the vacuum ODLRO macro-quantum coherent "supersolid" order parameter whose Goldstone phase argphi actually gives
Guv + /\zpf(vacuum)guv = KT*(LNIF Plates + Hawking-Unruh Radiation)
B = (hG/c^3)^1/2"d"(argphi)
Now, to be clear just what this means, we go to P. W. Milonni et al., "Radiation Pressure from the Vacuum: Physical Interpretation of the Casimir Force," Phys. Rev. A, vol. 38, 1621-1623 (1988). Here Milonni explicitly chose to calculate the Casimir force, not on the basis of energy changes as is the usual case, but rather on the basis of differences in Poynting vector (positive) radiation pressures of the boundary-dependent fields between and outside the plates. The result, as in the GR calculation above, is Eq. (6), Net P = - pi h c/480 d^4. Lest there remain any question as to exactly the interpretation to be given to this result, Milonni states explicitly (p. 1622, 1st column):
".. since the modes in the space outside the plate form a continuum, whereas those inside are restricted to discrete values of k_z, there are 'more' modes outside to push the plates together by radiation pressure than there are modes between the plates to push them apart." He then goes on to indicate that just counting the modes is not the whole story, since for the spherical case the same calculation leads to an expanding rather than collapsing geometry, but, nonetheless, the positive radiation pressure still holds in that "The simple analysis leading to Eq. (6) shows that the Casimir effect is just the zero-temperature limit of this classical (italics his) radiation force."
Hal I know this elementary stuff you are parroting back to me, but it misses my point entirely and is not relevant.
"The Question is: What is The Question?" (J.A. Wheeler)
Everything you say about is about Special Relativity without gravity! I have no argument with that other than it is incomplete. As soon as you include the equivalence principle everything changes dramatically and the direct bending of space-time by even a UNIFORM field of ZPE density cannot be avoided! Cosmology is very relevant here. The kind of special relativistic quantum field theory you cite above is completely inadequate conceptually to deal with the problem, that's why all The Big Shot Pundits are all in the Men's Hair Shop because they have pulled out their hair going bonkers worrying about this problem as well they should. ;-)
In summary, we have both the curved-space GR vacuum approach (DeWitt) of a type that you wish to use, and the classical-like ZPE radiation pressure approach (Milonni) leading to the same result, experimentally verified to high precision (5% by Lamoreaux at Univ. of Wash./LANL), 1 % by Mohideen et al. at UC Riverside).
All DeWitt did there was to show the Hawking-Unruh radiation effect induced by placing the neutral conducting plates on a non-geodesic world line in curved space-time. He would LOCALLY get same thing by accelerating the plates in flat space-time. So what?
Jack, until you have gone to the effort to study and understand this material, we will only continue to talk past each other with one-liner sound bites and rebuttals on the topic of Casimir models for charge clusters and related phenomena.
No Hal, the problem is very simple. Your calculation for the EVOs is no good because it really does contradict cosmological data and you completely missed what I was saying about the stability of the single electron even if there are no EVOs in Ken Shoulders sense as Ibison seems to think? You have misunderstood DeWitt I think and you did not calculate the size of his regularization I suspect. It will be small compared to what I am talking about.
On Sep 22, 2005, at 4:04 PM, cosifan (Robert Collins - a delusional not very intelligent groupie of Hal's) wrote:
If you use Einstein's exponential metric which JS
knows all about there are no such things as event horizons or
Yes, Mouse we know that, but the evidence is against that. Where is the evidence?
Meantime BACK INTO TO YOUR TEAPOT! I'm late, I'm late ... :-)
￼To give Hal his due, these issues of renormalization are very tricky and probably inconsistent anyway. Renormalization starts with assuming a point charge electron and it is not appropriate the micro-geon model. BTW one gets pretty good answer for things like Lamb shift with a cutoff at 10^-13 cm. This is consistent with strong short-range zero point energy dark energy cores /\zpf ~ (c^3/hG*) where G* ~ 10^40G. In other words, the whole problem must be looked at new.
Hal cites DeWitt on quantum field theory in curved space-time, to which my remarks were addressed. Then he jumped to a flat space-time calculation of the Casimir force which is completely irrelevant. Hal seems to say that it's OK to use w = +1/3 because the plates break translation symmetry in flat space-time. However, this sounds dubious because Lorentz group symmetry should still be OK. So Hal and Ibison seem to be at odds on w = +1/3 vs w = -1.
In any case, I do not think the QED calculations in flat space-time Hal cites are relevant to the problem even if one can get away with using w = +1/3 there.
My picture of the single extended electron is geometrodyamics with QED Casimir force as a term in the Hamiltonian of order (number @ from Hal's QED citation) hc/r where in Galilean limit for a uniform ZPE density inside the shell of charge
V ~ +@hc/mr + + e^2/mr + c^2/\zpfr^2 + J^2/2mr^2
Therefore, Hal's Casimir force is simply an effective re-scaling of the "charge" factor from e^2 to e^2 + @hc
J = rotational momentum
That is e*^2 = e^2(1 + @hc/e^2) = e^2(1 + @137) ~ 137@e^2
Where @ is the pure number from the QED Hal mentions. So Hal's point is simply one term in my model. No problem!
Therefore INCLUDING HAL's CASIMIR FORCE term from the QED (if it used w = + 1/3 so what?) my model has
V = 137@e^2/mr + J^2/mr^2 + c^2/\zpfr^2
The equilibrium is at
dV/dr = 0
The equilibrium is stable because
d^2V/dr^2 > 0
SIMPLE & PRETTY
Therefore, the basic renormalization procedure starting from a point charge may not be correct at all!
As Hal P said, Dark Energy only makes up a
small fraction of the total vacuum energy density of the Universe
or something like ~5% compared to the total vacuum energy density.
It's only that small fraction with w = -1 pushing the galaxies apart....Rmc
No Mouse you got that completely wrong as usual! In Hal's defense he never said that.
The dark energy pushing the galaxies apart in addition to the Hubble expansion is
a 73% effect not your 5% that you garbled with 4% of "atoms" below.
On Sep 22, 2005, at 11:16 AM, art wagner wrote:
Jack, I'd say that these two papers bode pretty well for your w = -1
position: (http://xxx.lanl.gov/abs/hep-th/0502203) and