On Sep 10, 2004, at 5:28 AM, Dr. Burinskii Alexander wrote from Moscow's Russian Academy of Sciences:
I know that De Witt completely understood Feynman and Schwinger's
I would like to add a few words on the De Witt approach since I find it is
very clear and consistent. Besides, there is a possibility to compare it
Guv + /\zpfguv = (8piG/c^4)Tuv
De Witt wrote the Einstein equation as follows
Guv = Tuv_regularized,
Tuv_regularized = Tuv - Tuv _vac,
In the form
Guv + (8piG/c^4) Tuv_vac = Tuv
De Witt equation is similar to your equation.
Guv + /\zpfguv = (8piG/c^4)Tuv
Yes, however Tuv_vac is restricted to the form (c^4/8piG)/\zpfguv
where /\zpf is a scalar dependent on "vacuum coherence" that is absent in all mainstream theories in the precise new way I use it (zero rank tensor both for local Lorentz group in tangent fiber and the GCT group in curved base space), i.e.
/\zpf = (Cutoff Length)^-2[[Cutoff Length]^3|Vacuum Coherence|^2 - 1]
Note this is a scalar for all symmetry groups so there is no "cutoff" violation of symmetry here!
Hal Puthoff, for example, wants to use
Cutoff Length = h/mc = 10^-11 cm
Cutoff Length = (hG/c^3)^1/2 = 10^-33 cm
In terms of symmetry and covariance that does not matter, but is an empirical matter.
Note of course that Puthoff's PV model violates the usual symmetry and covariance constraints of Einstein's gravity theory.
1. De Witt constructs the vacuum stress tensor T_vac=<0|Tuv|0> from the sum
of modes f_k which satisfy the operator D f_k=0. At least in flat space it
is on-shell equation.
Agreed. But I need to study the exact way he uses it. The ZPF, in this case virtual photon contribution, is from what is NOT from the poles of the Feynman integrals. What you write here, i.e.
Df_k = 0
is simply the locus of the pole's path of the integral for the Feynman photon propagator in the complex energy plane as a function of the momentum.
As a result, in flat space ZPF cannot give a contribution to /\ term.
Agreed, that the ON-MASS-SHELL pole contributions to the relevant integrals do not contribute to the /\zpf term. That's what I have been saying all along. Only the off-mass shell contribution contribute and, since in this globally flat micro-quantum PRE-INFLATIONARY FALSE VACUUM, with constant metric nuv(Minkowski) we have
MACRO-QUANTUM ODLRO Vacuum Coherence = 0
/\zpf in FALSE VACUUM ~ (Cutoff Length)^-2
The CREATION OF THE UNIVERSE (our "Hubble Bubble" in sense of Max Tegmark's "Parallel Universes" May 2003 Scientific American -- also found online BTW by Google) is the VACUUM PHASE TRANSITION, a collapse of phase space, in which now emerges in accord with P.W. Anderson's "More is different" Ansatz:
/\zpf in TRUE VACUUM ~ (Cutoff Length)^-2[(Cutoff Length)^3|ODLRO Vacuum Coherence|^2 - 1]
Where Einstein's emergent smooth curved space time metric tensor field is now
guv(Curved Space-Time) = nuv(False Vacuum) + (Elastic World Strain Tensor)uv
in Hagen Kleinert's sense http://www.physik.fu-berlin.de/~kleinert/
(Elastic World Strain Tensor)uv = (1/2)[du,v + dv,u]
This formula is found in Kleinert's work.
du is the local distortion of the vacuum from global flatness
It is the compensating gauge force field from locally gauging the 4-parameter translation sub-group of the 15 parameter conformal group. It obviously gives rise to Einstein's general coordinate transformations GCT
x^u'(P) = x^u'(x^u(P))
for space-time event P
To this work of Kleinert's I add my new original LOCAL MACRO-QUANTUM Bohm Hidden Variable "guidance constraint"
du(P) = (Cutoff Length)^2(Phase of the ODLRO Vacuum Coherence),u in 4D
Think of the analogous superfluid flow eq in 3D
Velocity of Hidden Variable = (h/m)Gradient of Phase of the Giant Pilot Wave)
This also works on micro-level of course in Bohm's theory.
Note, that in general we will have the ANHOLONOMY that the mixed second order partial derivatives of the LOCAL macro-quantum ODLRO phase do not commute! This means a TORSION FIELD from locally gauging the additional 6-parameter Lorentz group. We have at least 5 more parameters to locally gauge to get even MORE exotic compensating gauge force fields beyond Einstein's 1915 gravity theory that really comes only from spontaneously breaking (and restoring with the compensating local field du) the 4-parameter translation group vacuum symmetry!
* Remember these are all LOCAL smooth c-number emergent "More is different" MACRO-QUANTUM ODLRO fields. They are NOT to be re-micro-quantized. This is the meaning of "Einstein gravity is not consistent with renormalizable quantum field theories."
But such contributions may
appear a) in curved space and b) from longitudinal modes, so
Tuv_vac =/\_quant + T_Casimir ... + anything more.
No. Such contributions appear from ALL three spin 1 virtual photon polarization modes even in the globally flat totally random incoherent pre-inflationary false vacuum without any trace of gravity nor rest mass of spin 1/2 lepto-quarks and W bosons whatsoever. The problem there, however, is as I showed /\zpf is TOO BIG! One also needs to put in all the virtual lepto-quark particle-antiparticle pairs and all the weak and strong virtual bosons in addition to the virtual photons you discuss above. I don't think we need supersymmetry, but we can stick it in later to see if we really need it.
The micro-geons from the smooth COHERENT ODLRO c-number guv field have "Mass without mass" with all the virtues of string theory already! No more point particles! No more infinite renormalizations!
Remember a "geon" is dual to a tangled string!
We may not need extra-space dimensions, but we can accommodate them. But for now use parsimony. More with less. Keep the excess theoretical baggage down to a minimum!
2. The right sight of the De Witt equation Tuv is not
regularized now and contain all the quantum divergences.
Yeah, but that misses my new insight completely! It's a new ball game. De Witt has NO ODLRO. His theory is NO GOOD! It is only a pre-inflationary FALSE VACUUM theory without any NON-PERTURBATIVE phase transition to the post-inflationary true vacuum with ODLRO.
BTW the pre-inflationary false vacuum must be CONFORMAL without any rest mass at all! Rest mass only emerges with vacuum coherence in accord with Einstein's equivalence principle. Furthermore the post-inflation vacuum with gravity has less entropy than did the pre-inflationary false unstable vacuum without gravity. This explains the direction of the Arrow of Time of the Second Law of Thermodynamics, i.e. WHY it points in the direction of the expansion of the post-inflationary universe we are trapped inside of like Edwin Abbott's "Flatlanders."
In this form
I checked once more a few books and found that the Casimir ZPF in flat
vacuum space is formed by the on-shell modes, in particular plane wave
photons with 2 transverse polarizations.
* Then all those papers are wrong! What you are really saying is that the Van Der Waal's force alternative derivation of the Casimir force is the true explanation and that the ZPF model is self-contradictory and for some strange reason gives the correct answer FOR THE WRONG REASONS - this has happened before in physics.
The unique difference from the real photons is that E_vac = E_real/ 2. =h
\nu / 2.
I don't understand this last sentence.
Of course a quantum simple harmonic boson oscillator of frequency f has a ground (vacuum) state energy of + hf/2.
However, one cannot assume that f = ck INSIDE that vacuum!
f = ck is true ONLY for the n real photons in the excited eigenstate OUTSIDE the vacuum whose energy eigenvalue
En = nhf + (1/2)hf
Maybe I am wrong, but I believe, that excluding the on-shell VACUUM photons
you exclude the main part of the Casimir effect.
You must be wrong on elementary conceptual grounds of heuristic consistency, or, alternatively, all those papers are wrong. They violate the simple idea that by definition the fully interacting physical vacuum is the STRICT ABSENCE of ON-MASS-SHELL quanta! What you are citing is an obviously self-contradictory physical idea like 1 = 0 in mathematics!
If the latter: Never have so many been so wrong about an important physics idea!
I can agree with your following remarks:
AB The mass gap may be neglected for the very high frequencies and it
does not prevent to
I do not see how this last statement affects my simple argument that
you cannot argue /\ = 0 from cancellation between RANDOM virtual
photons and RANDOM virtual electron-positron pairs because of two
1. there is an extra longitudinal virtual photon mode
2. the mass-gap of the virtual electrons in Dirac's negative energy sea
means that the virtual photon modes below the gap escape any possible
This example was taken from very old suggestions.
It is working for superdense matter, but is not good example to explain /\_vac = 0. In supersymmetry counterpartners must have the same mass.
But that is all fantasy. Such things have never been observed - no evidence. You will note that ALL my theories here are evidence driven not mere pretty math! I mean by "evidence"
1. Gravity lensing of dark matter.
2. Type 1a supernovae anomalous red shifts
3. Anomalous violent events, quasars, gamma ray bursts etc.
4. Null results from dark matter detectors! Like Michelson-Morely experiment 100 years ago.
5. Paradox of the cosmological constant. Like blackbody radiation paradox of 100 years ago that led Planck to the quantum.
6. Small temperature fluctuations in the cosmic blackbody radiation WMAP and all that.
7. Leptoquarks inside hadrons shrink in size under increasingly larger magnification.
8. Universal Regge trajectories of hadronic resonances.
9. Cold Fusion
10. Ken Shoulders EVOs
11. Last but not least the flying saucer UFO data.
Meantime I derive
Guv + /\zpfguv = 0
If you put in vacuum T_uv=0 then the divergence of
/\zpfguv is compensated by the divergence of Guv.
I do not understand, is your G_uv divergent (or huge) in VACUUM?
You cannot use the old ideas of point particle field theory here.
My Guv is FINITE.
The exotic vacuum field equation for both dark energy and dark matter is an ODLRO macro-quantum c-number equation
Guv + /\zpfguv = 0
Now you can do quantum perturbation theory around this curved dynamical background c-number metric, for now I ignore adding the spin 2 quantum operator field huv. Better to work with RENORMALIZABLE spin 1 &du quantum field using gravitons as EPR "Bell state" pairs of spin 1 quanta.
NO MORE NAIVE Bianchi identities here!
i.e. when /\zpf =/= 0
you cannot use
Guv^;v = 0
Instead you must use
Guv^;v + /\zpf^,vguv = 0
if you assume guv^;v = 0
;v = covariant derivative
,v = ordinary partial derivative
also ;v is relative to the CONNECTION and that depends on whether
du,v = dv,u OR NOT? i.e. no torsion OR torsion?
i.e. on the kinds of topological Berry phase singularities in the LOCAL MACRO-QUANTUM Vacuum Coherence field that must be kept single-valued!
The torsion field can be ignored in ordinary vacuum where /\zpf = 0, but not so in exotic dark energy/matter vacua where /\zpf (a local dynamical scalar field) =/= 0.
The reverence to B. De Witt Phys Rep. 19(1975), 295.
"Reverence" is right. These old theories are now impotent and obsolete and I do not revere them uncritically! No one understood anything back then in 1975 and even less in 1961 where Hal Puthoff is still stuck in a Ground Hog Day time loop! :-)
Close description is in the book by Birell and Davies, but they use the on-shell scalar waves
I ordered that book and will look at what they say. :-)
Again they stick in guv with QFT adhoc. I derive guv from a non-perturbative ODLRO vacuum phase transition. Very different physical picture!
Best regards, Alexander