Energy without energy
Eric Davis alludes to Yilmaz's paper in his USAF teleportation report as I recall?
On May 4, 2005, at 5:43 PM, firstname.lastname@example.org wrote:
Jack wrote earlier
y = e^(1/x) Stepfunction(-x) = SUM of infinity of Feynman diagrams of a certain class in the false vacuum
[It is] the NON-PERTURBATIVE "BCS"(Nambu-Jona Lasino) basic formula that applies generally here.
What you propose is perturbation theory around x = 0, which is obvious nonsense.
y ~ |Vacuum ODLRO|
x ~ density of states per unit energy at Fermi surface of false vacuum x interaction first order perturbation theory matrix element between the virtual fermion-antifermion pair that forms the Vacuum ODLRO condensate in the inflation phase transition
This says you cannot do what Yilmaz proposes in principle!
Lim y as x -> 0- = 0
Lim y as x -> 0+ -> +infinity
That's WHY you cannot do it!
Sorry, I fail to see how this rules out g_uv = g_uv(phi_uv) or tensor vacuum t_uv on the RHS.
The formula is mathematically unsound as it stands without context and explanation. You cannot have double indices like that. What does it mean?
guv = (etae^PHI)uv
What does that mean?
g00 = (etae^PHI)00
What does that mean?
Does it mean
logg00 = logeta00 + PHI00
logz = log|z| + iargz
to base e in complex plane
What is eta00, and what is PHI00 PHYSICALLY for example? Why even introduce this exponential notation like polar representation of complex numbers without the i? Obviously the key idea is that you get Minkowski flat space-time when PHI -> 0, but WHY PHI = phi - 2phi~ in
Paul, until you can explain this simple example, what you are doing here is completely bogus. Maybe Yilmaz's theory is bogus I don't know. It's unintelligible. His papers are unreadable for me. You cannot explain them, which means, by Feynman's test, you do not understand them. There may not be anything there to understand? Maybe Mike Ibison can make an adequate defense of Yilmaz's theory, since obviously you are not able to do so.
Yilmaz even talked about the gauge symmetries of phi in his 1958 Phys Rev paper as related to the position
displacements of the observer in the gravitational field. Sound familiar?
Useless without the details.
You are not Roger Penrose, so that is completely understandable. He is only, perhaps the greatest living mathematical physicist, Professor at Oxford, FRS Knighted by The Queen. Why should we care what he thinks? ;-)
But this "energy problem" is a *foundational* issue, not a purely mathematical question.
Indeed, I have outlined what I think may be the ultimate resolution of WHY gravity vacuum energy is nonlocal.
The global DeRham integrals of a local "zero" density need not vanish in a multiply connected region (non-trivial cohomology) of integration because of the "holes" that are singularities in the single-valued Vacuum ODLRO out of which the local GR field equations emerge.
*The nonlocality of the gravity energy is a strong "Cosmic Trigger" signal that Einstein's GR is an emergent c-number IR effective field theory from vacuum ODLRO! Andrei Sakharov did not have the right idea when he thought that GR emerges from RANDOM ZPF. It emerges from the COHERING of the random ZPF in the INFLATION phase transition of false flat to stable curved vacuum. This led Puthoff, Haisch & Rueda & Co off on a doomed wild goose chase for the "origin of inertia" using the wrong SED theory of Trevor Marshall.
The nonlocality of gravity energy is an undecidable Godel question that requires a larger covering theory, i.e. Vacuum ODLRO. My supersolid paper of 1969 was the beginning of this idea as noted by George Chapline Jr.
On Feb 16, 2005, at 3:18 PM, George Chapline wrote:
Your solid He4 superfluid paper is wonderful! You actually once did something of very great importance - and apparently you didn't realize this. This paper is a precursor to quantum gravity, and much more important in that regard than string theory ( you can quote me).
re: Destruction of superflow in unsaturated 4He films and the prediction of a new crystalline phase of 4He with Bose-Einstein condensation. Physics Letters, Vol 30A, no 5 3 November 1969 pp 300-1
On Feb 14, 2005, at 2:46 PM, George Chapline wrote:
For the record I strongly encourage you to send a letter to Physics Today pointing out the contributions of yourself and Chester prior to Leggett.
My 1969 He4 ground state ODLRO supersolid prediction actually observed at U Penn only in 2003 is the model of the Diff(4) covariant "world crystal" "aether" of Hagen Kleinert's disclination-dislocation model of curvature and torsion.
In other words, you get a non-zero from "integrating" a "zero".
Remember Wheeler's "Geon" i.e.
"Mass without mass"
Mass is equivalent to energy.
E = Mc^2
The mass M of the Geon is NONLOCAL since Ruv = 0 everywhere locally in the Geon extended structure. It has NO LOCAL MASS DENSITY. The Geon is an extended nonlocal structure getting NOT-ZERO from ZERO from the non-trivial cohomology!
This is what Zielinski & Co fail to understand qualitatively and why the locality of the gravity energy is a BOGUS QUESTION!
"The Question is: What is The Question?" Wheeler
Einstein's 1916 vacuum equation (my /\zpf = 0) is simply
Ruv = 0
R = 0
Obviously then, the pure vacuum gravity stress-energy density tensor is trivially
t_uv(vac) = (c^4/8piG)Ruv = 0
Nevertheless, the global integral of the local zero energy density t_00(vac) is generally not zero. The standard method is to stick in an additional non-vanishing pseudo-tensor piece t_uv* that like (LC) vanishes at a point in a LIF.
However, the key theorem is the generalized Stoke's theorem in Cartan form language for the DeRham integrals
|C = ||dC
C is an ANTISYMMETRIC p-form.
| is the DeRham integral over a bounding p-cycle
dC is the ANTISYMMETRIC p + 1 form
|| is the p + 1 co-form with p-holes that has boundary that is the above bounding p-cycle.
Suppose, there is a p-hole. That means there are at least TWO non-bounding p-cycles that make the bounding p-cycle. There is the INNER non-bounding p-cycle that shrinks be as small as possible surrounding the hole. Its value is -Np(p-FLUX QUANTUM) where Np is a WINDING NUMBER. The p-FLUX QUANTUM is from the single-valuedness of the local Vacuum ODLRO order parameter that suffers a Goldstone Phase Singularity where the Higgs |Vacuum ODLRO| -> 0 defining the p-hole. See Michael Berry's papers for the general theory of these "topological defects".
Therefore, the value of on the MEASURABLE |C on the OUTER asymptotic "S-Matrix" observer non-bounding p-cycle is + Np(p-FLUX QUANTUM. You generally cannot measure the TWIN inner integral.
*This works even when dC = 0 LOCALLY i.e. C is CLOSED but NOT-EXACT!
Now, the problem is that GR is a SYMMETRIC theory not ANTI-SYMMETRIC. Therefore, the relation is indirect. The ANTISYMMETRIC A&P torsion forms are defined in the fermionic tetradic "square root" substratum of Einstein's SYMMETRIC bosonic curved tensor geometrodynamics.
The boson SYMMETRIC curved tensor Einstein geometrodynamics is a BILINEAR "BCS" non-perturbative PAIRING of the fermionic tetrad square roots Einstein-Cartan TORSION forms.
This is the Einstein Equivalence Principle EEP in its FULLNESS now seen in its full glory for the first time ever!
Behold EEP, post-INFLATION
guv(curved boson torsion-free tensor)
= eu^a(flat fermion torsion)(False Minkowski Vacuum)abev^b(flat fermion torsion)
You derive connection (LC)uvw and tidal curvature Ruvwl in the usual way from guv.
Meantime in the substratum
e = I + B
B ~ dx^uBu
B is the local compensating potential from locally gauging RIGID GLOBAL T4 to RUBBERY LOCAL Diff(4) with Xu'^u transformation functions on the local coordinate x^u & x^u' charts in open set topology of events P.
*Note that P is the QUOTIENT STRUCTURE MOD equivalence class of manifold points p connected by ACTIVE Diff(4)p _. p'.
Bu ~ Bu^a(Xa/Lp)argVacuumODLRO
Bu^a ~ Bu(LpP^a/ih)argVacuumODLRO
In operator language using the commutator [ , ]
Bu^a = Bu^a[(Xa/Lp),(LpP^a/ih)]
[(Xa/Lp),(LpP^a/ih)] = 1
* That is, the Heisenberg algebra is the required consistency condition!
The A&P substratum torsion is
F = dB
dF = 0
d*F = *J
if U(1) Abelian
Or, if Yang-Mills SU(2), SU(3) ...
D = d + B/
DF = 0 Bianchi identity
D*F = *J
* = Hodge Dual
See Baez's book on Knots, Gauge & Gravity.