Friday, April 15, 2005

The Theory of Everything for Everyone
On Apr 15, 2005, at 3:13 PM, wrote:

If you read the Arcos & Pereira paper, how do you understand the authors' position regarding the extraction of a localizable tensor vacuum stress-energy density
from the net gravitational-inertial stress-energy of the Einstein field in (1) their own teleparallel formalism; and (2) in the conventional curved-manifold formalism?

Jack, this question was specifically addressed to Art.

J: Yes, I know.

What A&P do, very nicely is to show the B field!

Z: In the context of a *teleparallel* theory.

J: They do not have my Vacuum ODLRO SBS idea, i.e. they do not write

B = (Lp/2pi)"dargVacuumODLRO"

argVacuumODLRO = Goldstone Phase of Higgs Field (post-inflation).

Z: Right. Of course not.

J: If B is closed non-exact 1-form that's A&P torsion "flux without flux".

Z: So you are saying that your "tetrad" B can be modeled as a torsion field?

J: Yes, it's the "potential" for the A&P torsion field not the Shipov torsion field. B is like A in EM, F = dB is like the EM field tensor, but here it is the A&P tetrad substratum torsion field tensor.

As R. Kiehn points out the most general p-form has 3 possible independent components

form = exact + closed not-exact + non-closed

If B has a non-closed piece I call that "flux with flux" i.e.

F = dB

If B is only closed and not-exact

Stokes theorem says |B = 0 on a bounding cycle but need not be zero on a non-bounding cycle that is only a piece of the total boundary that consists of several cycles when the manifold of integration of dB is not simply-connected.

If, in addition, there is macro-quantum vacuum ODLRO (a new independent physical idea)

B = (Lp/2pi)"dtheta" in sense described in John Baez's book on Gauge Fields, Knots & Gravity, then the "period integral" of 1-form over the boundary fragment, which is nevertheless a closed loop (nonbounding 1-cycle) is, from single-valuedness of the ODLRO order parameter

|B = NLp

N is integer winding number

This leads me to define another "Ghost of a departed quantity" (Bishop Berkeley)

NLp = (Area)dB'

Mean value theorem for integrals.

I put the ' to denote "flux without flux". The "Area" is inside the non-bounding cycle and all the other inner non-bounding cycles isolating phase singularities where |ODLRO| = 0 (like vortex cores in Type II superconductor of real EM flux with flux) shrink to zero (I mean small). Actually HeII quantized circulations may be "flux without flux" in this sense.

Thus in cylindrical coordinates for |ODLRO| = 0 along z-axis

dB' = NLp/pir^2

Even though technically dB = 0.

NLp is like a finite integral of a zero integrand only because we have ignored the inner cycles that add up to -NLp of course. But as physicists we can do that since we only actually measure the outer non-bounding cycle in the case of quantized vortices in superfluid HeII.

So this is an archetype analogy for the complete nonlocality of gravity energy in ordinary vacuum /\zpf = 0 i.e. gravity vacuum energy without gravity vacuum energy.

Integrating a local "zero" to get a "finite" total is not so crazy when the manifolds of integration are not simply-connected and the "holes" correspond to phase singularities, i.e. zeros in the ODLRO intensity.

The situation is like that of infinitesimals in calculus that are both zero and not zero in the heuristic sense. As physicists we don't care about what Feynman called "rigor mortis". For example the Feynman path integrals are mathematically non-rigorous yet we get good results from them.

If B is not closed that's torsion "flux with flux"


F = dB  is the A&P torsion field (not same as Shipov's).

I assume here G/H = S1 like Abelian Maxwell E&M, this is only a toy model

dF = 0

d*F = *J

The local stress-energy tensor of this torsion field is

~ F/\*F  i.e. a 4-form

But NOTE if B is closed and non-exact, then strictly speaking LOCALLY

F = dB = 0

Yet, from "flux without flux" the global integral is not zero even though the local density is!


Z: OK, I think I get it.

J: Yes, this is an interesting strategy. Penrose gives a good heuristic why total gravity ordinary vacuum energy really must be nonlocal so that Yilmaz's theory is asking the wrong question and so is Alex's. Valentini's new papers on the creative tension between locality & nonlocality add fuel to that fire. There are other arguments as well.

"Flux without flux" means

|B = ||dB = NLp,  N an integer

Strictly of course |B = 0 over a boundary, but here we take the incomplete integral over a non-bounding cycle and ignore the inner cycle that gives -NLp (Stoke's theorem) that shrinks to the topological defect Goldstone phase singularity where |Vacuum ODLRO| = 0 in the G/H order parameter space. Note, unlike micro-quantum theory, in macro-quantum theory the radius of S1 has independent physical meaning. Also see A. Valentini's latest papers on sub-quantum non-equilibrium signal nonlocality.  Let P be the non-equilibrium distribution, the non-local signal is an integral with kernel P - |psi|^2, in macro-quantum theory, I think this becomes ~ |ODLRO|^2, which of course is zero in nonlocal micro-quantum theory with "presponse" signal locality. That is, any system with ODLRO (in vacuum for virtual quanta E^2 =/= (pc)^2 + (mc^2)^2, in ground states  E^2 = (pc)^2 + (mc^2)^2 for real quanta) is "sub-quantal non-equilibrium". Call this the "Sarfatti Conjecture" since our conscious minds are pumped open giant quantum robust ODLRO systems immune to warm wet environmental decoherence of the Zurek-Tegmark kind.

Z: OK, looks good. Very interesting idea.

J: Valentini has a formula in one of his new papers

Nonlocal signal ~ Integral of stuff [P(sub-quantum non-equil) - P(sub-quantal equil)]

I think I can argue as a sufficient, though maybe not necessary, condition for signal nonlocality in macro-quantum theory

|OLDRO|^2 = [P(sub-quantum non-equil) - P(sub-quantal equil)]

I get this from theory of reduced density matrices as given by L. Onsager & O. Penrose.

P(sub-quantal equil) = "normal fluid" single-particle reduced density matrix in diagonal limit = Born probability density! (pair density matrix in case of fermions)

The macroscopic eigenvalue of first-order reduced density matrix is "sub-quantal non-equilibrium" in A. Valentini's sense and it is immune to warm wet decoherence. This is WHY Dick Bierman sees "presponse" in his data.

Z: I'm also curious about how you understand A&P's claim that that the teleparallel formalism is "physically equivalent" to the curved manifold formalism?
Again, this was addressed to Wagner.

In answer to R.Kiehn today

On Apr 15, 2005, at 5:00 PM, Jack Sarfatti wrote:

Clarification of notation

When I write

g(curved) =[(I + B)^T][(flat)]([I + B)]

That is just my lazy notation. I do not mean that as an equation in Cartan forms. All I mean by that is the well known

guv = eu^a(Minkowski)abev^b


eu^a = Iu^a + Bu^a

Iu^a is Kronecker Delta

B = dx^uBu^a(Pa(Goldstone Phase)/ih)

{Pa} is Lie Algebra of T4

It means simply one version of EEP

g(curved) = (I + B)(flat)(I + B)

Z: So you think that by "physical equivalence" A&P simply mean that they recover standard EEP? You think they mean "equivalence" as in "equivalence principle"? In other words -- "pun intended"?

J: Pun intended sure. What they mean is simply that starting from the zero curvature torsion tetrad substratum, one can use the formal EEP to derive standard vanilla 1916 GR curved torsionless model.

There is a kind of curvature/torsion duality here between the local gauge force and geometrodynamical pictures.

The torsion flat gauge force picture is the "square root" of the curved torsionless geometrodynamic picture.

So, the torsion picture is a covering theory of the geometrodynamics. It is closed to the Ashtekar picture!

That is, in the torsion tetrad substratum it is obvious how gravity is really simply the local gauge theory of T4 -> Diff(4.

In 1905 special relativity

x -> x' = x + xo -> conservation of total linear momentum px

t -> t' = t + to -> conservation of total energy E

These are GLOBAL displacements in Minkowski space-time making up the RIGID group T4 (with x & y).

It is completely trivially obvious that Diff(4) GCT's

x^u(P) -> x^u'(x^u(P))

at a fixed PHYSICAL EVENT P = equivalence class of manifold points p ~ p', p =/= p'

is by definition the local gauging of T4 to Diff(4) with compensating gauge force potential Bu^a where

guv(curved) = eu^a(Minkowski)abev^b

Z: I think they mean something much broader -- more like matrix mechanics vs. wave mechanics.

J: Frankly I don't care what they mean. What I care about here is what I mean. However, I suspect that what I mean and they mean are not that far apart.

This is exactly how curved space-time is Vacuum ODLRO emergent bottom -> up.

Back-of-the-envelope heuristics

The quantized Goldstone vibrations in argVacuum ODLRO are not spin 2 gravitons.


Are they like phonons?

More like phonons yes. They are not spin 2 at least not when G/H = S1 where

Vacuum ODLRO = PSI = Re^iS (Bohm Pilot Wave notation)

If Bu^a = X^a(PuS/ih) = X^aS,u

X^a is "position operator" conjugate to Pa in Minkowski space

i.e. X^a makes displacement in momentum Minkowksi space

Z = (X + Lp^2P/ih) & Z* =(X - Lp^2P/ih)

Give Wigner Phase Space Density Representation of Glauber & Squeezed macro-quantum coherent states

Z|z> = z|z>

z = re^itheta

Use the formalism of quantum optics

D(z) = e^(zA* - z*A) Glauber coherent states

S(w) = e^(wA*A* - w*AA) Bogoliubov pairing transformation for squeezed states.

w vacuum ODLRO squeezing parameter ~ BCS Nambu/Jona-Lasino gap function, i.e. rest masses of lepto-quarks?

No gravitons. No quantum foam. No quantum gravity.

Z: Well, you do have a true QFT layer beneath your BEC macro-condensate, don't you? That describes the micro-behavior of "off-mass-shell" electrons and positrons?

Yes, it's their pairing that is the "chaotic" inflation phase transition. The pairing binding energy powers the hot phase of the Big Bang. It's all pretty obvious intuitively. It fits Lenny Susskind's "landscape" with WEP and also Max Tegmark's Level I & Level II (see his homepage for pretty pictures)

Who ordered that?
What about Duff's argument for quantum gravity?
What happens when you reach rock bottom?

Z: Yes, of course this is the Sakharov emergent-gravity thesis. Same in Hu's papers, for example.

J: Same in general philosophy not in detail. This stuff is in the air. Mine is the simplest of em all. Are all the rest over-complicated or is my model simpler than is possible like Puthoff's PV and Haisch's EM SED ZPE "origin of inertia".

Is a theory of everything for everyone impossible? Do you have to be a fancy mathematician to grok it? Calabi-Yau and all that really needed? Too soon to tell.

You return to the false globally flat massless conformal vacuum of spin1/2 & spin 1 QFT with no gravity and no inertia, i.e. all rest m = 0

Z: But is it kinematically false?

J: I do not know what that even means. The center of the cyclone where |ODLRO| = R = 0 thats FALSE VACUUM. So it's physical as real as anything is.

Z: Or just unstable if construed as a physical vacuum?

J: It's real and unstable. It's as real as riding a unicycle.

Z: I still sense Einsteinian ambiguity and even confusion here.

J: The fault dear Z is in your mind and not beyond the stars.

Z: What did Sakharov say about this "emergence"?

J: Not much. Like Bohr he mumbled some things about "metric elasticity" and if you read Adler Rev Mod Phys 1982 you will see more very complicated stuff. It's not clear which comes first however. It's Chicken & Egg. Been up so long it looks like down to them. Adler seems to get Einstein-Hilbert action from SBS & estimates of G & /\, but it's far from obvious what he is doing. Also I don't see no tetrads there.

Z: What's wrong with a bi-metric approach at the macro-level? I can imagine that a bi-metric approach would fit your BEC model quite well if you were open to it.

J: Occam's razor. Parsimony. More with less. Excess Baggage. If it ain't broke don't fix it. Who ordered a second metric. That's an unimaginative act of desperation - not at all like Max Planck's.


E = pc for all real quanta

This is what you get for |Vacuum ODLRO| = 0 in the core of a topological defect in G/H order parameter space.

Note that the non-perturbative lepto-quark mass scale is

m ~ (hwD/c^2)e^1/rho(Ef)<0|V|0>Theta(-V)


1 Mev ~ 10^19Geve^-1/|x|

e^-1/|x| ~ 10^-22

Theta(x) = step function

V is the attractive interaction potential between the virtual electrons and positrons at the edge of the negative energy Dirac Sea with Fermi energy Ef = 0, but pf ~ h/L

Let V -> 0 from negative values where it is attractive i.e. V ~ -e^2/r, this gives m = 0 at V = 0-, m stays zero for repulsive V > 0.

rho is density of states of massless negative energy virtual electrons Fermi liquid at Ef per unit energy.

Subject: Z's confounding of tetrads with Diff(4) GCTs
Date: Thu, 14 Apr 2005 14:06:26 -0700

Admittedly Paul I suspect you are not the only one confused by this issue of how to separate intrinsic geometry from non-inertial local frame inertial g-forces especially since one cannot tell the difference without making local tidal geodesic deviation measurements.

On Apr 14, 2005, at 12:12 PM, wrote:

[JS] What I am telling you is that you cannot use a GCT X when B =/= 0 to make (LC)' = 0.

[Z] Then there is something wrong with your B. Of course you can always cancel net g-forces with a GCT.

[J] There is nothing wrong with B. In fact it is what you were looking for, but you looked in the wrong place - at the wrong level. Math is math. Diff(4) GCT non-dynamical Xu'^u connects non-geodesic LNIFu with non-geodesic LNIFu'. Indeed, you can always locally cancel the g inertial force of an LNIF by jumping to a coincident LIF, but you do that with a tetrad eu^a not with a GCT Xu'^u. The globally flat Minkowski space-time is degenerate i.e. eu^a = Kronecker delta Iu^a so that the u/a distinction vanishes and, indeed, in that case only, you can use GCT to get from an inertial frame to a non-inertial frame. Your intuition on Minkowski space-time does not carry over to curved space-time. Can I teach this Lazy Dog a new trick?

e.g. x -> x' - (1/2)gt^2
     t -> t' = t

in Newtonian limit.

In the B = 0 degenerate case where a = u so to speak

(Minkowski)uv = Iu^a(Minkowski)abIv^b

Now, take any Diff(4) GCT Xu'^u at all to get the PHONY 100% inertial force zero tidal warp pseudo-curved metric

gu'v'(Minkowski) = Xu'^u(Minkowski)uvXv'^v

B = 0

Ruvwl = Ru'v'w'l' = 0 everywhere-when in Minkowski

These Diff(4) GCT Xu'^u describe infinite sets of pairs of coincident possible local observers u & u' in arbitrary relative motion at event P. Mathematically Xu'^u is the overlap transition function of two local coordinate charts x^u & x^u' in same neighborhood of event P. P is an equivalence ~ class of bare manifold points p i.e. P is the coset of ~ p's. The space of events P is a coset quotient space under gauge equivalent active Diff(4) p -> p'.

There is a qualitative phase transition from the bottom -> up non-perturbative inflationary emergence of

B = (Lp/2pi)d(argVacuum ODLRO)

closed non-exact 1-form means period integrals of 1-form B on non-bounding 1-chain cycle need not vanish, but is NLp hence "flux without flux"? The boundary round a |Vacuum ODLRO| = 0 "hole" is two concentric opposite running cycles and we ignore the inner one to get "flux without flux" that is, in fact, measured by observers on the outer non-bounding 1-cycle. Goldstone phase = argVacuum ODLRO is not a unique 0-form (it is a set of partially overlapping functions) because of |Vacuum ODLRO| = 0 topological defects in the G/H quotient order parameter space of the inflationary vacuum phase transition. The defects give non-trivial cohomology/homology/homotopies for all the p-forms, p = 0,1,2,3,4 in 4D space-time. The macro-quantum order parameters out of which curved space-time emerges must be single-valued. It's not enough that |Vacuum ODLRO| match. The phases must match mod 2piN round a closed circuit in G/H that corresponds to some path in ordinary 3D-space. The number of circuits in each space need not be identical.

[JS] that Taylor series procedure

[Z]:  What "Taylor series procedure"?

[JS]: guv(P') = guv(P) + guv,w(P)(P'-P)^w + (1/2)guv,w,l(P)(P'-P)^w(P'-P)^l

Use the non-trivial tetrads e = (I + B)

Finding the local dynamical tetrad eu^a(P) requires the critical point

guv,w = (LC)uv,w - (LC)vu,w = 0 ? (from memory - error?)

This seems to require zero torsion to get orthodox EEP?

So what we really want is

gab,c = ea^ueb^vec^wguv,w = 0

P'is now in the tangent space

gab(P') ~ (Minkowski)ab + (1/2)gab,c,d(P)(P'-P)^c(P'-P)^d + ...

where second term on RHS is the actual tidal geodesic deviation (curvature) in the LIF.

Note also

guv(P) = (Iu^a + Bu^a(P))(Minkowski)ab(Iv^b + Bv^b(P))

and inversely

(Minkowski)ab = (Ia^u + Ba^u(P))guv(P)(Ib^v + Bb^v(P))

local all at same P

Therefore, the Taylor series can be reduced to expansions of the dynamical B field.

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