Sunday, June 12, 2005
The Devil Will Have His Due
bcc
Previews of Coming Attractions
1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.
Loop quantum gravity and superstrings? Who ordered them? They are both not even wrong.
Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.
Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then
|Post-Inflation Higgs Ocean>
= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>
a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).
|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.
The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?
On Jun 12, 2005, at 2:55 PM, iksnileiz@earthlink.net wrote:
I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
J: Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp Grad(Vacuum ODLRO)
4D Grad in a indices.
for the 4D Diff(4) macro-quantum supersolid world crystal is analogous to
v = (h/m)Grad[arg(Ground state ODLRO) for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note the elastic linear B term and the plastic nonlinear B^2 term.
Also, B while is not a spin-2 Diff(4) first rank tensor field all by itself, it is a Minkowski spacetime spin-1 Yang-Mills vector field.
Z: No surprise, since he is working with a different model.
Personally, I think you are way ahead of him.
J: I do explain many puzzling anomalies now observed!
J: Lubos is probably correct about the lack of contact of loop quantum gravity with observation and that it cannot even reproduce GR. Baez admitted that at GR 17. Of course string theory has its weaknesses too, but may be closer to observation? We also have to look at Wilczek's objections to some of Penrose's statements.
Z: Also, as I've mentioned, spacetime coordinate transformations, as *mathematically* defined, do not change any observer's world line.
J: That's what I call a kind of gauge freedom.
Z: You can call it that, and I appreciate your analogy, but I think the problem goes much deeper.
J: Too vague. Show how.
J: That is, all GCTs that do not change the state of motion of a detector are physically equivalent. An example of a physical GCT is starting in the rest LIF of a detector in space and then firing a rocket engine attached to the detector. The transformation, in that case, tetrad eu^a(P), that describes the relation between the momentarily coincident LIF with indices a & LNIF with indices u at same P. But you see here a complete local equivalence of the inertial force to the gravity since the physical difference is Bu^a in
eu^a(P) = Iu^a + Bu^a(P)
i.e. Bu^a(P) encodes the information of switching on the rocket engine!
You cannot locally distinguish inertial force from gravity force!
Z: But actually you can, as shown by Ohanian & Ruffini.
J: No, you still don't get it! You keep getting hung up on that. You do not understand what the word "locally" means. It means DO NOT MEASURE GEODESIC DEVIATION. Indeed, geodesic deviation is irrelevant to gravity force. The measurement procedures are orthogonal.
Obviously you can measure the local tidal curvature tensor at P in either an LIF or a LNIF makes no difference.
EEP means, YOU DO NOT MEASURE THE GEODESIC DEVIATION CURVATURE AT P because even if you do, then you STILL cannot tell the difference between an inertial force and a gravity force! Suppose the curvature is not zero so what? Think of y = y(x) and dy/dx. Measure y at xo. That does not tell you anything about dy/dx at xo if you have no prior knowledge of y(x). Indeed IN ALL CASES GRAVITY FORCE IS ALWAYS 100% INERTIAL FORCE. GRAVITY FORCE IS 100% INERTIAL FORCE in EVERY CASE IMAGINABLE.
Here inertial force is the NON-GRAVITY REACTION FORCE needed to PUSH the test particle OFF a timelike geodesic (relative to LC connection - I only do 1916 GR here).
The measurement of tidal curvature geodesic deviation is most cleanly done in the LIF where all gravity forces are strictly ZERO and special relativity applies locally to a good approximation.
Consider the SSS metric in only the radial direction to keep it simple
ds^2 = (1 - 2rs/r)(cdt)^2 - (1 - 2rs/r)^-1dr^2
This metric is only good for those HOVERING LNIFs at FIXED r > rs. Some NON-GRAVITY FORCE is pushing those HOVERING LNIFS off timelike geodesics. For the LIF observer the effective LOCAL metric is always to lowest order approximation
ds^2 = (cdt')^2 - dr'^2
even though geodesic deviation for the LIF observer is not zero!
The key is
(1/2)c^2Gradgoo = (1/2)c^2Grad(1 - 2rs/r) = c^2rs/r^2 = GM/r^2
= APPLIED UNIVERSAL NON-GRAVITY INERTIAL FORCE PER UNIT TEST MASS POINTING OUTWARD NEEDED TO KEEP THE HOVERING LNIF DETECTOR AT FIXED r.
IN FACT GRAVITY FORCE IS ELIMINATED 100%. What we call "gravity force" is 100% INERTIAL FORCE logically independent of curvature.
Of course in flat space-time you do not need any non-gravity force at all to keep a test particle "still" relative to a marker (neglecting their weak gravity of course).
Therefore, Paul you have been working on a non-problem! The gravity energy is also a non-problem, but much more subtle.
Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object".
Z: Spacetime "events" are addressed by coordinates,
This is wrong.
Z: Wrong?
J: Yes, wrong.
Z: Obviously "events" occur at definite locations on the spacetime manifold, and these 4D locations (points on the spacetime manifold) are assigned unique addresses by spacetime coordinate systems.
J: Not even wrong until you give an operational definition for "definite locations on a spacetime manifold". Rovelli is good on this issue.
Z: Mathematically, at least, changing CS *addresses* has to be sharply distinguished from changing *locations*.
J: Prove that with a mathematical example. Your words are too vague.
Rovelli is correct on that part. Events are coincidences like the collision of two point particles (toy model).
Z: Yes, but these coincidences occur at *definite locations in spacetime*
J: Wrong. Read Rovelli again on this. There is no such thing as
*definite locations in spacetime*
Define what you mean. Do you mean a collision of two point particles? If so, see Rovelli's discussion of the "Einstein hole problem" with the nice pictures.
that are merely assigned addresses by
spacetime coordinate systems.
Z: If Rovelli thinks that there is no mathematical distinction between an active Diff(4) rearrangement of manifold points (an actual deformation of the manifold) on the one hand, and a mere reshuffling of CS addresses, on the other, then
he is quite mistaken IMHO.
J: I do not understand what you just wrote. Your words are not even wrong. Give a mathematical example of what you mean here. If you cannot do that you have not really said anything worth saying on the issue.
You seem to think that the Diff (4) group creates physical deformations. That is not true at all. Only stress-energy density currents and self-interactions of the geometrodynamic field create physical deformations of the manifold. That's why we have Diff(4) covariance in the first place! That's why in
Guv(Gravity) + /\(ZPF Vacuum Energy)guv(Gravity) + (8piG/c^4)Tuv(Matter) = 0
We only have Diff(4) COVARIANT TENSORS!
Diff(4) is the LOCAL SYMMETRY GROUP it DON'T MAKE ANY PHYSICAL or "actual deformations". You have the wrong idea entirely!
Diff(4) is the LOCAL GAUGING of T4 with Bu^a as the induced compensating gauge potential. Also, you have Vacuum ODLRO in the inflation phase transition from the unstable rest-massless gravity-free conformal false vacuum to the stable curved vacuum with rest masses from Higgs ODLRO coherence and gravity and even dark energy/matter in which T4 is SPONTANEOUSLY BROKEN to allow CURVATURE! You do not get Gennady Shipov's torsion until you LOCALLY GAUGE so(1,3) in addition to T4. If IN ADDITION you spontaneously break so(1,3) in the vacuum then you will also get preferred velocity effects. Whether that happens or not, apart from Hubble flow (maximal isotropy of CMB) is purely empirical.
Z: but are not defined by them. So it should be obvious that such "events", just like manifold points, are absolutes with respect to such transformations.
J: Too vague. Give a precise mathematical example.
You have the wrong idea here. I mean you have garbled things above.
Z: No, I just disagree with your your version of Rovelli.
J: Well you are so vague that your words have no meaning to me.
Physical events are invariants to be sure, but "manifold points" are not.
Z: Manifolds are not *deformed* by mere coordinate changes.
J: Right, but neither are they deformed in active diffeomorphisms! That's the point!
Z: So as far as I can see, the effect of GCTs on manifold points and events is similar. Addresses are simply re-shuffled.
J: Yes, but that is the case for both active and passive Diff(4). The mathematically distinct manifold points A & B in Rovelli's nice discussion are not physically distinguishable, i.e. the collision of particles 1 & 2 is PUSHED FORWARD (or is it backward?) from A to B so that NOTHING MEASURABLE has changed in the active Diff(4) from A to B. P includes both A & B in the same equivalence class!
Now your way of thinking will work to some extent in special relativity quantum field theory and in classical mechanics and classical electromagnetism, but it does not work in GR and it took the great Einstein what 3 years? to understand this and today most physicists still do not really understand it!
See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~| A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
Z: In my POV, *none* of the mathematically defined coordinate transformations on the spacetime manifold has any physical meaning at all until such a meaning is attached to them, or to some subset of them.
Z: Chasing your own tail. Circular. Meaningless until you show an independent procedure.
Z: It's pretty obvious if you think about it.
J: Since I do not understand your English I do not know. If you cannot make your idea more mathematical or more specific in terms of gedankenexperiments you are not communicating to my mind at least.
Z: Mathematical coordinate changes in themselves do not change any observer's world line. But in order to change an observer's frame of reference, you must at the same time also change that observer's world line.
J: Yes, that I understand. I understand that if a LIF observer fires a rocket engine in space then she is transformed to a LNIF observer and that instant coincident local transformation (approximately to be sure) is not a Diff(4) thing at all but is a tetrad thing. But then if she changed the thrust it is a Diff(4) thing moving from one non-geodesic to another "instantly" at a "crossing point". But even then, the Diff(4) is a MERE DESCRIPTION of her PHYSICAL ACTION, e.g. throwing the switch or turning the dial on the thrust control panel.
Z: So there is a basic *contradiction* in the orthodox treatment that needs to be resolved. I'm resolving it.
J: No you have not. I just resolved it for you in my above remark - bull's eye!
I have no idea what you are talking about.
Z: I believe you. I'm afraid you'll have to wait until I write this up.
J: Read Andrew Marvel "To a coy mistress". Hal Puthoff has the same problem. Time and ET waits for no mortal. Promises, promises ...
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick, which is the geometrodynamic tetrad field e = I + B.
Note also Rovelli's remark that you cannot do spinors without using tetrads. See Kiehn's latest on MACRO spinor solutions of EM field solitons (if I got that right?).
Z: Fine.
* J: Kiehn thinks his spinor solitons explain Ken Shoulders EVOs. Perhaps, but I think I explain them with dark energy cores holding in the electric charge shell. On the other hand if the Vacuum ODLRO local field were itself some kind of macro-spinor field that could be interesting although I am not here sure if that idea makes any sense.
Z: This is *all* up in the clouds. Do you think Rovelli's indistinguishable points on the bare 4D manifold is not "up in the clouds"?
J: No, what he said there I find very clear. I have hardly read the rest of his book as yet.
Z: The abstract vector space that is constructed at each point on the manifold for which the tetrad forms a set of basis vectors need not have anything to do with the tangent bundle. Using a tetrad to span a tangent manifold is just a particular concrete interpretation of the abstract mathematical concept. All in the realm of pure mathematics, however.
J: So what? I don't see you saying anything important here.
Z: You can also choose a coordinate basis. That is not automatic either.
J:
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
Z: Yes, fine. I can see you've been studying this stuff.
J: Beginning to. There are some ambiguities in getting everything dimensionally consistent with factors of Lp. Mathematicans doing physics ignore all that setting everything = 1 and I think they make mistakes as a result e.g. mixed dimensions of the same components of the (LC) connection field for example. Some ~ r others ~ 1/r for SSS solution in some books. First rule in Physics 101 is that any equation should be consistent in units and physical dimensions.
Z: I think you may be right that at some point in the development the units should be put back in and careful attention should be paid to them.
J: I know I am right about that. Basic physics is being ignored by these mathematicians in physicist's clothing.
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
Z: If you construct such a tetrad field, yes it can be interpreted that way.
J: It's very important - that's Hagen Kleinert's key idea. Tensors were invented for elasticity theory in the 19th Century.
Z: I'm simply pointing out that this is a particular interpretation of the abstract notion of a tetrad.
J: So? What then? Right but trite unless you say something surprising beyond that.
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
Z: In the long-wave approximation this looks to me like a theory of continuous media in 4D.
J: That's Kleinert's idea. I have simply plugged into that with
Bu^a = Bu&^aargVacuumODLRO
Bu^a is a pure number. Therefore Bu is a length in that convention since &^a is 1/length
Z: OK.
J: Bu = Bu^adxa
dxa = (Mink)abdx^b
Bu = Bu&^aargVacuumODLROdxa
&^aargVacuumODLROdxa = 1
Z: OK.
J: What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro-quantum theory. I get diff(4) invariance + background-independence non-perturbatively trivially!
J: Hawking made this error at GR 17. Susskind makes it also. So does Lubos. Of course, I could be wrong, but we shall see.
Z: If you're right they are all barking up the wrong tree.
J: Yes, All The Kings Horses and All The King's Men - even The Astronomer Royal!
Z: I'm inclined to agree.
J: Micro-QM is linear, nonlocal, unitary with signal locality. Macro- QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
Z; I think it's an interesting and very promising approach.
J: BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
Z: YES.
Z: So does Penrose in "Road to Reality".
J: I think I gave the real answer as to why this is really a pseudo-problem:
BTW from my "Rovelli Notes": The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation.
The error you make Paul is to over-extend flat spacetime ideas to where they do not work.
Z: And from my POV you may simply be fetishizing curved spacetime, which may turn out to be simply a *geometric model* for the correct fundamental theory. That was Feynman's view.
J: Feynman's ideas here were not well developed. He was thinking only flat space-time background then as I recall. It was 25 years ago.
Z: In the discussion on "no curved spacetime" on Baez's web site, for example, you will see that even Steve Carlip admits that there is at present no local empirical basis for deciding between a flat-background model and a curved-spacetime model for
Einstein GR.
J: Of course most of the data are still weak field where the flat background works OK pragmatically.
Z: So it could be that a local flat-background model could exhaust the confirmed (and confirmable) empirical content of GR. The reality here is that we really don't know at this point how this will eventually shake down.
J: Conservation of total energy is simply a piece of T4 symmetry, i.e. time displacement invariance. It is certainly FALSE for the gravity vacuum.
Z: Depends on the theory. This is certainly the case in Einstein's theory. Inside Einstein GR, gravitational field energy isn't even *defined*.
J: GR is the only GOOD theory we have. There is no other. It works and so far has not been falsified. The whole attempt is wrong and that includes what Alex has proposed IMHO. Local conservation? Yes! Global conservation in general? No!
Z: I think the decomposition we are talking about is local, i.e., point by point.
J: What's your point? (Pun intended)
Z: As Einstein himself once said, "all physics is local". That's how he preserved his equivalence hypothesis.
J: See what I said above.
Z: Then in Einstein's theory, where physically does the energy carried away by gravitational waves go?
J: When there is the flat background in weak field there is no problem. Since "total energy" is meaningless in a curved spacetime, it need not go anywhere!
Z: Well, that could be viewed as a problem with the geometric model for GR. Einstein certainly regarded this as a serious problem in 1918, since he wrote several papers about it.
J: Simply a failure of nerve on his part perhaps? Not enough faith in his own equations? It happens frequently.
You know mathematically all they have is
Tuv^;v(Matter) = 0 locally
Then they make the split
Tuv^;v(Matter) = Tuv(Matter)^,v + parts that depend on products of the (LC) connection with Tuv(Matter)
They identify the sum of these products with tuv(Matter-Gravity)^,v.
LC is LC(Gravity) therefore LC(Gravity)Tuv(Matter) is dependent on both Matter & gravity.
Also note that Tuv(Matter) = &Action(Matter)/&guv
Where & is a functional derivative.
So what would tuv(gravity vacuum) even mean?
Does it mean
&Action(gravity)/&matter fields ?
Clearly not.
It must mean
&Action(Gravity)/&guv(Gravity)?
I suspect that is ZERO?
Back to original thread:
Where tuv(Matter-Gravity)^,v = 0 in an LIF since (LC) = 0 in an LIF by EEP.
Now we have something like the divergence theorem where
|||Div.Ad^3x = ||A.nd^2x
tuv(Matter-Gravity)^v is like DivA
So one can get an expression for tuv(Matter-Gravity). Does Pauli do this explicitly BTW? What's the equation number.
Z: You seem to be holding up the curved-manifold model as the measure of all things.
J: If it ain't broke don't fix it.
Z: I am saying it can itself be critically evaluated against other standards.
J: Show me. Hand waving not allowed.
Z: "No critical action without critical reaction". A metatheoretic "general relativity principle".:-)
J: Talk is cheap. Let's see the math.
"Total energy" conservation is an artifact of T4 symmetry. Gravity is the breaking of T4 symmetry. Without the symmetry there is no conservation law, e.g. Noether's theorem. Read Wigner.
Z: But your own tetrad/gauge field model shows how the effects of B and I can be separated.
J: So what? What's the connection?
e(curved) = I(flat) + B(curved)
Do a GCT X
e' = Xe
g(curved) = [I(flat) + B(curved)](flat)[I(flat) + B(curved)]
g'(curved) = X(I + B)(flat)X(I + B)
The globally flat case is B = 0 where
g'(curved) = XI(flat)XI
So what? What then? What's your next step?
recall e is a map from LIF to LNIF & back at SAME P (a "coincidence")
recall X is a map from LNIF to LNIF' & back again at same P
Note different manifold points A =/= B FORMALLY are same PHYSICAL P when
B = active Diff(4)A
So what?
Locally there is no problem of course.
Z: Yes there is -- Einstein's field stress-energy is not general covariant.
J: First write down the formula for that. Or if you cannot tell me which equation in Pauli shows the formula for that. I have Pauli with me here in NYC. First let's see what exactly you are talking about.
My B is also NOT a Diff(4) tensor Paul.
Only e = I + B is the Diff(4) tensor. So what?
Remember
e' = I + B'
But
e' = Xe = XI + XB
But
XI =/= I
Rather
XI = I' =/= I
Therefore
e' = I + XI + XB - I
Therefore
B' = XB + XI - I
Therefore,
XI - I is the INHOMOGENEOUS part of the Yang-Mills spin-1 FLAT vector potential in the tetradic substratum where
B(curved) ~ 4DGrad(Goldstone Phase of Vacuum ODLRO)
F = DB
D = d + B/\ = Cartan exterior gauge covariant derivative making p-forms into p+1 forms
where B is a 1-form and *B is a Hodge-dual 3-form relative to Minkowski metric that is the exact metric in the tetradic substratum.
Note that Stokes theorem is
|B = ||dB
| is over the closed loop boundary c of surface s
|B =/= 0 even though B ~ grad(Goldstone Phase) when the Higgs |Vacuum ODLRO| -> 0 at a Goldstone PHASE SINGULARITY making the effective manifold of the vacuum condensate MULTIPLY-CONNECTED like the normal fluid vortex cores in superfluid He4. This causes an ANHOLONOMY (mixed partial derivatives of the Goldstone phase do not commute). What is happening is that the line integral |B is no longer a over the outer closed loop that is also a boundary because of the "hole" where |Vacuum ODLRO| -> 0. That is, like the TWO 2D wormhole mouths in an Einstein-Bridge connecting two 3D parallel universes, there are TWO separated closed loops that together form the boundary over which Stokes theorem applies. If we only measure the outer line integral we get "flux-without-flux". Similarly in the wormhole mouth, if we only are in one universe we see a net charge (flux) coming out of the wormhole mouth even though the total flux is zero out of both wormhole mouths because in Gauss's law divE = 0 in vacuum.
To repeat: This, in effect, gives a phantom "Flux without flux" through the surface s IF we ignore the inner line integral enclosing the return flux in the hole that is something like a phantom string if the "vorticity" core penetration length area is small compared to the area of s.
Furthermore, since the Vacuum ODLRO field is single-valued, the fluxes are quantized.
DF = 0 are the "Bianchi identities" in this Yang-Mills self-interacting field.
D*F = *J is the source equation.
The topology here is analogous to a wormhole where the two closed surfaces are like the wormhole mouths.
The stress-energy current density is shared between the gravity and matter fields in
Tuv(Matter)^,v + tuv(Matter-Gravity)^,v = 0
in 1916 GR.
Z: Right.
J: So show me the explicit formula for tuv(Matter-Gravity) - cite equation in Pauli OK.
Note that here tuv(Gravity)^;v = 0 separately, therefore the sharing is not as direct as it could be when the (LC) Bianchi identities are violated by torsion and non-metricity.
What we really want is
tuv(Gravity)^;v + tuv(Exotic Vacuum)^;v + Tuv(Matter)^;v = 0
with none of the terms on LHS separately zero, but all sharing the currents!
1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.
You can get a global conservation approximately only with asymptotic flat space-times.
Z: Yes, and that's the best that can be done in Einstein's theory. So this problem was never actually solved by Einstein, even while he himself recognized it as a serious problem.
J: There is nothing to solve because of Noether's theorem. It's a false problem. Total global energy conservation breaks down when T0 symmetry breaks down in the Vacuum ODLRO and in the local gauging of T4 to Diff(4). Local conservation of stress-energy current densities still holds. What is true locally need not be true globally.
There is a theorem that U(1) gauge invariance demands that the photon have zero rest mass. U(1) is spontaneously broken in the superconducting ODLRO ground state and the photon inside that macro-quantum ground state has a rest mass
m = h/c(penetration depth of magnetic field)
Electric charge however is still conserved. The EM potential Au is the compensating field from locally gauging global U(1) on the electron field down to local U(1).
This is analogous to locally gauging global T4 down to local Diff(4) GCTs X with tetrad warp field Bu^a. Note that the tangent fiber index a is like the internal index of a self-interacting non-Abelian Yang-Mills spin-1 Poincare group first rank tensor (4-vector) field. The "internal" fiber group is so(1,3) in this Yang-Mills setting. The Lie algebra of so(1,3) is like TWO SU(2) groups one for the 3 space-space rotations and one for the 3 boost space-time rotations all at LOCAL FIXED P.
Bu^a has a coherent signal c-number ODLRO part and some random quantum noise because the Higgs vacuum is a macro-quantum squeezed Glauber state (like in quantum nonlinear optics). We can squeeze the orthogonal Higgs amplitude & Goldstone phase quadratures in the local phase space fiber (N, theta) at P.
Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.
Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then
|Post-Inflation Higgs Ocean>
= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>
a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).
|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.
The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?
For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries 3gij is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super- geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
Z: I would have to think about this.
J: Shelly Goldstein has shown this in detail.
Z: OK.
J: All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Z: Yilmaz has worked out the detailed math for his particular implementation of this idea. For a scalar auxiliary field you get an exponential solution for the SSS problem, which agrees very closely with the Schwarzschild metric. It's all in his papers.
J: Yilmaz's theory is complete nonsense IMHO. Not even wrong. It solves nothing. It explains nothing. It leads nowhere. It is obscure.
Z: I'm simply pointing out that by definition a gravitational vacuum source field doesn't go away even when all gravitating matter is removed.
J: Right but trite. I said that long ago in both my books from 2002 on Amazon.com. It's obvious. What is not obvious is how to apply that to the observations and I have done that too.
Z: Of course, a zero point field that is always present in the vacuum falls in a grey zone.
J: Too vague. Examples of that are the galactic halo gravity lenses & flat stellar rotation curves, the Pioneer anomalies, the voids, and the interior of electrons and EVOs. Electrons look like points because of a huge space warp at scale of 1 fermi. Lubos Motl is wrong that GR is not important on scale of 1 fermi. Lepto-quarks are micro geons like Kerr-Newman vacuum solutions with effective G* from dark energy /\zpf cores ~ 10^40G (see also A. Burinski). They also mimic strings because they obey
J(Spin) ~ Regge Slope (Energy)^2
as I showed in 1973 which caused Abdus Salam to invite me to ICTP in Trieste. Ask Jagdish Mehra. He was there and knows what happened.
http://qedcorp.com/APS/ice9.wav
Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
Z:Right.
J: You seem to contradict yourself.
Z: Nope.
J: In any case what you wrote above is so vague I do not know what you were trying to say.
Z: A vacuum source field means that R_uv =/= 0 in the vacuum, since this source field itself produces curvature. It also carries a "baseline" energy-momentum density.
J: Right but trite. In fact most regions of spacetime have /\zpf ~ 0 at most scales. This puts the base line at ~ ZERO!
Z: Thus it is natural to include it in the field Lagrangian, in which case it will show up in the field equations derived from this Lagrangian. Why is that "vague"?
J: Because you have not written a formula! Also you did not say anything like that at all to begin with. The Einstein-Hilbert action density with /\ is written down routinely as R + /\ (both have dim 1/Area - multiply by string tension c^4/8piG
Z: If you want to see a specific implementation of this idea, with detailed math, look at Yilmaz's papers.
J: Hogwash. I don't need no Yilmaz for that. Also he does not have the correct formulas. He does not have /\guv terms at all. Yilmaz's theory is a dead horse fly in your soup.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro- quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super- solid” or “world crystal”.
Z: It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
J: It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro- scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
Z: But we are not fish swimming in Maxwell's *classical mechanical* ether. Hence "departed".
J: This is where Rovelli's philofawzy is good. More on that later.
Z: The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
J: This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem!
Z: OK. If it's really not a problem, then it's not a problem.
J: If you read PW Anderson you will see why. Actually I have explained it many times. It's the released binding energy when the ionized virtual e+-e- plasma of the false vacuum FUSES in the inflation to the vacuum ODLRO condensate of bound virtual positronium! The released energy heats up the real quark-gluon plasma post-inflation.
Z: OK.
J: The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
Z: Yes, I know there is a lot of literature on this. I'll try and get hold of Anderson's "Career". And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
J: That's Puthoff's dead end. I will not go there.
Z: Just a question.
J: "The Question is: What is The Question?" Not all questions need to be answered. Some questions are not worth answering because the question is not interesting. Theoretical physics is the art of asking good questions.
Z: Wouldn't it be reasonable to expect that the properties of your all-pervading positronium BEC would determine at least some optical characteristics of the vacuum?
J: Indeed it does. It makes guv!
Z: OK. What about vacuum light propagation speed?
J: That's like asking how to calculate Young's modulus in a crystal. Not interesting.
Z: Obviously gravitation has an effect on light propagation, so your BEC field must have some connection to the observed speed of propagation of light.
J: I get guv that's enough. Light is ds^2 = 0. I follow Einstein there.
Z: But you can't deny that if your vacuum BEC exists, then light has to travel through it to get from A to B.
J: Yes, but QED shows direct effects are MINISCULE!
Z: OK -- but that's not the same as "zero".
J: Quibble. Atomic BECs slow down speed of light, but they are real atoms on mass shell not virtual quanta inside the vacuum.
Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
Z:Hal's theory is a toy model that was designed to be used as a heuristic tool for "engineering".
J: Hal's toy is badly broken. It has not done anything important there at all. Where are the engineering plans for saucers that fly? They don't exist - I mean not based on PV.
Z: It's not an exact quantum theory of the physical vacuum, and it doesn't claim to be.
J: The truth is that PV has failed to deliver on any of its promises in 20 years! Time is up for Hal. The Devil will have his due! :-)
bcc
Previews of Coming Attractions
1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.
Loop quantum gravity and superstrings? Who ordered them? They are both not even wrong.
Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.
Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then
|Post-Inflation Higgs Ocean>
= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>
a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).
|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.
The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?
On Jun 12, 2005, at 2:55 PM, iksnileiz@earthlink.net wrote:
I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
J: Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp Grad(Vacuum ODLRO)
4D Grad in a indices.
for the 4D Diff(4) macro-quantum supersolid world crystal is analogous to
v = (h/m)Grad[arg(Ground state ODLRO) for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note the elastic linear B term and the plastic nonlinear B^2 term.
Also, B while is not a spin-2 Diff(4) first rank tensor field all by itself, it is a Minkowski spacetime spin-1 Yang-Mills vector field.
Z: No surprise, since he is working with a different model.
Personally, I think you are way ahead of him.
J: I do explain many puzzling anomalies now observed!
J: Lubos is probably correct about the lack of contact of loop quantum gravity with observation and that it cannot even reproduce GR. Baez admitted that at GR 17. Of course string theory has its weaknesses too, but may be closer to observation? We also have to look at Wilczek's objections to some of Penrose's statements.
Z: Also, as I've mentioned, spacetime coordinate transformations, as *mathematically* defined, do not change any observer's world line.
J: That's what I call a kind of gauge freedom.
Z: You can call it that, and I appreciate your analogy, but I think the problem goes much deeper.
J: Too vague. Show how.
J: That is, all GCTs that do not change the state of motion of a detector are physically equivalent. An example of a physical GCT is starting in the rest LIF of a detector in space and then firing a rocket engine attached to the detector. The transformation, in that case, tetrad eu^a(P), that describes the relation between the momentarily coincident LIF with indices a & LNIF with indices u at same P. But you see here a complete local equivalence of the inertial force to the gravity since the physical difference is Bu^a in
eu^a(P) = Iu^a + Bu^a(P)
i.e. Bu^a(P) encodes the information of switching on the rocket engine!
You cannot locally distinguish inertial force from gravity force!
Z: But actually you can, as shown by Ohanian & Ruffini.
J: No, you still don't get it! You keep getting hung up on that. You do not understand what the word "locally" means. It means DO NOT MEASURE GEODESIC DEVIATION. Indeed, geodesic deviation is irrelevant to gravity force. The measurement procedures are orthogonal.
Obviously you can measure the local tidal curvature tensor at P in either an LIF or a LNIF makes no difference.
EEP means, YOU DO NOT MEASURE THE GEODESIC DEVIATION CURVATURE AT P because even if you do, then you STILL cannot tell the difference between an inertial force and a gravity force! Suppose the curvature is not zero so what? Think of y = y(x) and dy/dx. Measure y at xo. That does not tell you anything about dy/dx at xo if you have no prior knowledge of y(x). Indeed IN ALL CASES GRAVITY FORCE IS ALWAYS 100% INERTIAL FORCE. GRAVITY FORCE IS 100% INERTIAL FORCE in EVERY CASE IMAGINABLE.
Here inertial force is the NON-GRAVITY REACTION FORCE needed to PUSH the test particle OFF a timelike geodesic (relative to LC connection - I only do 1916 GR here).
The measurement of tidal curvature geodesic deviation is most cleanly done in the LIF where all gravity forces are strictly ZERO and special relativity applies locally to a good approximation.
Consider the SSS metric in only the radial direction to keep it simple
ds^2 = (1 - 2rs/r)(cdt)^2 - (1 - 2rs/r)^-1dr^2
This metric is only good for those HOVERING LNIFs at FIXED r > rs. Some NON-GRAVITY FORCE is pushing those HOVERING LNIFS off timelike geodesics. For the LIF observer the effective LOCAL metric is always to lowest order approximation
ds^2 = (cdt')^2 - dr'^2
even though geodesic deviation for the LIF observer is not zero!
The key is
(1/2)c^2Gradgoo = (1/2)c^2Grad(1 - 2rs/r) = c^2rs/r^2 = GM/r^2
= APPLIED UNIVERSAL NON-GRAVITY INERTIAL FORCE PER UNIT TEST MASS POINTING OUTWARD NEEDED TO KEEP THE HOVERING LNIF DETECTOR AT FIXED r.
IN FACT GRAVITY FORCE IS ELIMINATED 100%. What we call "gravity force" is 100% INERTIAL FORCE logically independent of curvature.
Of course in flat space-time you do not need any non-gravity force at all to keep a test particle "still" relative to a marker (neglecting their weak gravity of course).
Therefore, Paul you have been working on a non-problem! The gravity energy is also a non-problem, but much more subtle.
Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object".
Z: Spacetime "events" are addressed by coordinates,
This is wrong.
Z: Wrong?
J: Yes, wrong.
Z: Obviously "events" occur at definite locations on the spacetime manifold, and these 4D locations (points on the spacetime manifold) are assigned unique addresses by spacetime coordinate systems.
J: Not even wrong until you give an operational definition for "definite locations on a spacetime manifold". Rovelli is good on this issue.
Z: Mathematically, at least, changing CS *addresses* has to be sharply distinguished from changing *locations*.
J: Prove that with a mathematical example. Your words are too vague.
Rovelli is correct on that part. Events are coincidences like the collision of two point particles (toy model).
Z: Yes, but these coincidences occur at *definite locations in spacetime*
J: Wrong. Read Rovelli again on this. There is no such thing as
*definite locations in spacetime*
Define what you mean. Do you mean a collision of two point particles? If so, see Rovelli's discussion of the "Einstein hole problem" with the nice pictures.
that are merely assigned addresses by
spacetime coordinate systems.
Z: If Rovelli thinks that there is no mathematical distinction between an active Diff(4) rearrangement of manifold points (an actual deformation of the manifold) on the one hand, and a mere reshuffling of CS addresses, on the other, then
he is quite mistaken IMHO.
J: I do not understand what you just wrote. Your words are not even wrong. Give a mathematical example of what you mean here. If you cannot do that you have not really said anything worth saying on the issue.
You seem to think that the Diff (4) group creates physical deformations. That is not true at all. Only stress-energy density currents and self-interactions of the geometrodynamic field create physical deformations of the manifold. That's why we have Diff(4) covariance in the first place! That's why in
Guv(Gravity) + /\(ZPF Vacuum Energy)guv(Gravity) + (8piG/c^4)Tuv(Matter) = 0
We only have Diff(4) COVARIANT TENSORS!
Diff(4) is the LOCAL SYMMETRY GROUP it DON'T MAKE ANY PHYSICAL or "actual deformations". You have the wrong idea entirely!
Diff(4) is the LOCAL GAUGING of T4 with Bu^a as the induced compensating gauge potential. Also, you have Vacuum ODLRO in the inflation phase transition from the unstable rest-massless gravity-free conformal false vacuum to the stable curved vacuum with rest masses from Higgs ODLRO coherence and gravity and even dark energy/matter in which T4 is SPONTANEOUSLY BROKEN to allow CURVATURE! You do not get Gennady Shipov's torsion until you LOCALLY GAUGE so(1,3) in addition to T4. If IN ADDITION you spontaneously break so(1,3) in the vacuum then you will also get preferred velocity effects. Whether that happens or not, apart from Hubble flow (maximal isotropy of CMB) is purely empirical.
Z: but are not defined by them. So it should be obvious that such "events", just like manifold points, are absolutes with respect to such transformations.
J: Too vague. Give a precise mathematical example.
You have the wrong idea here. I mean you have garbled things above.
Z: No, I just disagree with your your version of Rovelli.
J: Well you are so vague that your words have no meaning to me.
Physical events are invariants to be sure, but "manifold points" are not.
Z: Manifolds are not *deformed* by mere coordinate changes.
J: Right, but neither are they deformed in active diffeomorphisms! That's the point!
Z: So as far as I can see, the effect of GCTs on manifold points and events is similar. Addresses are simply re-shuffled.
J: Yes, but that is the case for both active and passive Diff(4). The mathematically distinct manifold points A & B in Rovelli's nice discussion are not physically distinguishable, i.e. the collision of particles 1 & 2 is PUSHED FORWARD (or is it backward?) from A to B so that NOTHING MEASURABLE has changed in the active Diff(4) from A to B. P includes both A & B in the same equivalence class!
Now your way of thinking will work to some extent in special relativity quantum field theory and in classical mechanics and classical electromagnetism, but it does not work in GR and it took the great Einstein what 3 years? to understand this and today most physicists still do not really understand it!
See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~| A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
Z: In my POV, *none* of the mathematically defined coordinate transformations on the spacetime manifold has any physical meaning at all until such a meaning is attached to them, or to some subset of them.
Z: Chasing your own tail. Circular. Meaningless until you show an independent procedure.
Z: It's pretty obvious if you think about it.
J: Since I do not understand your English I do not know. If you cannot make your idea more mathematical or more specific in terms of gedankenexperiments you are not communicating to my mind at least.
Z: Mathematical coordinate changes in themselves do not change any observer's world line. But in order to change an observer's frame of reference, you must at the same time also change that observer's world line.
J: Yes, that I understand. I understand that if a LIF observer fires a rocket engine in space then she is transformed to a LNIF observer and that instant coincident local transformation (approximately to be sure) is not a Diff(4) thing at all but is a tetrad thing. But then if she changed the thrust it is a Diff(4) thing moving from one non-geodesic to another "instantly" at a "crossing point". But even then, the Diff(4) is a MERE DESCRIPTION of her PHYSICAL ACTION, e.g. throwing the switch or turning the dial on the thrust control panel.
Z: So there is a basic *contradiction* in the orthodox treatment that needs to be resolved. I'm resolving it.
J: No you have not. I just resolved it for you in my above remark - bull's eye!
I have no idea what you are talking about.
Z: I believe you. I'm afraid you'll have to wait until I write this up.
J: Read Andrew Marvel "To a coy mistress". Hal Puthoff has the same problem. Time and ET waits for no mortal. Promises, promises ...
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick, which is the geometrodynamic tetrad field e = I + B.
Note also Rovelli's remark that you cannot do spinors without using tetrads. See Kiehn's latest on MACRO spinor solutions of EM field solitons (if I got that right?).
Z: Fine.
* J: Kiehn thinks his spinor solitons explain Ken Shoulders EVOs. Perhaps, but I think I explain them with dark energy cores holding in the electric charge shell. On the other hand if the Vacuum ODLRO local field were itself some kind of macro-spinor field that could be interesting although I am not here sure if that idea makes any sense.
Z: This is *all* up in the clouds. Do you think Rovelli's indistinguishable points on the bare 4D manifold is not "up in the clouds"?
J: No, what he said there I find very clear. I have hardly read the rest of his book as yet.
Z: The abstract vector space that is constructed at each point on the manifold for which the tetrad forms a set of basis vectors need not have anything to do with the tangent bundle. Using a tetrad to span a tangent manifold is just a particular concrete interpretation of the abstract mathematical concept. All in the realm of pure mathematics, however.
J: So what? I don't see you saying anything important here.
Z: You can also choose a coordinate basis. That is not automatic either.
J:
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
Z: Yes, fine. I can see you've been studying this stuff.
J: Beginning to. There are some ambiguities in getting everything dimensionally consistent with factors of Lp. Mathematicans doing physics ignore all that setting everything = 1 and I think they make mistakes as a result e.g. mixed dimensions of the same components of the (LC) connection field for example. Some ~ r others ~ 1/r for SSS solution in some books. First rule in Physics 101 is that any equation should be consistent in units and physical dimensions.
Z: I think you may be right that at some point in the development the units should be put back in and careful attention should be paid to them.
J: I know I am right about that. Basic physics is being ignored by these mathematicians in physicist's clothing.
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
Z: If you construct such a tetrad field, yes it can be interpreted that way.
J: It's very important - that's Hagen Kleinert's key idea. Tensors were invented for elasticity theory in the 19th Century.
Z: I'm simply pointing out that this is a particular interpretation of the abstract notion of a tetrad.
J: So? What then? Right but trite unless you say something surprising beyond that.
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
Z: In the long-wave approximation this looks to me like a theory of continuous media in 4D.
J: That's Kleinert's idea. I have simply plugged into that with
Bu^a = Bu&^aargVacuumODLRO
Bu^a is a pure number. Therefore Bu is a length in that convention since &^a is 1/length
Z: OK.
J: Bu = Bu^adxa
dxa = (Mink)abdx^b
Bu = Bu&^aargVacuumODLROdxa
&^aargVacuumODLROdxa = 1
Z: OK.
J: What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro-quantum theory. I get diff(4) invariance + background-independence non-perturbatively trivially!
J: Hawking made this error at GR 17. Susskind makes it also. So does Lubos. Of course, I could be wrong, but we shall see.
Z: If you're right they are all barking up the wrong tree.
J: Yes, All The Kings Horses and All The King's Men - even The Astronomer Royal!
Z: I'm inclined to agree.
J: Micro-QM is linear, nonlocal, unitary with signal locality. Macro- QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
Z; I think it's an interesting and very promising approach.
J: BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
Z: YES.
Z: So does Penrose in "Road to Reality".
J: I think I gave the real answer as to why this is really a pseudo-problem:
BTW from my "Rovelli Notes": The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation.
The error you make Paul is to over-extend flat spacetime ideas to where they do not work.
Z: And from my POV you may simply be fetishizing curved spacetime, which may turn out to be simply a *geometric model* for the correct fundamental theory. That was Feynman's view.
J: Feynman's ideas here were not well developed. He was thinking only flat space-time background then as I recall. It was 25 years ago.
Z: In the discussion on "no curved spacetime" on Baez's web site, for example, you will see that even Steve Carlip admits that there is at present no local empirical basis for deciding between a flat-background model and a curved-spacetime model for
Einstein GR.
J: Of course most of the data are still weak field where the flat background works OK pragmatically.
Z: So it could be that a local flat-background model could exhaust the confirmed (and confirmable) empirical content of GR. The reality here is that we really don't know at this point how this will eventually shake down.
J: Conservation of total energy is simply a piece of T4 symmetry, i.e. time displacement invariance. It is certainly FALSE for the gravity vacuum.
Z: Depends on the theory. This is certainly the case in Einstein's theory. Inside Einstein GR, gravitational field energy isn't even *defined*.
J: GR is the only GOOD theory we have. There is no other. It works and so far has not been falsified. The whole attempt is wrong and that includes what Alex has proposed IMHO. Local conservation? Yes! Global conservation in general? No!
Z: I think the decomposition we are talking about is local, i.e., point by point.
J: What's your point? (Pun intended)
Z: As Einstein himself once said, "all physics is local". That's how he preserved his equivalence hypothesis.
J: See what I said above.
Z: Then in Einstein's theory, where physically does the energy carried away by gravitational waves go?
J: When there is the flat background in weak field there is no problem. Since "total energy" is meaningless in a curved spacetime, it need not go anywhere!
Z: Well, that could be viewed as a problem with the geometric model for GR. Einstein certainly regarded this as a serious problem in 1918, since he wrote several papers about it.
J: Simply a failure of nerve on his part perhaps? Not enough faith in his own equations? It happens frequently.
You know mathematically all they have is
Tuv^;v(Matter) = 0 locally
Then they make the split
Tuv^;v(Matter) = Tuv(Matter)^,v + parts that depend on products of the (LC) connection with Tuv(Matter)
They identify the sum of these products with tuv(Matter-Gravity)^,v.
LC is LC(Gravity) therefore LC(Gravity)Tuv(Matter) is dependent on both Matter & gravity.
Also note that Tuv(Matter) = &Action(Matter)/&guv
Where & is a functional derivative.
So what would tuv(gravity vacuum) even mean?
Does it mean
&Action(gravity)/&matter fields ?
Clearly not.
It must mean
&Action(Gravity)/&guv(Gravity)?
I suspect that is ZERO?
Back to original thread:
Where tuv(Matter-Gravity)^,v = 0 in an LIF since (LC) = 0 in an LIF by EEP.
Now we have something like the divergence theorem where
|||Div.Ad^3x = ||A.nd^2x
tuv(Matter-Gravity)^v is like DivA
So one can get an expression for tuv(Matter-Gravity). Does Pauli do this explicitly BTW? What's the equation number.
Z: You seem to be holding up the curved-manifold model as the measure of all things.
J: If it ain't broke don't fix it.
Z: I am saying it can itself be critically evaluated against other standards.
J: Show me. Hand waving not allowed.
Z: "No critical action without critical reaction". A metatheoretic "general relativity principle".:-)
J: Talk is cheap. Let's see the math.
"Total energy" conservation is an artifact of T4 symmetry. Gravity is the breaking of T4 symmetry. Without the symmetry there is no conservation law, e.g. Noether's theorem. Read Wigner.
Z: But your own tetrad/gauge field model shows how the effects of B and I can be separated.
J: So what? What's the connection?
e(curved) = I(flat) + B(curved)
Do a GCT X
e' = Xe
g(curved) = [I(flat) + B(curved)](flat)[I(flat) + B(curved)]
g'(curved) = X(I + B)(flat)X(I + B)
The globally flat case is B = 0 where
g'(curved) = XI(flat)XI
So what? What then? What's your next step?
recall e is a map from LIF to LNIF & back at SAME P (a "coincidence")
recall X is a map from LNIF to LNIF' & back again at same P
Note different manifold points A =/= B FORMALLY are same PHYSICAL P when
B = active Diff(4)A
So what?
Locally there is no problem of course.
Z: Yes there is -- Einstein's field stress-energy is not general covariant.
J: First write down the formula for that. Or if you cannot tell me which equation in Pauli shows the formula for that. I have Pauli with me here in NYC. First let's see what exactly you are talking about.
My B is also NOT a Diff(4) tensor Paul.
Only e = I + B is the Diff(4) tensor. So what?
Remember
e' = I + B'
But
e' = Xe = XI + XB
But
XI =/= I
Rather
XI = I' =/= I
Therefore
e' = I + XI + XB - I
Therefore
B' = XB + XI - I
Therefore,
XI - I is the INHOMOGENEOUS part of the Yang-Mills spin-1 FLAT vector potential in the tetradic substratum where
B(curved) ~ 4DGrad(Goldstone Phase of Vacuum ODLRO)
F = DB
D = d + B/\ = Cartan exterior gauge covariant derivative making p-forms into p+1 forms
where B is a 1-form and *B is a Hodge-dual 3-form relative to Minkowski metric that is the exact metric in the tetradic substratum.
Note that Stokes theorem is
|B = ||dB
| is over the closed loop boundary c of surface s
|B =/= 0 even though B ~ grad(Goldstone Phase) when the Higgs |Vacuum ODLRO| -> 0 at a Goldstone PHASE SINGULARITY making the effective manifold of the vacuum condensate MULTIPLY-CONNECTED like the normal fluid vortex cores in superfluid He4. This causes an ANHOLONOMY (mixed partial derivatives of the Goldstone phase do not commute). What is happening is that the line integral |B is no longer a over the outer closed loop that is also a boundary because of the "hole" where |Vacuum ODLRO| -> 0. That is, like the TWO 2D wormhole mouths in an Einstein-Bridge connecting two 3D parallel universes, there are TWO separated closed loops that together form the boundary over which Stokes theorem applies. If we only measure the outer line integral we get "flux-without-flux". Similarly in the wormhole mouth, if we only are in one universe we see a net charge (flux) coming out of the wormhole mouth even though the total flux is zero out of both wormhole mouths because in Gauss's law divE = 0 in vacuum.
To repeat: This, in effect, gives a phantom "Flux without flux" through the surface s IF we ignore the inner line integral enclosing the return flux in the hole that is something like a phantom string if the "vorticity" core penetration length area is small compared to the area of s.
Furthermore, since the Vacuum ODLRO field is single-valued, the fluxes are quantized.
DF = 0 are the "Bianchi identities" in this Yang-Mills self-interacting field.
D*F = *J is the source equation.
The topology here is analogous to a wormhole where the two closed surfaces are like the wormhole mouths.
The stress-energy current density is shared between the gravity and matter fields in
Tuv(Matter)^,v + tuv(Matter-Gravity)^,v = 0
in 1916 GR.
Z: Right.
J: So show me the explicit formula for tuv(Matter-Gravity) - cite equation in Pauli OK.
Note that here tuv(Gravity)^;v = 0 separately, therefore the sharing is not as direct as it could be when the (LC) Bianchi identities are violated by torsion and non-metricity.
What we really want is
tuv(Gravity)^;v + tuv(Exotic Vacuum)^;v + Tuv(Matter)^;v = 0
with none of the terms on LHS separately zero, but all sharing the currents!
1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.
You can get a global conservation approximately only with asymptotic flat space-times.
Z: Yes, and that's the best that can be done in Einstein's theory. So this problem was never actually solved by Einstein, even while he himself recognized it as a serious problem.
J: There is nothing to solve because of Noether's theorem. It's a false problem. Total global energy conservation breaks down when T0 symmetry breaks down in the Vacuum ODLRO and in the local gauging of T4 to Diff(4). Local conservation of stress-energy current densities still holds. What is true locally need not be true globally.
There is a theorem that U(1) gauge invariance demands that the photon have zero rest mass. U(1) is spontaneously broken in the superconducting ODLRO ground state and the photon inside that macro-quantum ground state has a rest mass
m = h/c(penetration depth of magnetic field)
Electric charge however is still conserved. The EM potential Au is the compensating field from locally gauging global U(1) on the electron field down to local U(1).
This is analogous to locally gauging global T4 down to local Diff(4) GCTs X with tetrad warp field Bu^a. Note that the tangent fiber index a is like the internal index of a self-interacting non-Abelian Yang-Mills spin-1 Poincare group first rank tensor (4-vector) field. The "internal" fiber group is so(1,3) in this Yang-Mills setting. The Lie algebra of so(1,3) is like TWO SU(2) groups one for the 3 space-space rotations and one for the 3 boost space-time rotations all at LOCAL FIXED P.
Bu^a has a coherent signal c-number ODLRO part and some random quantum noise because the Higgs vacuum is a macro-quantum squeezed Glauber state (like in quantum nonlinear optics). We can squeeze the orthogonal Higgs amplitude & Goldstone phase quadratures in the local phase space fiber (N, theta) at P.
Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.
Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then
|Post-Inflation Higgs Ocean>
= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>
a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).
|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.
The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?
For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries 3gij is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super- geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
Z: I would have to think about this.
J: Shelly Goldstein has shown this in detail.
Z: OK.
J: All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Z: Yilmaz has worked out the detailed math for his particular implementation of this idea. For a scalar auxiliary field you get an exponential solution for the SSS problem, which agrees very closely with the Schwarzschild metric. It's all in his papers.
J: Yilmaz's theory is complete nonsense IMHO. Not even wrong. It solves nothing. It explains nothing. It leads nowhere. It is obscure.
Z: I'm simply pointing out that by definition a gravitational vacuum source field doesn't go away even when all gravitating matter is removed.
J: Right but trite. I said that long ago in both my books from 2002 on Amazon.com. It's obvious. What is not obvious is how to apply that to the observations and I have done that too.
Z: Of course, a zero point field that is always present in the vacuum falls in a grey zone.
J: Too vague. Examples of that are the galactic halo gravity lenses & flat stellar rotation curves, the Pioneer anomalies, the voids, and the interior of electrons and EVOs. Electrons look like points because of a huge space warp at scale of 1 fermi. Lubos Motl is wrong that GR is not important on scale of 1 fermi. Lepto-quarks are micro geons like Kerr-Newman vacuum solutions with effective G* from dark energy /\zpf cores ~ 10^40G (see also A. Burinski). They also mimic strings because they obey
J(Spin) ~ Regge Slope (Energy)^2
as I showed in 1973 which caused Abdus Salam to invite me to ICTP in Trieste. Ask Jagdish Mehra. He was there and knows what happened.
http://qedcorp.com/APS/ice9.wav
Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
Z:Right.
J: You seem to contradict yourself.
Z: Nope.
J: In any case what you wrote above is so vague I do not know what you were trying to say.
Z: A vacuum source field means that R_uv =/= 0 in the vacuum, since this source field itself produces curvature. It also carries a "baseline" energy-momentum density.
J: Right but trite. In fact most regions of spacetime have /\zpf ~ 0 at most scales. This puts the base line at ~ ZERO!
Z: Thus it is natural to include it in the field Lagrangian, in which case it will show up in the field equations derived from this Lagrangian. Why is that "vague"?
J: Because you have not written a formula! Also you did not say anything like that at all to begin with. The Einstein-Hilbert action density with /\ is written down routinely as R + /\ (both have dim 1/Area - multiply by string tension c^4/8piG
Z: If you want to see a specific implementation of this idea, with detailed math, look at Yilmaz's papers.
J: Hogwash. I don't need no Yilmaz for that. Also he does not have the correct formulas. He does not have /\guv terms at all. Yilmaz's theory is a dead horse fly in your soup.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro- quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super- solid” or “world crystal”.
Z: It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
J: It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro- scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
Z: But we are not fish swimming in Maxwell's *classical mechanical* ether. Hence "departed".
J: This is where Rovelli's philofawzy is good. More on that later.
Z: The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
J: This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem!
Z: OK. If it's really not a problem, then it's not a problem.
J: If you read PW Anderson you will see why. Actually I have explained it many times. It's the released binding energy when the ionized virtual e+-e- plasma of the false vacuum FUSES in the inflation to the vacuum ODLRO condensate of bound virtual positronium! The released energy heats up the real quark-gluon plasma post-inflation.
Z: OK.
J: The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
Z: Yes, I know there is a lot of literature on this. I'll try and get hold of Anderson's "Career". And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
J: That's Puthoff's dead end. I will not go there.
Z: Just a question.
J: "The Question is: What is The Question?" Not all questions need to be answered. Some questions are not worth answering because the question is not interesting. Theoretical physics is the art of asking good questions.
Z: Wouldn't it be reasonable to expect that the properties of your all-pervading positronium BEC would determine at least some optical characteristics of the vacuum?
J: Indeed it does. It makes guv!
Z: OK. What about vacuum light propagation speed?
J: That's like asking how to calculate Young's modulus in a crystal. Not interesting.
Z: Obviously gravitation has an effect on light propagation, so your BEC field must have some connection to the observed speed of propagation of light.
J: I get guv that's enough. Light is ds^2 = 0. I follow Einstein there.
Z: But you can't deny that if your vacuum BEC exists, then light has to travel through it to get from A to B.
J: Yes, but QED shows direct effects are MINISCULE!
Z: OK -- but that's not the same as "zero".
J: Quibble. Atomic BECs slow down speed of light, but they are real atoms on mass shell not virtual quanta inside the vacuum.
Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
Z:Hal's theory is a toy model that was designed to be used as a heuristic tool for "engineering".
J: Hal's toy is badly broken. It has not done anything important there at all. Where are the engineering plans for saucers that fly? They don't exist - I mean not based on PV.
Z: It's not an exact quantum theory of the physical vacuum, and it doesn't claim to be.
J: The truth is that PV has failed to deliver on any of its promises in 20 years! Time is up for Hal. The Devil will have his due! :-)
Loop Quantum Gravity? Failed?
On Jun 12, 2005, at 4:52 AM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
On Jun 11, 2005, at 4:58 PM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on "Quantum Gravity".
OK, that makes sense to me.
I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp(argVacuumODLRO)^,a for the 4D Diff(4) macro-quantum supersolid world crystal
analogous to
v = (h/m)GradargGroundstateODLRO for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note that elastic linear B term and the plastic nonlinear B^2 term.
Also, B while not a spin2 Diff(4) first rank tensor field all by itself, is a Minkowski spacetime spin 1 Yang-Mills vector field.
No surprise, since he is working with a different model.
Personally, I think you are way ahead of him.
Lubos is probably correct about the lack of contact of loop quantum gravity with observation and that it cannot even reproduce GR. Baez admitted that at GR 17. Of course string theory has its weaknesses too but may be closer to observation? We also have to look at Wilczek's objections to some of Penrose's statements.
Maybe Alex can explain to you why he and I propose to draw a fundamental distinction between raw mathematical spacetime CSs, on the one hand, and physical spacetime CSs ("moving CSs") that in GR represent observer reference frames, on the other.
Yes, he did, but I am not convinced that his idea is any better than mine, which is that a local frame (inertial or non-inertial) is an equivalence class of local coordinate charts at P that do not change the motion of the detector.
I think that's a different issue.
Maybe.
Also, as I've mentioned, spacetime coordinate transformations, as *mathematically* defined, do not change any observer's world line.
That's what I call a kind of gauge freedom. That is, all GCTs that do not change the state of motion of a detector are physically equivalent. An example of a physical GCT is starting in the rest LIF of a detector in space and then firing a rocket engine attached to the detector. The transformation, in that case, tetrad eu^a(P), that describes the relation between the momentarily coincident LIF with indices a & LNIF with indices u at same P. But you see here a complete local equivalence of the inertial force to the gravity since the physical difference is Bu^a in
eu^a(P) = Iu^a + Bu^a(P)
i.e. Bu^a(P) encodes the information of switching on the rocket engine!
You cannot locally distinguish inertial force from gravity force!
Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object".
Spacetime "events" are addressed by coordinates,
This is wrong. Rovelli is correct on that part. Events are coincidences like the collision of two point particles (toy model).
but are not defined by them. So it should be obvious
that such "events", just like manifold points, are absolutes with respect to such transformations.
You have the wrong idea here. I mean you have garbled things above. Physical events are invariants to be sure, but "manifold points" are not.
See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~| A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
In my POV, *none* of the mathematically defined coordinate transformations on the spacetime manifold has any physical meaning at all until such a meaning is attached to them, or to some subset of them.
Chasing your own tail. Circular. Meaningless until you show an independent procedure.
In my model, you define a *parallel set of GCTs* to which physical meaning is attached. This parallel set of GCTs is a *copy* of a subset of the mathematical GCTs (Einstein's "moving coordinates") which is given a physical interpretation in terms of a set of observer frames.
I do not understand your remark here. It's too vague. Define "copy", define "observer frame". Relate your key terms to the mathematical symbols of GR. Provide operational gedankenexperiments. I have no idea what you are talking about.
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick which is the geometrodynamic tetrad field e = I + B.
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved,
Yes, but you have to be careful about how the coordinate-basis tetrad is physically interpreted. There is more than one possible interpretation.
Rovelli et-al show a completely coordinate-free Cartan form tetrad e. In fact the tetrad e is a 1-form independent of coordinates. Torsion and curvature are 2-forms. No problem!
Of course -- in the abstract, the tetrad is mathematically defined in a a coordinate-free manner as a set of basis vectors spanning a vector space that is constructed at each point on the manifold.
Note also Rovelli's remark that you cannot do spinors without using tetrads. See Kiehn's latest on MACRO spinor solutions of EM field solitons (if I got that right?).
But then this tetrad field can be further *interpreted* in terms of the set of tangent manifolds (tangent bundle). This is not automatic.
Too vague. I don't know what you mean. "interpreted"? How? Give an example. Your head is too much in the clouds.
You can also choose a coordinate basis. That is not automatic either.
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
Yes, fine.
I can see you've been studying this stuff.
Beginning to. There are some ambiguities in getting everything dimensionally consistent with factors of Lp. Mathematicans doing physics ignore all that setting everything = 1 and I think they make mistakes as a result e.g. mixed dimensions of the same components of the (LC) connection field for example. Some ~ r others ~ 1/r for SSS solution in some books. First rule in Physics 101 is that any equation should be consistent in units and physical dimensions.
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
As I'm sure you know, the tetrad starts out simply as a coordinate- independent basis for a any 4D vector space defined at each point on the spacetime manifold.
Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
If you construct such a tetrad field, yes it can be interpreted that way.
It's very important - that's Hagen Kleinert's key idea. Tensors were invented for elasticity theory in 19th Century.
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
In the long-wave approximation this looks to me like a theory of continuous media in 4D.
That's Kleinert's idea. I have simply plugged into that with
Bu^a = Bu&^aargVacuumODLRO
Bu^a is a pure number. Therefore Bu is a length in that convention since &^a is 1/length
Bu = Bu^adxa
dxa = (Mink)abdx^b
Bu = Bu&^aargVacuumODLROdxa
&^aargVacuumODLROdxa = 1
but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do.
OK.
They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there.
Maybe not.
We will see as I read Rovelli's book.
OK.
What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro- quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Hawking made this error at GR 17. Susskind makes it also. So does Lubos. Of course, I could be wrong, but we shall see.
I'm inclined to agree.
Micro-QM is linear, nonlocal, unitary with signal locality. Macro- QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
I think it's an interesting and very promising approach.
BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
YES.
So does Penrose in "Road to Reality".
I think I gave the real answer as to why this is really a pseudo- problem:
BTW from my "Rovelli Notes"
The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation.
The error you make Paul is to over-extend flat spacetime ideas to where they do not work. Conservation of total energy is simply a piece of T4 symmetry, i.e. time displacement invariance. It is certainly FALSE for the gravity vacuum. The whole attempt is wrong and that includes what Alex has proposed IMHO. Local conservation? Yes! Global conservation in general? No!
Then in Einstein's theory, where physically does the energy carried away by gravitational waves go?
When there is the flat background in weak field there is no problem. Since "total energy" is meaningless in a curved spacetime, it need not go anywhere! "Total energy" conservation is an artifact of T4 symmetry. Gravity is the breaking of T4 symmetry. Without the symmetry there is no conservation law, e.g. Noether's theorem. Read Wigner.
Locally there is no problem of course. The stress-energy current density is shared between the gravity and matter fields in
Tuv(Matter)^,v + tuv(Matter-gravity)^,v = 0
in 1916 GR.
You can get a global conservation approximately only with asymptotic flat space-times.
How does it get there?
I agree that inside Einstein GR, strictly speaking, there is no such thing as gravitational vacuum stress-energy.
For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries 3gij is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super- geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
I would have to think about this.
Shelly Goldstein has shown this in detail.
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Or, more generally, you can introduce *some* kind of source field for vacuum G_uv.
This provides an objective localizable physical "container" for the energy lost through gravitational radiation -- which is not the situation in orthodox GR.
No, you are confusing apples (zero point dark energy) and oranges (classical gravity waves).
No, not at all. I'm just saying that adding a *gravitational* vacuum source field for G_uv is *one* way out of this, because then you have somewhere for the gravitationally radiated energy to go that can be defined objectively,
i.e., in an observer-coordinate-free (frame-independent) manner.
This is not even wrong. You have no math to justify this confused idea.
Of course, a gravitating ZPF might also be a kind of "vacuum source field", but not a *gravitational* vacuum source field , which latter is still present even in the absence of all matter, including EM fields.
Meaningless if you cannot show a math model illustration.
Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
Right.
You seem to contradict yourself. In any case what you wrote above is so vague I do not know what you were trying to say.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro-quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro-scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
But we are not fish swimming in Maxwell's *classical mechanical* ether.
Hence "departed".
This is where Rovelli's philofawzy is good. More on that later.
The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem!
OK. If it's really not a problem, then it's not a problem.
If you read PW Anderson you will see why. Actually I have explained it many times. It's the released binding energy when the ionized virtual e+-e- plasma of the false vacuum FUSES in the inflation to the vacuum ODLRO condensate of bound virtual positronium! The released energy heats up the real quark-gluon plasma post-inflation.
The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
Yes, I know there is a lot of literature on this. I'll try and get hold of Anderson's "Career".
And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
That's Puthoff's dead end. I will not go there.
Just a question.
Wouldn't it be reasonable to expect that the properties of your all-pervading positronium BEC would determine at least some optical characteristics of the vacuum?
Indeed it does. It makes guv!
I get guv that's enough. Light is ds^2 = 0. I follow Einstein there.
But you can't deny that if your vacuum BEC exists, then light has to travel through it to get from A to B.
Yes, but QED shows direct effects are MINISCULE!
Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
Hal's theory is a toy model that was designed to be used as a heuristic tool for "engineering".
It has not done anything important there at all. Where are the engineering plans for saucers that fly? They don't exist - I mean not based on PV.
It's not an exact quantum theory of the physical vacuum, and it doesn't claim to be.
The truth is that PV has failed to deliver on any of its promises in 20 years! Time is up for Hal. The Devil will have his due! :-)
On Jun 12, 2005, at 4:52 AM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
On Jun 11, 2005, at 4:58 PM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on "Quantum Gravity".
OK, that makes sense to me.
I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp(argVacuumODLRO)^,a for the 4D Diff(4) macro-quantum supersolid world crystal
analogous to
v = (h/m)GradargGroundstateODLRO for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note that elastic linear B term and the plastic nonlinear B^2 term.
Also, B while not a spin2 Diff(4) first rank tensor field all by itself, is a Minkowski spacetime spin 1 Yang-Mills vector field.
No surprise, since he is working with a different model.
Personally, I think you are way ahead of him.
Lubos is probably correct about the lack of contact of loop quantum gravity with observation and that it cannot even reproduce GR. Baez admitted that at GR 17. Of course string theory has its weaknesses too but may be closer to observation? We also have to look at Wilczek's objections to some of Penrose's statements.
Maybe Alex can explain to you why he and I propose to draw a fundamental distinction between raw mathematical spacetime CSs, on the one hand, and physical spacetime CSs ("moving CSs") that in GR represent observer reference frames, on the other.
Yes, he did, but I am not convinced that his idea is any better than mine, which is that a local frame (inertial or non-inertial) is an equivalence class of local coordinate charts at P that do not change the motion of the detector.
I think that's a different issue.
Maybe.
Also, as I've mentioned, spacetime coordinate transformations, as *mathematically* defined, do not change any observer's world line.
That's what I call a kind of gauge freedom. That is, all GCTs that do not change the state of motion of a detector are physically equivalent. An example of a physical GCT is starting in the rest LIF of a detector in space and then firing a rocket engine attached to the detector. The transformation, in that case, tetrad eu^a(P), that describes the relation between the momentarily coincident LIF with indices a & LNIF with indices u at same P. But you see here a complete local equivalence of the inertial force to the gravity since the physical difference is Bu^a in
eu^a(P) = Iu^a + Bu^a(P)
i.e. Bu^a(P) encodes the information of switching on the rocket engine!
You cannot locally distinguish inertial force from gravity force!
Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object".
Spacetime "events" are addressed by coordinates,
This is wrong. Rovelli is correct on that part. Events are coincidences like the collision of two point particles (toy model).
but are not defined by them. So it should be obvious
that such "events", just like manifold points, are absolutes with respect to such transformations.
You have the wrong idea here. I mean you have garbled things above. Physical events are invariants to be sure, but "manifold points" are not.
See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~| A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
In my POV, *none* of the mathematically defined coordinate transformations on the spacetime manifold has any physical meaning at all until such a meaning is attached to them, or to some subset of them.
Chasing your own tail. Circular. Meaningless until you show an independent procedure.
In my model, you define a *parallel set of GCTs* to which physical meaning is attached. This parallel set of GCTs is a *copy* of a subset of the mathematical GCTs (Einstein's "moving coordinates") which is given a physical interpretation in terms of a set of observer frames.
I do not understand your remark here. It's too vague. Define "copy", define "observer frame". Relate your key terms to the mathematical symbols of GR. Provide operational gedankenexperiments. I have no idea what you are talking about.
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick which is the geometrodynamic tetrad field e = I + B.
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved,
Yes, but you have to be careful about how the coordinate-basis tetrad is physically interpreted. There is more than one possible interpretation.
Rovelli et-al show a completely coordinate-free Cartan form tetrad e. In fact the tetrad e is a 1-form independent of coordinates. Torsion and curvature are 2-forms. No problem!
Of course -- in the abstract, the tetrad is mathematically defined in a a coordinate-free manner as a set of basis vectors spanning a vector space that is constructed at each point on the manifold.
Note also Rovelli's remark that you cannot do spinors without using tetrads. See Kiehn's latest on MACRO spinor solutions of EM field solitons (if I got that right?).
But then this tetrad field can be further *interpreted* in terms of the set of tangent manifolds (tangent bundle). This is not automatic.
Too vague. I don't know what you mean. "interpreted"? How? Give an example. Your head is too much in the clouds.
You can also choose a coordinate basis. That is not automatic either.
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
Yes, fine.
I can see you've been studying this stuff.
Beginning to. There are some ambiguities in getting everything dimensionally consistent with factors of Lp. Mathematicans doing physics ignore all that setting everything = 1 and I think they make mistakes as a result e.g. mixed dimensions of the same components of the (LC) connection field for example. Some ~ r others ~ 1/r for SSS solution in some books. First rule in Physics 101 is that any equation should be consistent in units and physical dimensions.
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
As I'm sure you know, the tetrad starts out simply as a coordinate- independent basis for a any 4D vector space defined at each point on the spacetime manifold.
Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
If you construct such a tetrad field, yes it can be interpreted that way.
It's very important - that's Hagen Kleinert's key idea. Tensors were invented for elasticity theory in 19th Century.
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
In the long-wave approximation this looks to me like a theory of continuous media in 4D.
That's Kleinert's idea. I have simply plugged into that with
Bu^a = Bu&^aargVacuumODLRO
Bu^a is a pure number. Therefore Bu is a length in that convention since &^a is 1/length
Bu = Bu^adxa
dxa = (Mink)abdx^b
Bu = Bu&^aargVacuumODLROdxa
&^aargVacuumODLROdxa = 1
but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do.
OK.
They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there.
Maybe not.
We will see as I read Rovelli's book.
OK.
What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro- quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Hawking made this error at GR 17. Susskind makes it also. So does Lubos. Of course, I could be wrong, but we shall see.
I'm inclined to agree.
Micro-QM is linear, nonlocal, unitary with signal locality. Macro- QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
I think it's an interesting and very promising approach.
BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
YES.
So does Penrose in "Road to Reality".
I think I gave the real answer as to why this is really a pseudo- problem:
BTW from my "Rovelli Notes"
The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation.
The error you make Paul is to over-extend flat spacetime ideas to where they do not work. Conservation of total energy is simply a piece of T4 symmetry, i.e. time displacement invariance. It is certainly FALSE for the gravity vacuum. The whole attempt is wrong and that includes what Alex has proposed IMHO. Local conservation? Yes! Global conservation in general? No!
Then in Einstein's theory, where physically does the energy carried away by gravitational waves go?
When there is the flat background in weak field there is no problem. Since "total energy" is meaningless in a curved spacetime, it need not go anywhere! "Total energy" conservation is an artifact of T4 symmetry. Gravity is the breaking of T4 symmetry. Without the symmetry there is no conservation law, e.g. Noether's theorem. Read Wigner.
Locally there is no problem of course. The stress-energy current density is shared between the gravity and matter fields in
Tuv(Matter)^,v + tuv(Matter-gravity)^,v = 0
in 1916 GR.
You can get a global conservation approximately only with asymptotic flat space-times.
How does it get there?
I agree that inside Einstein GR, strictly speaking, there is no such thing as gravitational vacuum stress-energy.
For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries 3gij is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super- geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
I would have to think about this.
Shelly Goldstein has shown this in detail.
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Or, more generally, you can introduce *some* kind of source field for vacuum G_uv.
This provides an objective localizable physical "container" for the energy lost through gravitational radiation -- which is not the situation in orthodox GR.
No, you are confusing apples (zero point dark energy) and oranges (classical gravity waves).
No, not at all. I'm just saying that adding a *gravitational* vacuum source field for G_uv is *one* way out of this, because then you have somewhere for the gravitationally radiated energy to go that can be defined objectively,
i.e., in an observer-coordinate-free (frame-independent) manner.
This is not even wrong. You have no math to justify this confused idea.
Of course, a gravitating ZPF might also be a kind of "vacuum source field", but not a *gravitational* vacuum source field , which latter is still present even in the absence of all matter, including EM fields.
Meaningless if you cannot show a math model illustration.
Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
Right.
You seem to contradict yourself. In any case what you wrote above is so vague I do not know what you were trying to say.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro-quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro-scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
But we are not fish swimming in Maxwell's *classical mechanical* ether.
Hence "departed".
This is where Rovelli's philofawzy is good. More on that later.
The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem!
OK. If it's really not a problem, then it's not a problem.
If you read PW Anderson you will see why. Actually I have explained it many times. It's the released binding energy when the ionized virtual e+-e- plasma of the false vacuum FUSES in the inflation to the vacuum ODLRO condensate of bound virtual positronium! The released energy heats up the real quark-gluon plasma post-inflation.
The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
Yes, I know there is a lot of literature on this. I'll try and get hold of Anderson's "Career".
And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
That's Puthoff's dead end. I will not go there.
Just a question.
Wouldn't it be reasonable to expect that the properties of your all-pervading positronium BEC would determine at least some optical characteristics of the vacuum?
Indeed it does. It makes guv!
I get guv that's enough. Light is ds^2 = 0. I follow Einstein there.
But you can't deny that if your vacuum BEC exists, then light has to travel through it to get from A to B.
Yes, but QED shows direct effects are MINISCULE!
Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
Hal's theory is a toy model that was designed to be used as a heuristic tool for "engineering".
It has not done anything important there at all. Where are the engineering plans for saucers that fly? They don't exist - I mean not based on PV.
It's not an exact quantum theory of the physical vacuum, and it doesn't claim to be.
The truth is that PV has failed to deliver on any of its promises in 20 years! Time is up for Hal. The Devil will have his due! :-)
Saturday, June 11, 2005
Rovelli's Quantum Gravity Book
On Jun 11, 2005, at 4:58 PM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on Quantum Gravity".
Z: OK, that makes sense to me. I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
J: Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp(argVacuumODLRO)^,a for the 4D Diff(4) macro-quantum supersolid world crystal
analogous to
v = (h/m)GradargGroundstateODLRO for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note that elastic linear B term and the plastic nonlinear B^2 term.
Also, B while not a spin2 Diff(4) first rank tensor field all by itself, is a Minkowski spacetime spin 1 Yang-Mills vector field.
Z: Maybe Alex can explain to you why he and I propose to draw a fundamental distinction between raw mathematical spacetime CSs, on the one hand, and physical spacetime CSs ("moving CSs") that in GR represent observer reference frames, on the other.
J: Yes, he did, but I am not convinced that his idea is any better than mine, which is that a local frame (inertial or non-inertial) is an equivalence class of local coordinate charts at P that do not change the motion of the detector. Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object". See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~|A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick which is the geometrodynamic tetrad field e = I + B.
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved,
Z: Yes, but you have to be careful about how the coordinate-basis tetrad is physically interpreted. There is more than one possible interpretation.
J: Rovelli et-al show a completely coordinate-free Cartan form tetrad e. In fact the tetrad e is a 1-form independent of coordinates. Torsion and curvature are 2-forms. No problem!
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
Z: As I'm sure you know, the tetrad starts out simply as a coordinate-independent basis for a any 4D vector space defined at each point on the spacetime manifold.
J: Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do.
Z: OK.
J: They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there.
Z: Maybe not.
J: We will see as I read Rovelli's book.
Z: OK.
Z: What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc. Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro- quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Z: I'm inclined to agree.
J: Micro-QM is linear, nonlocal, unitary with signal locality. Macro-QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
Z: I think it's an interesting and very promising approach.
J: BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
Z: YES. So does Penrose in "Road to Reality".
J: I think I gave the real answer as to why this is really a pseudo-problem:
BTW from my "Rovelli Notes"
The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation. For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super-geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Z: Or, more generally, you can introduce *some* kind of source field for vacuum G_uv. This provides an objective localizable physical "container" for the energy lost through gravitational radiation -- which is not the situation in orthodox GR.
J: No, you are confusing apples (zero point dark energy) and oranges (classical gravity waves). Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro- quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro-scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem! The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
That's Puthoff's dead end. I will not go there. I get guv that's enough. Light is ds^2 = 0. I follow Einstein there. Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
On Jun 11, 2005, at 4:58 PM, iksnileiz@earthlink.net wrote:
Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on Quantum Gravity".
Z: OK, that makes sense to me. I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.
J: Rovelli starts from there, but he has no idea that ALSO the dimensionless
Bu^a ~ BuLp(argVacuumODLRO)^,a for the 4D Diff(4) macro-quantum supersolid world crystal
analogous to
v = (h/m)GradargGroundstateODLRO for the 3D macro-quantum superfluid
g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"
Note that elastic linear B term and the plastic nonlinear B^2 term.
Also, B while not a spin2 Diff(4) first rank tensor field all by itself, is a Minkowski spacetime spin 1 Yang-Mills vector field.
Z: Maybe Alex can explain to you why he and I propose to draw a fundamental distinction between raw mathematical spacetime CSs, on the one hand, and physical spacetime CSs ("moving CSs") that in GR represent observer reference frames, on the other.
J: Yes, he did, but I am not convinced that his idea is any better than mine, which is that a local frame (inertial or non-inertial) is an equivalence class of local coordinate charts at P that do not change the motion of the detector. Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object". See Rovelli's explanation of Einstein's solution of the "hole problem".
For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~|A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.
That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick which is the geometrodynamic tetrad field e = I + B.
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved,
Z: Yes, but you have to be careful about how the coordinate-basis tetrad is physically interpreted. There is more than one possible interpretation.
J: Rovelli et-al show a completely coordinate-free Cartan form tetrad e. In fact the tetrad e is a 1-form independent of coordinates. Torsion and curvature are 2-forms. No problem!
e = eu^a&adx^u
e is a dimensionless Cartan 1-form
&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length
dx^u is a 1-form basis in base space with dimension length
You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.
e.g.
[dx^a,dx^b] = Wab^cdx^c
Wab^c = Jim Corum's object of anholonomy with dimension length
Z: As I'm sure you know, the tetrad starts out simply as a coordinate-independent basis for a any 4D vector space defined at each point on the spacetime manifold.
J: Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field
eu(P) = eu^a&a = (Iu^a + Bu^a)&a
where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.
nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0
but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do.
Z: OK.
J: They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there.
Z: Maybe not.
J: We will see as I read Rovelli's book.
Z: OK.
Z: What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc. Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro- quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Z: I'm inclined to agree.
J: Micro-QM is linear, nonlocal, unitary with signal locality. Macro-QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
Z: I think it's an interesting and very promising approach.
J: BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
Z: YES. So does Penrose in "Road to Reality".
J: I think I gave the real answer as to why this is really a pseudo-problem:
BTW from my "Rovelli Notes"
The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation. For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries is
H(pure gravity)(BIT Wave Function of Multiverse) = 0
leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super-geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
Z: Or, more generally, you can introduce *some* kind of source field for vacuum G_uv. This provides an objective localizable physical "container" for the energy lost through gravitational radiation -- which is not the situation in orthodox GR.
J: No, you are confusing apples (zero point dark energy) and oranges (classical gravity waves). Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro- quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.
It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro-scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.
The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?
This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem! The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.
And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?
That's Puthoff's dead end. I will not go there. I get guv that's enough. Light is ds^2 = 0. I follow Einstein there. Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?
Thursday, June 09, 2005
Quantum Gravity?
On Jun 9, 2005, at 4:31 PM, Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on "Quantum Gravity". I will be seeing Alex in NYC if I can manage to leave my air conditioned room. Very humid!
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved, but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do. They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there. We will see as I read Rovelli's book.
What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro-quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Micro-QM is linear, nonlocal, unitary with signal locality. Macro-QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro-quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
On Jun 9, 2005, at 4:31 PM, Jack Sarfatti wrote:
Paul
Rovelli calls the "tetrad field" the "gravity field" in his new book on "Quantum Gravity". I will be seeing Alex in NYC if I can manage to leave my air conditioned room. Very humid!
The Ashtekar idea is a much more fancy way of doing what I have done more simply, i.e. the basic field is the tetrad = flat + curved, but Ashtekar & Co do not use local gauge invariance & vacuum ODLRO directly the way I do. They do not seem to even be conscious of vacuum ODLRO - but maybe I have underestimated them there. We will see as I read Rovelli's book.
What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro-quantum theory. I get diff(4) invariance + background independence non-perturbatively trivially!
Micro-QM is linear, nonlocal, unitary with signal locality. Macro-QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.
Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.
BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III
All you can say is
Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua
With
TOTAL Tuv^;v = 0
Therefore, any total energy-momentum = 0
Universe is a "free lunch".
In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro-quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super-solid” or “world crystal”.
Monday, June 06, 2005
Weak field approximation only? No.
On Jun 6, 2005, at 9:04 AM, ... wrote:
Dear Jack,
It is good, I agree fully with these ideas.
Maybe I am wrong, but it seems to me that the equation
eu^a = Iu^a + Bu^a
has to be valid only for the weak field approximation.
No definitely not - it is strong field and completely non-perturbative in origin. There is nothing in the principle of local gauge invariance that restricts it to weak field. That would mean QED & Yang-Mills were also a weak field approximations since Au^a plays same role in QED & Yang-Mills as Bu^a does in GR.
All the gauge potentials emerge from simply localizing rigid global symmetries of the dynamical action of some initial action. In the case of QED it is the action for the Dirac electron spinor field. In the case of GR it would be the trivial pre-Einstein-Hilbert action symmetric under rigid T4, i.e. zero action density ~ R = 0 with a Lagrange multiplier forcing Ruvwl = 0 identically I suppose. The idea is that the Einstein-Hilbert action density ~ (c^4/G) R =/= 0 emerges from B =/= 0.
In addition from ODLRO B^a ~ LpP^a/ih i.e. spontaneous broken T4 vacuum symmetry on top of local gauging of T4 to Diff(4).
Pa generates T4
Please, decode also such terms as ODLRO.
Vast literature from the 1940s or so. Google: Off-Diagonal-Long-Range-Order Oliver Penrose, Lars Onsager, density matrices. Much discussion of it in "A Career in Theoretical Physics" P.W. Anderson (World Scientific).
e.g. let psi be a 2nd quantized destruction boson operator at x - say in NR quantum many body problem in Fock occupation number space for example.
<0|psi*(x')psi(x)|0> is first reduced density matrix in the ground state |0> of the many body system.
ODLRO is the c-number factorization
<0|psi*(x')psi(x)|0> ---> <0'|psi*(x')|0'><0'|psi(x)|0'> + <0'|psi*(x')psi(x)|0'>
In a ground state phase transition from |0> ---> |0'>
|0> is unstable micro-quantum ground state
|0'> is more stable macro-quantum ground state
|0'> is a SQUEEZED GLAUBER state with two complex parameters z & s.
z gives the displacement of the Gaussian in the complex plane (phase space of Wigner function) and s gives the squashing of the degenerate Gaussian circle to an ellipse in phase space of the two quadratures psi* + psi & i(psi* - psi). Squeeze the normal vacuum one way to get repulsive dark energy of negative zero point pressure and the other to get attractive dark matter of positive zero point pressure? (Half-baked speculation of mine). s has the Bogoliubov pair correlations between different I & IV sections of the Penrose conformal diagram (e.g. Schwarzschild case) outside event horizon related to Unruh-Hawking radiation seen by accelerated observers.
<0'|psi(x)|0'> is the LOCAL macro-quantum COHERENT order parameter that obeys a NONUNITARY Landau-Ginzburg equation with SIGNAL NONLOCALITY & no Born probability rule. Micro-quantum theory with SIGNAL LOCALITY is violated when we have ODLRO!
B^a ~ (LpP^a/ih)arg<0'|psi(x)|0'>
B^a = Bu^adx^u
Lp^2 = hG/c3
This is spontaneous breakdown of real quanta ground state ("vacuum" for virtual quanta) symmetry for some group G of the dynamical action of the many-quanta system.
In the superconductor G ---> U(1)em internal fiber group for the electron field.
Rest mass of photon inside the super-conductor is precursor of rest mass of lepto-quarks in the U(1)xSU(2)xSU(3)xT4 local gauging with spontaneous broken vacuum symmetry not only in INTERNAL SU(2)weak force, but EVEN MORE IMPORTANTLY, in the T4 space-time group!
In Einstein relativity G ---> T4 space-time translation group that requires zero tidal geodesic deviation curvature for it to be the symmetry group of the, in this case, trivial constrained geometrodynamic action ZERO for the Einstein-Cartan tetrad field.
In special relativity SR, the tetrad field is the trivial non-dynamical Iu^a identity Kronecker-delta. In general relativity GR, as a local gauge theory, the tetrad field acquires a DYNAMICAL WARP FIELD Bu^a, i.e. now it is
eu^a = Iu^a + Bu^a
eu^a is a Diff(4) tensor under Diff(4) localization of T4 in the u index (base space)
eu^a is a O(1,3) tensor in the a index (tangent fiber space that still admits P^a) generated by the Sab Lie algebra of 6 space-time rotations whose conjugate phases are the "Ricci rotation coefficients".
Shipov's torsion theory, IN ADDITION, locally gauges O(1,3) to get 10-dim "space" of the oriented "point test particle" rather than the 4-dim "space-time" of the non-oriented point test particle. This adds another field Su^a to the Einstein-Cartan tetrad
eu^a = Iu^a(Minkowski non-dynamical) + Bu^a(tidal curvature disclination) + Su^a(torsion dislocation)
Where the EEP (Einstein Equivalence Principle) generalizes to
guv(curvature + torsion) = eu^a(Minkowski)abev^b
Geodesics in the extended geometry are not geodesics in the smaller geometry.
On Jun 6, 2005, at 9:04 AM, ... wrote:
Dear Jack,
It is good, I agree fully with these ideas.
Maybe I am wrong, but it seems to me that the equation
eu^a = Iu^a + Bu^a
has to be valid only for the weak field approximation.
No definitely not - it is strong field and completely non-perturbative in origin. There is nothing in the principle of local gauge invariance that restricts it to weak field. That would mean QED & Yang-Mills were also a weak field approximations since Au^a plays same role in QED & Yang-Mills as Bu^a does in GR.
All the gauge potentials emerge from simply localizing rigid global symmetries of the dynamical action of some initial action. In the case of QED it is the action for the Dirac electron spinor field. In the case of GR it would be the trivial pre-Einstein-Hilbert action symmetric under rigid T4, i.e. zero action density ~ R = 0 with a Lagrange multiplier forcing Ruvwl = 0 identically I suppose. The idea is that the Einstein-Hilbert action density ~ (c^4/G) R =/= 0 emerges from B =/= 0.
In addition from ODLRO B^a ~ LpP^a/ih i.e. spontaneous broken T4 vacuum symmetry on top of local gauging of T4 to Diff(4).
Pa generates T4
Please, decode also such terms as ODLRO.
Vast literature from the 1940s or so. Google: Off-Diagonal-Long-Range-Order Oliver Penrose, Lars Onsager, density matrices. Much discussion of it in "A Career in Theoretical Physics" P.W. Anderson (World Scientific).
e.g. let psi be a 2nd quantized destruction boson operator at x - say in NR quantum many body problem in Fock occupation number space for example.
<0|psi*(x')psi(x)|0> is first reduced density matrix in the ground state |0> of the many body system.
ODLRO is the c-number factorization
<0|psi*(x')psi(x)|0> ---> <0'|psi*(x')|0'><0'|psi(x)|0'> + <0'|psi*(x')psi(x)|0'>
In a ground state phase transition from |0> ---> |0'>
|0> is unstable micro-quantum ground state
|0'> is more stable macro-quantum ground state
|0'> is a SQUEEZED GLAUBER state with two complex parameters z & s.
z gives the displacement of the Gaussian in the complex plane (phase space of Wigner function) and s gives the squashing of the degenerate Gaussian circle to an ellipse in phase space of the two quadratures psi* + psi & i(psi* - psi). Squeeze the normal vacuum one way to get repulsive dark energy of negative zero point pressure and the other to get attractive dark matter of positive zero point pressure? (Half-baked speculation of mine). s has the Bogoliubov pair correlations between different I & IV sections of the Penrose conformal diagram (e.g. Schwarzschild case) outside event horizon related to Unruh-Hawking radiation seen by accelerated observers.
<0'|psi(x)|0'> is the LOCAL macro-quantum COHERENT order parameter that obeys a NONUNITARY Landau-Ginzburg equation with SIGNAL NONLOCALITY & no Born probability rule. Micro-quantum theory with SIGNAL LOCALITY is violated when we have ODLRO!
B^a ~ (LpP^a/ih)arg<0'|psi(x)|0'>
B^a = Bu^adx^u
Lp^2 = hG/c3
This is spontaneous breakdown of real quanta ground state ("vacuum" for virtual quanta) symmetry for some group G of the dynamical action of the many-quanta system.
In the superconductor G ---> U(1)em internal fiber group for the electron field.
Rest mass of photon inside the super-conductor is precursor of rest mass of lepto-quarks in the U(1)xSU(2)xSU(3)xT4 local gauging with spontaneous broken vacuum symmetry not only in INTERNAL SU(2)weak force, but EVEN MORE IMPORTANTLY, in the T4 space-time group!
In Einstein relativity G ---> T4 space-time translation group that requires zero tidal geodesic deviation curvature for it to be the symmetry group of the, in this case, trivial constrained geometrodynamic action ZERO for the Einstein-Cartan tetrad field.
In special relativity SR, the tetrad field is the trivial non-dynamical Iu^a identity Kronecker-delta. In general relativity GR, as a local gauge theory, the tetrad field acquires a DYNAMICAL WARP FIELD Bu^a, i.e. now it is
eu^a = Iu^a + Bu^a
eu^a is a Diff(4) tensor under Diff(4) localization of T4 in the u index (base space)
eu^a is a O(1,3) tensor in the a index (tangent fiber space that still admits P^a) generated by the Sab Lie algebra of 6 space-time rotations whose conjugate phases are the "Ricci rotation coefficients".
Shipov's torsion theory, IN ADDITION, locally gauges O(1,3) to get 10-dim "space" of the oriented "point test particle" rather than the 4-dim "space-time" of the non-oriented point test particle. This adds another field Su^a to the Einstein-Cartan tetrad
eu^a = Iu^a(Minkowski non-dynamical) + Bu^a(tidal curvature disclination) + Su^a(torsion dislocation)
Where the EEP (Einstein Equivalence Principle) generalizes to
guv(curvature + torsion) = eu^a(Minkowski)abev^b
Geodesics in the extended geometry are not geodesics in the smaller geometry.
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