On Oct 11, 2010, at 5:16 PM, Paul Zielinski wrote:
String/membrane theory is "bimetric," i.e. G = GNewton(1 + ae^-r/b) in the static limit.
[Z] I would argue that any theory in which Einstein gravity emerges at the phenomenological level is inherently
"bimetric" once the term is understood correctly.
[JS] Yes. Quite obviously the SPIN 1 compensating T4(x) local gauge geometrodynamic tetrad fields e^I eq. 2.50 and it's associated spin-connection fields w^I^J eq. 2.51in Rovelli's notation "Quantum Gravity" are fields on a FORMAL global Minkowski background with Poincare group indices I,J,K ...
I suppose by "formal" you simply mean here that the post-inflation physical spacetime geometry is not Minkowski?
Physically they are simply LIFs - however there is no single GIF only a fiber bundle of LIFs projected down to a manifold of possible physical events (local coincidences - scattering events)
Well, that is just GR in its modern formulation.
In your model, Einstein gravity emerges from an inflation process. Pre-inflation, I assume you are starting
with a flat Minkowski spacetime?
Yes, of course - there are no intrinsic non-trivial geometrodynamic emergent fields only the unstable global Minkowski solution with massless quark-leptons and massless internal symmetry gauge bosons.
OK. So your model for the physical vacuum is not purely relational.
Not sure if that distinction means anything in quantum gravity since one needs a Tuv to bend spacetime - although vacuum geons exist from self-gravity. I suppose geon solutions disprove the classical naive relationism? Also, the zero point energy in the unstable false-vacuum has a Tuv so one can never eliminate a Tuv - no such thing as the classical vacuum.
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So contrary to what Woodward has been arguing you don't need background independence. And there is no place for Mach's
principle, since inertia arises from local interactions between moving matter and the post-inflation condensate?
Yes, and no, it depends on how "Mach's Principle" is defined. I replace it by the Future Hologram Conjecture. If you look at the 3D + 1 hologram image it's as you say. If you look deeper at the anyonic 2D + 1 future event horizon hologram topological computer retrocausally projecting that image - it's weirder to be radically conservative. ;-)
And ending up with a condensate which is a physical model for a curved
physical metric field?
Background independence is a Red Herring.
That's what I've always said. No one even seems to be able to define it adequately.
It is simply, for the special case of Einstein's 1916 GR, the universal gauge invariance of the global dynamical action of all matter fields and their local field equations from the action principle &S = 0 with respect to the localized 4-parameter Abelian translation group T4(x) whose Lie algebra elements are the global total linear 4-momenta of the matter fields.
Are you saying that Kibble-Utiyama localized T4 is mathematically equivalent to the group Diff(R^4) of active diffeomorphisms D: R^4 -> R^4?
YES! Though that is not properly understood by almost all the Pundits!
More with less.
More is different.
Keep it simple, though not simpler than is possible.
Jettison excess formal baggage.
Physically, what GR allows you to do, which SR does not allow you to do, is to construct local invariants from data on the same events taken in locally coincident frames, each of which is in arbitrary motion.
Isn't that just general covariance applied to Einstein's coordinate frame model, translated into the language of tetrads/moving frames?
Yes, but it's simply an application of the battle-tested local gauge principle extended from compact internal symmetry invariance groups to non-compact symmetry groups whose invariance at the matter action level DEFINES the geometrodynamic c-number vacuum condensate emergent fields that is the warp and woof of the fabric of spacetime.
Acceleration is ABSOLUTE relative to the bundle or jet of local timelike geodesics. This is local-frame invariant & independent of local coordinates.
And the inertial trajectories are *physically* determined in your model by *local* interaction of moving matter with the condensate?
Tricky issue. To first approximation the moving matter is a test particle without direct back-reaction on the geometrodynamic fields from the Tuv sources. So the interaction is only one-way in many problems. Similarly in quantum theory where one gets signal locality only when the hidden variables are test particles relative to the Bohm quantum potential.
And the resulting phenomenology is all modeled geometrically as geodesics on a curved 4D manifold a la Einstein/Cartan? Plus a gauge gravity layer a la
NO NEED FOR MACH'S PRINCIPLE as classically understood.
If "Mach's principle" is understood as a methodological preference between alternative descriptions, OK. If understood as a physical hypothesis
(Einstein's interpretation), I would have thought there is no place for it in your model.
Yes and no as I tried to explain above - the new idea is holography i.e. advanced ANYONIC action 2D + 1 ---> FERMION-BOSON 3D + 1
But then you say you can get some version of "Mach's principle" from a holographic principle.
The absolute state of no-acceleration is a timelike geodesic defined by the local frame invariants buil t from the geometrodynamic tetrad/spin connection fields - that are trivial & unstable for the case of global zero curvature.
Yes but you have to relate this to the underlying physical model.
I did - inflation --> vacuum coherence --> emergent geometrodynamic fields analog to v = (h/m)GradS in deBroglie mechanics
it seems that all we need is SU3 QCD vacuum coherence described by Wilzcek in "Lightness of Being" to get the tetrad/spin connections of gravity
- consistent with Abdus Salam's old f-gravity in hindsight.
Note SU3 has 8 generators. I need their 8 conjugate phases to get tetrads and spin connections.
Note also that STRONG SU3 seems to have two EM-WEAK U1xSU2 subgroups each with 4 generators and I need two sets of phases PHI & THETA to get the tetrads and spin connections - SOME KIND OF WICK ROTATION FROM INTERNAL COMPACT TO SPACE-TIME NON-COMPACT GROUPS?
tetrads^I = diag M^I^J = PHI^[JdTHETA^I]
spin connections ^I^J = M^[I,J]
d^2 = 0 Cartan's operator
So how does the condensate locally control the inertial trajectories of freely moving bodies, consistent with the geometric model?
Or is inertia a non-local effect in your model?
Mach's Principle reconstructed as holographic imaging from our future event horizon is another story.
As a description perhaps, but as a physical explanation of inertia?
I have no need of that hypothesis - the Higgs - Yukawa couplings explain the rest masses of the leptons and quarks, W mesons & Wilczek explained the rest
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So, is inertia the result of local interaction of matter with the condensate,
or is it a non-local interaction with remote matter at the
far reaches of the Cosmos?
No, that model is no good at all.
It's not matter on our future horizon it's BITS in THE HOLOGRAM MIND OF GOD!
IT FROM BIT
AT CHILDHOOD'S END IS THE WORD
I mean in terms of physical explanation, not just phenomenological description, which I think was
what Mach was talking about.
Or are you saying something else?
To get beyond Einstein's 1916 GR extend to the Poincare and the conformal groups.
If these are understood as active diffeomorphisms, maybe.
Vacuum/Ground state solutions of the field equations may spontaneously break that symmetry, similarly to the way a superconductor breaks the U1 internal EM symmetry.
Here the original quanta are replaced by elementary excitations (quasi-particles & collective modes) in the long-wave IR limit, e.g. the massless quasi-electrons in 2D flat graphene sheets (presently limited to tiny flakes) whose effective coupling to light is 300xvacuum fine structure "constant". Similarly for gravity in special superconducting meta-materials, possibly graphene-based, I suggest as a Popper-falsifiable hypothesis.
OK so these electrons are delocalized over the entire sheet?
Yes, pretty much. Nick Herbert thinks that is of profound importance for his mind-matter transduction gizmos.
Well I wouldn't dismiss the idea out of hand.
I think you'll find that my comments about background independence are
not incorrect as you claim. I suspect that this claim may be the result
of confusion of what background independence actually is -- a confusion
easily understood because background independence means the opposite of
what one might intuitively think.
A confusion that is easily understood since no one seems to be able to give a clear definition
of "background independence".
I gave a very clear definition formally as local T4(x) gauge transformations.
So T4 is a group of active diffeomorphisms? And localized T4 gives you Diff(R^4)?
Physically as transformations between locally coincident small detectors each in arbitrary possibly off-geodesic & rotating motions including applied torques.
The historical origins of all this go
back to the '50s and '60s and the Rosen [the same as the EPR and "bridge"
Rosen] "bi-metric" theory of gravity where the usual Einstein metric
theory is supplemented by a global Minkowski "background" spacetime.
Actually they go back to the devastating 1917 Kretschmann argument which trivialized general
covariance from the physical standpoint. Kretschmann's argument clearly de-linked general
relativity from general covariance. A way had to be found to rescue Einstein's notion of "general
relativity", and the conceptual vacuum was filled (as it were) by Anderson's "principle of reciprocity"
and his "no absolute objects" rule -- leading to the contemporary principle of active diffeomorphism
invariance currently promoted by Rovelli, Smolin, and others.
I agree a lot of excess baggage here.
Including Anderson's "no absolute objects" idea?
Isn't the Lorentz signature of the metric an absolute structure? How do you get rid of that?
Huh? I never said I get rid of it.
Rhetorical question. The answer is that you can't, any more than you can make the dimensionality of the manifold
depend on the matter distribution. The point is that there is always some fixed underlying spacetime structure in GR.
I think I have gotten this down to the essential physics in a Zen like, more with less operational way.
It's true any physical theory can be made "background independent" - indeed in my T4(x) definition the equivalence principle means that all physical theories must be background independent.
I thought the argument was based on general covariance of the field equations? Given Kretschmann, how can general
covariance guarantee active diffeomorphism invariance?
I don't use that jargon.
OK that is all in Rovelli. I thought you were piggybacking on Rovelli?
I only use battle-tested local gauge invariance extended from internal to spacetime symmetry groups keeping the global actions invariant.
OK so it's more Kibble than Rovelli?
OK so your answer is: Einstein's equivalence principle. Hole argument.
reconstruct EEP as universality of the the local gauging of the non-compact symmetry groups for all matter fields no exceptions - unlike internal groups.
I think that is broader than EEP, but OK.
Background independence, in my opinion, is simply the particular application of the local gauge principle to the universal symmetry groups that define the spacetime fabric.
I think you need to make it clear that you are talking about a group T4(x) of localized active diffeomorphisms.
Yes, I mean little detectors making measurements whizzing through space - that's the class of situations the theory is a description of - specifically how to check their data when they are in local coincidence, but each in arbitrary motion with g-forces on the detectors allowed.
Well that is all described in canonical GR by *passive* diffeomorphisms. In your gauge gravity picture this is
now described in terms of active diffeomorphisms?
I guess that could make sense, since the tetrads are covariant objects.
Too much math obscures the physics here!
Fine, but it's even worse if you get the math wrong.
Otherwise it's not clear that you have a true "gauge" symmetry (as opposed to a covariance principle).
A difference that does not make a difference.
Well this is Rovelli's distinction. Personally I think there is much less than meets the eye there. Relationalists
(like Woodward) make a big fandango out of this, but when you boil it all down there is no "there" there if you
After considerable debate, folks agreed that the Minkowski background
metric added nothing whatsoever of physical meaning to Einstein's GR,
Rovelli in "Quantum Gravity" says global Minkowski spacetime is simply an unstable vacuum solution to Einstein T4(x) covariant field equations - with invariant global action integrals S over all 4D spacetime.
Same wine, different mathematical bottles.
OK so Rovelli is also talking about a false vacuum?
The "folks" who agreed on this, agreed on this. Others did not, and still don't.
the metric of GR describe the actual physical state of spacetime.
You need to use ds^2 = guvdx^udx^v = gu'v'dx^u'dx^v' as the actual physical state, not the detector-dependent representations guv or gu'v'/
Clearly bimetric theories involve a physical metric in addition to a reference metric.
I have no idea what Woodward is talking about here,
In any bimetric version of GR you have a deformable physical metric in addition to a Minkowski
reference metric. The physical metric is determined by the matter distribution just as in plain
Formally, the Einstein Equivalence Principle (EEP) simply means a class of coincident LIF can be realized in which the metric is approximately Minkowski over a scale small compared to the locally variable radii of curvature.
Yes, exactly. Although Einstein's principle deems this to be (at least "locally") *completely physically equivalent* to a Minkowski model.
This can be interpreted as an exact generalized relativity principle (Einstein) for the homogeneous case, or as a mere correspondence
principle for the general case that is only approximately valid, with respect to a limited class of measurements.
So this is an obvious red herring. Straw man.
is why GRT is called background independent.
That is not why GRT is called background independent.
OK I think I see your point about the "confusion". :-)
A background-dependent theory is one that presupposes the existence of a global Minkowski metric spacetime into which physical stuff is loaded. The loading stuff (fields and particles and the like) has no effect on the metric at all.
This is simply false.
This is all related to the "relationalist" vs. "substantivalist" debate regarding the physical
vacuum of GR. The relationalist idea is that if all gravitating matter is removed, then
there is no metric and no spacetime -- that the spacetime of GR represents *only*
relations between material bodies. The substantivalist position is that after all matter is
removed you still have a physical spacetime with a Minkowski metric (aside from
I have to assume that this is not Jack's position, since if zll gravitating material sources are removed
one could still have a condensate consisting of virtual particles. The relationalist position is that physical
spacetime represents nothing more than relationships between material bodies -- if you take away the
material bodies, there is no spacetime and no physical metric.
De Sitter famously showed that Einstein's field equations have vacuum solutions, and
this along with Kretschmann's earlier 1917 critique upset Einstein's earlier "Machian"
Not to mention the fact that gravity waves are allowed solutions in Einstein's theory.
Intuitively, the background metric is independent of the contents of
Just as the quiescent state of a guitar string (understood as a zero vibrational energy
reference state) is independent of how it is plucked.
But, counterintuitively, such theories are called background
dependent because the background spacetime is prior to the contents found
in it, and they depend for their existence on the prior existence of the
Exactly -- the unperturbed background inertial field (Minkowski spacetime) subsists ontologically
prior to and independently of the existence of gravitating matter. But that does not mean that the
physical metric describing this field cannot be physically perturbed by matter. That is the point of
the physical spacetime metric in bimetric theories!
Yes, if Woodward is right here, then why do bimetric theories have two metrics? If bimetric theories are
no different from special relativity plus gravity? Surely only a single metric would be needed?
There are two important points here, for our purposes anyway. First,
because of the prior nature of spacetime in background dependent theories
(that the spacetime is unaffected by its contents),
This is just wrong. The actual idea is that a flat spacetime can subsist ontologically in the absence of
gravitating matter. The actual physical metric is of course still perturbed by the presence of gravitating
This "substantivalist" interpretation is clearly supported by the formalism of GR, since the field equations
do in fact have pure vacuum solutions.
You seem to be confusing the question of ontological priority with the question of gravitational deformation
of the physical metric. No one in the substantivalist or bimetric camps claims that physical spacetime is
always flat regardless of the presence of matter!
nothing you put into
the spacetime has any effect at all on the spacetime.
I think this is called "special relativity". Bimetric theories of matter are not at all the same as special relativity,
contrary to what you seem to be arguing here.
That means that no
matter what you do, you cannot warp the background spacetime -- which is
the real spacetime.
This is Minkowski special relativity. This has nothing to do with "background dependence".
You seem to be seriously confused here.
So there are no wormholes or warp drives possible in
Not in special relativity, which is what you appear to be talking about.
Second, Hal's PV approximation to GRT is a background
dependent theory. A global Minkowski spacetime is ASSUMED, and the
propagation of light, when it deviates from striaght lines in the
Minkowski spacetime, is attributed to variations in the index of
refraction of a material medium (virtual e-p pairs in the PV model) in
the background spacetime.
No, the deformation of the physical metric is simply modeled (for engineering purposes)
as a vacuum polarization effect.
By ASSUMPTION, no amount of any stuff placed
into the background Minkowski spacetime can cause any warping of the
You're talking about Minkowski SR here, right?
This has nothing to do wiith background dependent or bimetric interpretations of GR.
I don't think you have understood the meaning of "background dependence".
Should you check with Hal, I expect he will tell you that
this is indeed the case for the PV approximation to GRT. The PV model is
just a heuristic approximation to GRT intended to simplify otherwise more
PV is not relevant here, since it is intended only as a naive approximate engineering model.
It is not offered as an alternative to GR, or even as the basis for an alternative interpretation
of GR, as far as I'm aware.
Should you read the paper in light of the foregoing, you'll find that I
have used "background independence" consistently with the above.
Consistently incorrect, yes.
background independent --
I'm sorry James but this is nonsense. GR has background dependent and background independent
interpretations,but even the Andersonian background independent "no absolute objects" interpretations
are only partially valid. GR still has absolute background structure. For example, the Lorentz signature of
the metric is an absolute invariant in any viable interpretation of GR, regardless of how matter is
distributed in spacetime, and regardless of whether there is any gravitating matter at all.
which is why it is physically meaningful to
talk about wormholes and warp drives as real physical possibilities.
This is nonsense. Bimetric theories don't allow gravitational deformation of the physical spacetime?
Horse feathers. Poppycock.
Other theories like PV and string theory are background dependent. As
such, they presume the reality of spacetime to be, for example, a global
Minkowski spacetime. Since that spacetime is not affected by its
material contents, wormholes and warp drives are by assumption
It just means that if you remove all gravitating matter from spacetime, there is still a "there"
there. This is fully supported by the formalism of GR, since GR has pure vacuum solutions --
as shown long ago by de Sitter.
If you want to see stargates and warp drives become a reality, keep your
fingers crossed that Einstein was right about the background independence
of GRT, and that reality conforms to GRT.
So e.g. Rosen's bimetric theory doesn't admit a Rosen bridge? I beg to disagree.
I've attached a paper "Who's Afraid of Background Independence" by Rickles, raising a number
of points regarding background dependence vs. background independence that you may
> If we can make a low-power high Tc superconducting warp/wormhole
> drive I am sure graphene sheets will be the key substrate.
> BTW a point about James Woodward's incorrect argument about
> background independence being spoiled inside the material.
> By the same false reasoning one can argue that special relativity is
> spoiled inside the material because the speed of light in material
> is clearly not invariant.
> Just remember locality demands that (index of refraction)^4G/c^4 is
> the gravity coupling inside the material because the speed of light
> in vacuum is from scattering off virtual electron-positron pairs and
> in a material we also have real particle charges. It's the same
> thing as far as gravity is concerned because of the equivalence
> principle. The fact that the universe is accelerating is proof
> positive that virtual particles inside the vacuum (anti) gravitate
> equally with real particles outside the vacuum.