Reformulation of Loop gravity in progress, comment?

Dickfore

It is true that in Condensed Matter Physics (CM) every field theory is an effective long length scale theory (notice the tendency to use units of length instead of energy in CM). Also, it is "trivial" that the "true" underlying theory is that of non-relativistic outer-shell electrons and heavy inert ionic cores interacting through Coulomb interactions. That is all there is to the "microscopic" physics.

However, I don't think leaps in scientific discoveries are made by postulating some "weird" microscopic physics (a la String Theory) and going backwards to longer length scales where previous theories gave good agreement with experiment to test whether your new theory gives the same predictions.

I think one needs to consider possible next order corrections to the current theory.

Let me give an example. QED was not dreamed up by Feynman, Schwinger and Tomonaga. It was a crown achievement of a long series of refinements that started with Sommerfeld's relativistic Bohr model. Sommerfeld's model predicted the lifting of the accidental degeneracy in the Coulomb field (the energies depend only on the principal, but not on the orbital quantum number in the non-relativistic Kepler problem). This splitting is α² times smaller than the spacing of the hydrogen terms, where α = 1/137. That is why the small parameter is called the fine-structure constant. It turns out it is a wonderful small parameter with respect to which we can develop a perturbation theory.

Another (relativstic) effect of the same order is the spin-orbit interaction. Namely, a moving magnetic dipole in a static electric field sees a magnetic field, and feels an extra potential energy. There are some fine points about numerical factors due to the proper relativistic treatment of the gyromagnetic ratio of the electron and Thomas precession. I think these are taken into account by the semi-empirical Pauli equation.

It was Dirac who developed a relativistic equation for the electron, and predicted a g-factor for the electron of exactly g = 2! He also started quantizing the EM field and obtained the result for the coefficient of spontaneous emission of a photon. However, he encountered one insurmountable mathematical difficulty. That of the infinities in some of the integrals for second-order corrections.

This is where the 1946 Nobel trio comes in with the procedure of renormalization. Additionally, their theory predicts that g - 2 is a quantity of the order of α². Notice that we need a completely different experiment than spectroscopy to measure this effect. Namely, the fine-structure is proportional to g, and to α². But, the difference g - 2 is itself proportional to α², which is beyond precision. One needs to put the free electron in a strong external magnetic field to measure a simple second order effect.

And this is where the story of QED ends. Feynman did not solve the mysteries of the atomic nucleus. This was a different success story from several decades later.

The point is, it is wonderful that we are ignorant beings. Feynman was never aware of electroweak symmetry breaking, yet, he made a theory that is in perfect agreement with experiments.

I think that we need to clarify first where the state-of-the art experimental status is for GR at present. I am no expert, but, it is my impression that laboratory sized experiments are very crude. The best tests come from astronomy/cosmology. Then, we need to identify a small parameter. Some may say "non-perturbative results" are also of interest. But, one must remember that Physics is, by itself, a successive asymptotic approach to the exact model. Sure, it may be that the zeroth order approximation is not a non-interacting theory, but there is still a small parameter (like 1/N in QCD). Then, we need to see what is the next order correction to GR.

Notice that:
[tex]
\alpha = \frac{e^2}{\hbar \, c}
[/tex]
It is proportional to the square of the coupling constant, and that is why the interaction is a small perturbation. But, it is also inversely proportional to Planck's constant. Thus, in the limit of non-quantum Physics ([itex]\hbar \rightarrow 0[/itex]), it would tend to infinity! One needs to clarify what is the role of quantum effects in QED from the above.

GR is truly non-quantum. Thus, we need to clarify in what sense are quantum corrections small compared to GR.

atyy

Quantum GR with quantum corrections to classical GR is usually considered in a framework like http://arxiv.org/abs/gr-qc/9607039 , analogous to QED. In this framework, quantum GR is good up to near the Planck scale.

marcus

I should have included the view of current status and developments of Loop gravity from the perspective of Jerzy Lewandowski. He has been actively involved in both the canonical quantization side of LQG and the inclusion of matter fields (as well as schematizing spinfoam LQG).

JL will be the lead organizer of the major triennial GR conference next year---GR20 will be held at Warsaw. The other large international General Relativity conference (also held once every three years) is the Marcel Grossmann meeting. MG13 is next month in Stockholm. Here also Lewandowski plays an important role: he leads two 4-hour sessions on LQG and Spinfoam QG at the Stockholm conference. He is also doing the overview of LQG at the Prague conference on Relativity and Gravitation that is being held this month. He is the main organizer of the Loop session at this year's Group Theory in Physics conference, a biennial event, and has been invited to lecture at a LQG school in Beijing later this summer. So this is a representative figure and I think it's worth studying his brief overview carefully.

==quote from MG13 conference program (typo corrected)==

Jerzy LEWANDOWSKI

Parallel Sessions QG1a and QG1b - Loop Quantum Gravity, Quantum Geometry, Spin Foams

Description: Loop Quantum Gravity (LQG), a framework suited to quantize general relativity, has seen rapid progress in the last three years. The results achieved strongly suggest that the goal of finding a working and predictive quantum theory of gravity is within reach. For specific kinds of matter couplings, a way to drastically simplify the dynamics and its physical interpretation has been discovered. It gives rise to a set of examples of theories of gravity coupled to the fields in which the canonical quantization scheme can be completed. Independently, there have been important breakthroughs in the path integral formulation of the theory related to the so called Spin Foam Models. The session will review the results of canonical Loop Quantum Gravity and Spin Foam Models with the emphasis on the models admitting local degrees of freedom without the symmetry (or any other) reduction. Related approaches to quantum gravity will be also welcome. The common theme is the background independent quantization of Einstein's gravity and the occurrence of quantum geometry.
==endquote==
http://www.icra.it/mg/mg13/par_sessi...tm#lewandowski

atyy

He's probably referring to http://arxiv.org/abs/1009.2445.

marcus

Yes probably, among other things. That paper is 2 years old and his overview of the session says says rapid progress in the last 3 years. I would guess there is more development to report along the lines you indicate.

BTW I don't think it's clear that Ted Jacobson was mistaken in his memorable quote about "canonically quantizing the Einstein equation". His opinion may have swung back and forth, and may still---the discussion is not over. Just as a reminder:

..Ted Jacobson put this message implicitly in his paper on GR as a thermodynamical equation of state.
http://arxiv.org/abs/gr-qc/9504004
The title has the phrase "the Einstein Equation of State" so you can get it by googling...
the abstract has this memorable comment:
This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.
...

Obviously we are not talking about phonons and quantizing crystal lattice vibrations, so it's quite clear that it is NOT appropriate to quantize the equation of sound in air.
And yet the fundamental objects are molecules, behaving according to QM.
So the illustration shows that one might have a correct quantum theory (e.g. of geometry) with an Equation of State (e.g. the Einstein GR) where the quantum theory does NOT result from canonically quantizing the EoS.

If you quantized the equation of sound in air you would not get the quantum mechanics of air molecules. Something like that may (or may not) apply in the case of GR.

I think that is all his statement means, and it's a significant point which so far remains valid. Do you agree? Athough it's not completely clear, I think from reading your post #33 that perhaps you may.

atyy

Jacobson's opinion has not swung back and forth. His main point has always been the same.

marcus

Thanks. I can kind of see it that way too. He and Rovelli are friends and I imagine they will be discussing this, since the issue has come up in such a pronounced way of late. It could be interesting to see where this goes.

atyy

I don't think your interpretation of Jacobson's statement is his. His point was that new degrees of freedom must be introduced, like strings. The spirit of his point would be against spin foams in the Rovellian interpretation.

marcus

My interpretation is straightforward and literal. I don't see how yours is based on his actual words, or on what was expressed without introducing additional complication.
But so be it. We each have our own interpretation, and we cannot read Ted's mind to check if we are or were in the past right.

However we will see how things go in the future! It's an exciting time. I am looking forward to the next few months and then Loops 2013 taking place at Perimeter.

atyy

Hmm, but isn't the Rovellian view of spin foams to covariantly quantize gravity so as to canonically quantize gravity?

http://relativity.livingreviews.org/.../fulltext.html (section 6.7)
"A recent derivation as the quantization of a discretization of general relativity is in [105, 104], which can also be seen as an independent derivation of the loop-gravity canonical formalism itself. "

marcus

I'm not talking right now about what you think is the "Rovellian" this or that which you interpret from his 2008 essay.
what we are talking about is our interpretation of what Jacobson said might or might not be the case. I think its interesting to seriously consider that it may (or may not) be inap to canon'ly qu'tize GR eqn like it would be inap to qu'tize the eqn of sound in air.

That is, the classical eqn just might happen to be the equation of state of, say, a spinfoam quantum geometry system.

Where you do not get the quantum "molecules" description by applying some conventional "quantization" ritual to the equation of state. A ritual which has certainly worked wonderfully in the past with other equations but may (or may not) be the way to proceed with this equation.

I think the possibility is really interesting---that GR is the equation of state of, say, a spinfoam quantum geometry.

That doesn't mean that the approaches followed by Lewandowski Warsaw group, or currently by the Marseille group, are NOT interesting. But let's focus right now of the Jacobson idea.
=====================
Just as a footnote: I think that was the second element I identified back in post #19 when I tried to characterize the present situation:
A. unclamping the Immirzi parameter, Bianchi's entropy result.
B. this TJ thermodynamical equation of state idea
C. the cohesive flock of tetrads picture where you introduce the sign of the tetrad
(may have interesting consequences)

http://physicsforums.com/showthread....96#post3948196

These are all (but especially B and C I think) risky gambits and that is probably one reason the Loop program has been doing well in the past 5 or so years. It is a small community that stays focused on the main goal of background independent QFT and takes calculated risks. But that's merely interpretative side-comment and not so important.

atyy

Well, the Smolin paper you quoted in your post #19 argues against Jacobson's idea. http://arxiv.org/abs/1205.5529 "In his groundbreaking paper, [1], Jacobson argued that classical general relativity could emerge from a quantum statistical mechanics system that is not the quantization of classical general relativity. This point is well taken, but neither is it excluded that the thermodynamic system the Einstein equations are emergent from would happen to be a quantization of general relativity"

marcus

Smolin obviously likes TJ's general idea and he's designating an interesting variation where the right "molecules" turn out to have already been arrived at via a path-integral Feynman-like gambit---the spinfoam approach.

As LS says "neither is it excluded" that things might work out that way. I think that would be delightful and mentioned that possibility in my earlier post #19. It's a quibble whether you consider spinfoam dynamics to have been arrived at "Diracly" by canonical quantization. I certainly don't, but if you like to think of it that way then there is that minor "argues against" to point out at the level of detail FWIW.

I think there it's an exciting time and all these various related ideas and possibilities are on the table.

There are major conferences this month and next in Prague and Stockholm (Prague "Relativity and Gravitation" and Stockholm "MG13"). Hopefully major people involved will get together to talk one place or another, maybe stop off at Marseille. We probably won't learn anything much until the dust settles.

atyy

Exactly. There are two parts to Jacobson's idea. The first technical part is the relation between thermodynamics and gravity. This is not disputed. The second "spiritual" part is that gravity is emergent from new degrees of freedom. This is disputed, and spin foams in the Rovellian approach are against this idea.

marcus

Not against, though! Because in that particular scenario the spinfoams ARE the "new degrees of freedom".

Or if you like the field or flock of tetrads that play an important role in Rovelli's latest papers (but have been there all along in the spinfoam approach) ARE the "new degrees of freedom".

So no essential contradiction. Everything, as I was saying, is on the table, probably some new synthesis is brewing.

atyy

No, spin foams are not "new" in the Jacobson sense. The Rovellian spin foams are quantizations of general relativity. This is why Smolin says that Jacobson could be wrong on that point.

marcus

By your personal interpretation of what "Jacobson sense" means.
You seem to want to control the meanings of words like "Rovellian" and perhaps you will be talking about the true meaning of "Jacobsonian".

Tom often objects that one DOESN'T actually get spinfoam dynamics by a canonical Dirac quantization of GR equation and the relation between the approaches isn't clear.

And on the other hand you now seem to be complaining that one actually DOES get spinfoam dynamics by some kind of (rigorous conventional I suppose) quantization and therefore the spinfoam degrees of freedom are not "new in the true Jacobsonian sense". Or some such thing.

All this breathless quibbling about who said what when in which refined "sense". Why not just relax and see what a few exceptionally creative lucky people make of it?