Reformulation of Loop gravity in progress, comment?

[marcus]

The May 2012 "discrete symmetries" paper arXiv 1205.0733 signals a reformulation getting under way, I think. I'm curious to know how other people read this.

There's been a pattern of the theory getting a major overhaul every 2 years or so.
Many of us remember the 2008 reformulation, symbolized by the letters EPRL and FK.
Then in 2010 there was the "new look" paper in February that finally led to the Zakopane lectures formulation just 12 months later.

The May paper in effect proposes a change at the foundations level. It starts off by showing that the theory is solidly based on the classic Holst action: equation (8).
The theory is built up as a discrete 2-complex adaptation of that action.
Then the paper points out a key term (∗ + 1/γ) at the heart of equation (8) and proposes to change it by introducing the sign of the tetrad e. The action should, in other words, be sensitive to the orientation of the "vierbein" one of the two variables that go into the action.

If this is carried out at the classical level it has major repercussions at the quantum level, as the paper shows. So to recapitulate we have a 4d manifold M the basic Holst action is S[e,ω] where e is a foursome of 1-forms with values in the auxilliary Minkowski space M and ω is a connection.
Introduced now is a function s which takes on only three values 0,±1 and equals sgn(det(e)). And this function s is inserted in the key term of equation (8).

So instead of the classic Holst action we now have a modification with either
(s ∗ + 1/γ) or (∗ + s/γ).

Briefly, you may recall from the Zakopane formulation of Loop gravity (arXiv 1102.3660) that at the quantum level one gets rid of the 4d manifold. At that point one is dealing with a purely combinatorial object--the 2-cell complex C analogous to an abstract graph but in one higher dimension. It is not embedded in any continuum, and it represents the process by which abstract spin networks (states of geometry) evolve. You get the transition amplitudes from that. The Hilbert space H_Γ of quantum states of geometry is based on an abstract graph Γ.

Now we have to see how all that goes through when it is put on a new classical basis. What happens to the Zakopane formulation when you introduce into it the function s, the orientation of the tetrad. And also the paper considers discrete symmetries such as time-reversal.

For reference:
http://arxiv.org/abs/1205.0733
Discrete Symmetries in Covariant LQG
Carlo Rovelli, Edward Wilson-Ewing
(Submitted on 3 May 2012)
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergences.
Comments: 8 pages
Bianchi's Colloquium talk 30 May at Perimeter, in case it provides something of relevance to this topic:
http://pirsa.org/12050053

 

[Dickfore]

I am going to wait and see when this theory gets a final formulation and makes predictions that are different from current theories.

 

[marcus]

So far, the predictions carry over, during reformulation. So if anyone is actually interested in the prospect of TESTS of Loop gravity, then they can look at some links in:
https://www.physicsforums.com/showthread.php?t=579809

This link is slow (old Stanford/SLAC system) but still working:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
It currently gives 51 papers relating to ways and means for observational testing of Loop that have appeared 2009 or later.

This faster link uses the new Stanford search tool called "Inspire" and goes back further in time, but only finds 50 papers--still pretty good:
http://inspirehep.net/search?ln=en&...earch=Search&sf=&so=d&rm=citation&rg=100&sc=0

Obviously the phenomenologists (professional theory-testers on the lookout for ways to test other people's theories, they win either way it goes ) have not waited for Loop to be declared "final version". They have gone ahead. A testable theory can still be developing--there may be no guarantee that any particular version is "final". So if you wait to be told that some theory is final you may just keep on waiting and never do anything.

 

[Dickfore]

Are these works published in some peer-reviewed journals?

 

[marcus]

Are these works published in some peer-reviewed journals?

Most of them, I would say. Look at the listing yourself. Just use the links. The Spires and Inspire listing gives the publication data

 

[Dickfore]

I started with the first link you had posted in the other thread you linked about experimental test of LQG. It is:

Experimental Search for Quantum Gravity, by Sabine Hossenfelder
arXiv:1010.3420v1

The Journal reference for this paper is:
"Classical and Quantum Gravity: Theory, Analysis and Applications," Chapter 5, Edited by V. R. Frignanni, Nova Publishers (2011)

It seems that this not a peer-reviewed journal, but a newly published book. The publisher is:

Nova Science Publishers

I Googled them, and I have found links similar to this one:
http://forums.randi.org/showthread.php?t=112742

Even the Wikipedia entry on them:
http://en.wikipedia.org/wiki/Nova_Publishers
portrays tham with criticism.

Are you sure these are not a dubious bunch?

 

[marcus]

Are you sure these are not a dubious bunch?

Hee hee I don't know who you mean by "these" but the ones I meant when I gave you the Spires and Inspire links are certainly not a "dubious bunch".

Try the spires link: number one of the 51 papers is:
1) Cosmological footprints of loop quantum gravity.
J. Grain, (APC, Paris & Paris, Inst. Astrophys.) , A. Barrau, (LPSC, Grenoble & IHES, Bures-sur-Yvette) . Feb 2009. (Published Feb 27, 2009). 7pp.
Published in Phys.Rev.Lett.102:081301,2009.
e-Print: arXiv:0902.0145 [gr-qc]
Cited 45 times

You can ignore the Physicsforums link I gave you since I extracted from it the two Stanford/Slac search tool links: spires and inspire. If you don't already know about them now would be a good time to learn. Good luck!

 

[Dickfore]

I meant the publishers, sorry for the confusion.

 

[marcus]

I see, no problemo. Well here are the Spire and Inspire links again. There's quite a lot of interesting stuff! Many of the papers discuss tests that would need improved orbital instruments, but still within the range of proposed missions.
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
It currently gives 51 papers relating to ways and means for observational testing of Loop that have appeared 2009 or later.

This uses the new Stanford search tool called "Inspire" and goes back further in time, but only finds 50 papers--still pretty good:
http://inspirehep.net/search?ln=en&...earch=Search&sf=&so=d&rm=citation&rg=100&sc=0

My main point was that the phenomenologists (professional theory-testers who think up and study ways to test other people's theories) have not waited for Loop to be declared "final version" but have gone ahead.

 

[marcus]

The main topic here is of course the reformulation of Loop quantum geometry which appears to have started with this May 2012 "Discrete Symmetries" paper.

The question in my mind could perhaps be put this way: "Is it beautiful or not?"

Did Nature intend for us to include the ORIENTATION of the tetrad variable in the geometrical picture? If it needs to be done, is the way proposed here beautiful enough?

That's just my take, you may think about it in entirely different terms.

For newcomers to the topic, the tetrad is a four-leg local expression of the geometry which is defined at each point of the manifold and takes the place of the metric tensor in the Holst version of General Relativity which Loop uses. There is an auxiliary Minkowski space M at each point (similiar to a tangent space but with more structure) and this tetrad is a foursome of one-forms valued in the Minkowski space.

So at each point of the manifold the tetrad (denoted "e") is given by a 4x4 matrix and has a DETERMINANT, which can be zero (degenerate case) or positive or negative. So we can define the function s = sgn(det e) which is either zero or +1 or -1.

Formulating GR in terms of e rather than the metric g was, I think, an approach pioneered by Ashtekar. In some sense e is like a square root of g. The metric does not know about the orientation of the tetrad, because when you square it always comes out positive.

So one can wonder about this: does Nature know about the orientation of the tetrad? Is there an "anti-geometry" that corresponds to every geometry? Is there a physical significance to "inside-out"? If Nature does not know, and it all looks the same to her, then wouldn't it be superfluous elaboration or kludgy/klunky to include orientation in the picture? But maybe she does know.

In any case I think it's definitely something to explore. This function s, the sign or orientation of the tetrad, needs to be introduced into the picture and the consequences worked out.

Ed and Carlo (easier to say than Wilson-Ewing and Rovelli) have identified TWO ALTERNATE WAYS of putting s into the Holst action. They call the two new actions S' and S". It is interesting to see how different the results are, in the quantum theory, and it's not clear which is the best choice. I'm curious to know which alternative will be selected.
=============================
EDIT to reply to Tom's post #11:
"I guess spinors couple to tetrades directly and therefore see their orientation" Yes! I hadn't thought of that. If they mentioned that in the paper, my eye just missed it. Thanks for pointing it out.

 

[tom.stoer]

I guess spinors couple to tetrades directly and therefore see their orientation

 

[marcus]

I guess spinors couple to tetrades directly and therefore see their orientation

Thanks for pointing that out. I see that there are two separate ways to time-reverse orientation of a tetrad = {e_t, e₁, e₂, e₃}

One can leave the internal Minkowski space alone and simply reverse the single timelike leg of the foursome.
So e_t → -e_t And the rest we do not touch. I am using the notation of equation (12) in the paper.

That can be called a manifold time reversal because it is done at the level of the manifold, with one of the one-forms defined on the manifold.

Or one can perform a time-reversal in the Minkowski space on EACH leg of the foursome at the level of the "internal" Minkowski coordinates. So for each e_i we look at the coordinates e⁰, e¹, e², e³ of the image of the map in the Minkowski space. And we change the e⁰ of each leg but leave the other coordinates of the leg alone.
e⁰ → -e⁰ for each of the four legs of the tetrad.

This can be called the internal time reversal because it works at the level of the auxiliary or internal Minkowski space. I use the notation of equation (3).

They say that the total time reversal where both are done is what has more often been considered in the literature. This could be worth thinking about. They write the total time reversal
T = ^mT ⁱT, meaning the composition: do ^intT and also do ^manif

=======
To have it handy close by, so we don't have to scroll up and down so much, I'll copy here the abstract of the paper we are discussing:

http://arxiv.org/abs/1205.0733
Discrete Symmetries in Covariant LQG
Carlo Rovelli, Edward Wilson-Ewing
(Submitted on 3 May 2012)
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergence.
8 pages

 

[MTd2]

Are you sure these are not a dubious bunch?

It depends to whom you ask. String Theorists, in general, will disregard any paper about LQG even if they are published in the prestigious journals. Peer review outside their circles is as good as nothing.

 

[marcus]

There is something interesting about one of the two alternative actions S' and S".
S"[e,ω] is capable of taking on negative values under internal time reversal, in a way that makes it fundamentally different.
S"[e,ω]=∫e^IΛe^JΛ( ∗ + s/γ) F_{I J}

The first term is just the original tetrad action
S_T[e] = ∫e^IΛe^JΛ ∗ F_{I J}
and this differs from the Einstein Hilbert precisely because it changes sign under time reversal.

The second term is the familiar Holst term but modified with the signum which again makes it change sign
∫e^IΛe^JΛ (s/γ) F_{I J}
which it otherwise would not do under internal time reversal (see last paragraph on page 1 of the paper.)

So when you put these two terms together you get an action S"[e,ω] which does something fundamentally different (from either the Einstein-Hilbert S_EH or the conventional Holst actions): internal time reversal flips the sign.

I'll let the authors explain why this might be interesting:
==quote arXiv 1205.0733==
One argument by analogy in favour of S_T and S′′, on the other hand, is the fact that in non-relativistic physics the action of a trajectory moving backward in time has the opposite sign to the action of the same trajectory moving forward in time. The action for a process is S = E∆T, and if ∆T changes sign, so does S. This property is lost in S_EH because of general covariance, which implies that there is no way of distinguishing a forward moving spacetime from backward moving one. But it is present in S_T and S′′ as they depend on the sign of s.

We close with a comment on the interpretation of regions with opposite s. In Feynman’s picture one obtains quantum amplitudes summing over the particle’s paths in space. The idea that in this context particles running backward in time represent antiparticles forms the intuitive basis of the Stückelberg-Feynman form of positron theory [33, 34]. According to a beautiful argument given by Feynman in [35], special relativity requires such particles running back in time to exist, if the energy must be positive. This is because positive energy propagation spills necessarily outside the light cone. But a propagation of this kind is spacelike and therefore can be reinterpreted as backward in time in a different Lorentz frame. Therefore there must exist propagation backward in time in the theory and this represents a (forward propagating) antiparticle. Thus, according to Feynman, the existence of antiparticles follows directly from quantum mechanics and special relativity. Can an analogous argument be formulated in quantum gravity?

Consider a gas of particles in space-time used to define a physical comoving coordinate system. These define a time function with respect to which the gravitational field can be seen as evolving. In the quantum theory, however, the gravitational field can fluctuate off-shell so that the trajectories are somewhere space-like. But then there is a coordinatization of space-time with respect to which the particles run backward in time. In turn, the metric in this coordinatization runs backwards in time with respect to the time defined by the physical reference field. In other words, we are again in the situation where a solution running backward in time must be included in the path integral. These are only speculative remarks, but they suggest that the contribution of the tetrad fields with negative determinant —negative internal time— should perhaps not be dismissed lightly a priori.

Can this intuition be relevant for the dynamics of spacetime itself and shed some light on the physical interpretation of a region with a flipped internal time direction? Can a region with the opposite internal time direction be thought of as a spacetime running backward in time, or an “anti-spacetime”?
==endquote==

[35] R. Feynman, “The reason for antiparticles,” in Elementary Particles and the Laws of Physics: The 1986 Dirac memorial Lectures. Cambridge University Press, 1987.

 

[marcus]

As I interpret Feynman's argument there is a reason here to be cautious about equating shape dynamics with approaches to full quantum relativity such as Loop.
SD gives up foliation independence. It fixes one absolute foliation of spacetime. SD accepts an idea of universal absolute simultaneity. One can say once and for all which events are simultaneous and which are not.
(Some similarity here with other approaches being explored such as CDT and possibly Horava-style as well.)

What if this practice of fixing on a unique prior foliation is unrealistic? Feynman seems to be arguing that on the most fundamental basis (quantum mechanics itself) there must be particles following time-reversed trajectories. Extending his argument to a gas of particles in a quantum geometry, one suspects that there might of necessity, for the most basic reasons, be patches of time-reversed geometry. At least if one allows fissures of degenerate geometry to separate the patches.

With this complication in mind, do we entrust physics to a unique prior foliation? What if both regions and anti-regions exist? Rovelli and Wilson-Ewing don't mention this problem with SD, if it is a problem, or refer to shape dynamics at all. They only touch briefly, and frankly as speculation, on the idea of patches of time-reversed geometry. The idea is quite speculative and I think one can't really go very far with it at this point.

 

[marcus]

As I see it the most serious competition to Loop gravity at present comes from theories of conformal gravity such as described, for example, in this talk:
http://pirsa.org/12050061
Conformal Gravity and Black Hole Complementarity
Gerard t'Hooft
So when we are gauging the cogency of this new formulation of Loop in arxiv 1205.0733 there is an implicit weighing against, for instance, what 't Hooft has to say in the pirsa 12050061 talk.

The talk was briefly discussed in another thread:
https://www.physicsforums.com/showthread.php?t=605984
which also contains some links to related papers by 't Hooft.

 

[marcus]

Another serious challenge to Loop comes from spontaneous dimensional reduction, discussed by Steve Carlip, and the possibility that conformal symmetry is achieved at very small scale where the spacetime dimension approaches d=2.
He gave a good clear talk about this at the "Conformal Nature" conference:
http://pirsa.org/12050072/
Two-dimensional Conformal Symmetry of Short-distance Spacetime
Speaker(s): Steve Carlip
Abstract: Evidence from several approaches to quantum gravity hints at the possibility that spacetime undergoes a "spontaneous dimensional reduction" at very short distances. If this is the case, the small scale universe might be described by a theory with two-dimensional conformal symmetry. I will summarize the evidence for dimensional reduction and indicate a tentative path towards using this conformal invariance to explore quantum gravity.
Date: 11/05/2012 - 9:00 am

Carlip's talk (despite being in speculative territory) had a cautious "commonsensical" delivery. I found it easier to understand and a helpful counterpoise to the somewhat more visionary talk by 't Hooft, mentioned earlier:
http://pirsa.org/12050061
Conformal Gravity and Black Hole Complementarity
Gerard t'Hooft

The conference homepage:
http://www.perimeterinstitute.ca/Events/Conformal_Nature_of_the_Universe/Conformal_Nature_of_the_Universe/

 

[marcus]

Rovelli's new formulation of spacetime geometry, which allows regions which are evolving backwards in time, could have effects which are in principle observable. The abstract of this paper--which was awarded honorable mention in the 2012 Gravity ResearchFoundation essay contest--just appeared (on page 4 of the following document):

http://www.gravityresearchfoundation.org/pdf/abstracts/2012abstracts.pdf (#5)
How to Measure an Anti-Spacetime by Marios Christodoulou, Aldo Riello, Carlo Rovelli, Centre de Physique Théorique, Case 907, Luminy, F-13288 Marseille, EU;
Abstract – Can a spacetime region with a negative lapse function be detected, in principle? Fermions do not couple to the metric field and require a tetrad field: we show that this implies that a fermion interference effect could detect a negative lapse region, distinguishing “forward evolving” from “backward evolving” spacetimes having a gravitational field described by the same metric.
==========

Since we are now on a new page, I will recopy the abstract of the main paper we are discussing in this thread. This paper has a detailed reformulation of classical gravity in a modified Holst action allowing for internal time reversal, and the corresponding reformulation of Loop gravity based on it.

http://arxiv.org/abs/1205.0733
Discrete Symmetries in Covariant LQG
Carlo Rovelli, Edward Wilson-Ewing
(Submitted on 3 May 2012)
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergence.
8 pages

 

[marcus]

The reformulation of Loop now being explored is complex, and some parts seem still tentative.
I see three main initiatives:

A. Immirzi-less BH entropy.
Bianchi and others find S = A/4. The coefficient of area no longer depends on Immirzi parameter γ. So gamma is unclamped. arxiv:1204.5122 arxiv:1205.5325

B. un-Diracly quantizing GR.
Jacobson proposed a new goal. Find the correct quantum "molecules" of spacetime geometry for which Einstein's GR equation is the thermodynamic equation of state.
It could turn out that the Spinfoam description of geometric evolution already provides the correct degrees of freedom, and GR is simply the equation of state of spinfoam.
So that instead of quantizing GR Diracly, one has quantized it un-Diracly.
arxiv:1204.6349 arxiv:1205.5529

C. The sign of the tetrad--could one detect a region of "antispacetime"?
One possible crude picture of spacetime geometry is that of a partially coherent swarm of tetrads. Like flocking birds or shoals of fish, these tetrads tend to be oriented coherently with their neighbors. But in principle, divisions might occur: there could appear patches with opposite orientation. The set-up described in the May paper "Discrete Symmetries in Covariant LQG" arxiv:1205.0733 allows for this to happen. The usual Holst action is modified in a significant way---by introducing the sign of the tetrad, a symbol s which can be +1, 0, or -1 depending on the sign of the determinant of the tetrad.
Since fermions couple to the tetrad, phase can evolve in either of two senses and a double slit experiment can in principle detect reversed geometry by a shift of the interference pattern.

 

[marcus]

I guess one thing to discuss a little is how to think about the tetrad formulation that is growing up here. The basic tetrad action (omitting indices) is:
S[e]=∫e∧e∧∗F

F is the curvature tensor associated with the tetrad field e. The star ∗ denotes a kind of scrambling called Hodge dual. So ∗F is a scrambled or "Hodged" version of the curvature present in the tetrad e.

We might suppose that the tetrad e wants to adjust itself so as to avoid unnecessary curvature. Minimizing needless bother might be one of the things on its mind

As a crude laymanoid analogy you know how a particle trajectory minimizes an action which is a summed combination of time and energy, and spacetime is the trajectory of evolving geometry so since there is no privileged time we can think of the spacetime as time itself, made by a swarm of tetrads.
We can, by analogy, think of e∧e as the measure of time
and we can think of ∗F as the measure of energy. And together they make the action, which Nature finds desirable to minimize.

And indeed curvature, bending, is often confusable with energy. "Dark energy" is actually a curvature constant. If geometry wants to minimize this ∫e∧e∧∗F it could be because it does not want to be needlessly rumpled.

As a formality the mathematical account tells how the tetrad e determines a "tortionless spin-connection" ω[e] (which records the rock and roll of the tetrad as it varies from place to place) and then F is the curvature of this connection ω. So there is an extra mathematical step in getting from tetrad e to curvature tensor F.
But mentally, if we wish, we can ignore the ω step and simply associate F directly with the tetrad.

 

[marcus]

So S[e]=∫e∧e∧∗F can be seen as a very natural "action" for a trajectory of geometry which is a spacetime, analogous to the trajectory of a particle in a fixed geometry.
And it's already better than the Einstein-Hilbert action because it has a tetrad that fermions can couple to. E-H action is based on the metric g, rather than the tetrad.

But S[e]=∫e∧e∧∗F does not seem to be the final version. People are exploring certain slight elaborations, like this one called Holst action
S_H[e]=∫e∧e∧(∗ + 1/γ)F

(employing a positive real number γ) and most recently in the paper this thread is about, by Rovelli and Wilson-Ewing, there was one using the SIGN of e, denoted with a small letter s.

S_R2[e]=∫e∧e∧(∗ + s/γ)F

I'm denoting it R2 because it was the second one of two that they proposed to try out.
I've left off the indices but you can recover them by looking at the paper.
===================

The business about ω, mentioned earlier. Given a tetrad field e, you might see an equation
de + ω∧e = 0
Intuitively this means (to me at least) that if you make a small shift in some direction then the tetrad e will rock a bit, and this slight change de in e is exactly captured by the connection ω, because it can be reproduced by wedging e with ω. So ω knows exactly how the tetrad is going to change when you move a little bit in whatever direction.

That connection ω is what we take the curvature of, to get the F that goes into the action integral. That's true whether the integral is the ordinary Holst or some recent modification of it like Rovelli and Wilson-Ewing's versions R1 and R2.

 

[atyy]

@marcus, is the "new" theory you are referring to that which comes from S' or from S''?

It's interesting that they say S' is related to Engle's A spin-foam vertex amplitude with the correct semiclassical limit.

Rovelli and Engle seem to disagree on what a correct semiclassical limit is. I think Engle would argue for S' since it gives exp(iRegge), but S" gives cos(Regge). Rovelli doesn't mention the cosine as disqualifying S".

 

[marcus]

I'm glad you are thinking about this! Have you figured out what the spinfoam vertex amplitudes would be, corresponding to these two different classical variations on the Holst action? At this point I don't see how the differences translate into spinfoam terms, nor do I see how either classical action can be disqualified at this stage. I'm interested in your intuition about this.

 

[atyy]

I'm glad you are thinking about this! Have you figured out what the spinfoam vertex amplitudes would be, corresponding to these two different classical variations on the Holst action? At this point I don't see how the differences translate into spinfoam terms, nor do I see how either classical action can be disqualified at this stage. I'm interested in your intuition about this.

They give the amplitudes in Eq 35 (S') and Eq 39 (S"), and the respective semiclassical limits in Eq 43 & 44. Engle has argued that Eq 44 is not the desired semiclassical limit, but I believe Rovelli disagrees with him on this point. Engle's proposal seems similar to S', according to Rovelli and Wilson-Ewing.

Here's Engle's reason for thinking Eq 44 is not the desired semiclassical limit "For the purpose of semiclassical calculations with the spin-foam model, it is important that all terms in the asymptotics other than eiSRegge be eliminated. The only proposal so far in the literature for this is to eliminate the extra terms by selecting the boundary state to be peaked on the group variables as well as the conjugate canonical bivectors [29–31]. ... Although this works for a single simplex, because the strategy is based on specifying a boundary state, it is not immediately clear if this solution will work for simplicial complexes with interior tetrahedra."

I think the Han and Zhang analyses for an arbitrary number of simplices are relevant, but am not sure:
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory

 

[marcus]

They give the amplitudes in Eq 35 (S') and Eq 39 (S"), and the respective semiclassical limits in Eq 43 & 44. Engle has argued that Eq 44 is not the desired semiclassical limit, but I believe Rovelli disagrees with him on this point. Engle's proposal seems similar to S', according to Rovelli and Wilson-Ewing.

Yes, Rovelli and Wilson-Ewing explain on page 6 in the paragraph after equation (44) why they think having both terms does not disqualify the S" option.

I think there is only a superficial resemblance between RWE equation (44) and what you say Engle was arguing against, since in the RWE case each of the two terms is evaluated over an entire connected region. Whereas in the original EPRL amplitude (as they explain) the evaluation was cell-by-cell.

So, if their explanation is correct, Engle would NOT find himself arguing against their S" or their equation (44) He was concerned with the earlier EPRL amplitude and a superficially similar, but not identical, asymptotic behavior.

In any case, this is still speculative. The paper, at that point, is only looking ahead and uses the phrase "it is natural to expect". The paper presents the two classical actions and does not actually work out the resulting spinfoam vertex amplitudes. It will be interesting to see what actually comes out of this in spinfoam terms.

 

[atyy]

Yes, Rovelli and Wilson-Ewing explain on page 6 in the paragraph after equation (44) why they think having both terms does not disqualify the S" option.

I think there is only a superficial resemblance between RWE equation (44) and what you say Engle was arguing against, since in the RWE case each of the two terms is evaluated over an entire connected region. Whereas in the original EPRL amplitude (as they explain) the evaluation was cell-by-cell.

So, if their explanation is correct, Engle would NOT find himself arguing against their S" or their equation (44) He was concerned with the earlier EPRL amplitude and a superficially similar, but not identical, asymptotic behavior.

In any case, this is still speculative. The paper, at that point, is only looking ahead and uses the phrase "it is natural to expect". The paper presents the two classical actions and does not actually work out the resulting spinfoam vertex amplitudes. It will be interesting to see what actually comes out of this in spinfoam terms.

I think they are just saying the semiclassical expression is correct for the given quantization. I don't think they say it is the desired semiclassical limit. If a non-degenerate region is a region of classical spacetime we see, shouldn't that region be made from exp(Regge) not cos(Regge)?

 

[tom.stoer]

just a comment: it should be clear that the correct semiclassical limit is a necessary but not a sufficient condition for a "correct" theory

 

[marcus]

just a comment: it should be clear that the correct semiclassical limit is a necessary but not a sufficient condition for a "correct" theory

Probably we each have our own idea of what more to ask from a theory (besides appropriate behavior in limit). We can have an interesting discussion of what is "theoretical correctness" or "TC" for short.

For me, two things are most important, for a TC quantum theory of geometry:
1. it should recover GR either as a large scale limit or (as Ted Jacobson suggests) as its thermodynamical EoS.
2. it should make predictions about features of the CMB ancient light which future observation can discover or not discover.

In short what I expect (per the Francis Bacon tradition of empirical science) is cogent testable explanation. I don't have detailed requirements as to what form the explanation takes.

What about you? How would you describe your idea of "theoretical correctness" in its most essential elements? I think your idea may be different from mine, but I forget just what it is that you absolutely require.

I'm interested to know how you would boil it down to two or three lines, as I did a moment ago. And what it is that you require today, since your perspective may have evolved.

 

[Dickfore]

It must provide a testable theoretical prediction different from GR.

 

[marcus]

It must provide a testable theoretical prediction different from GR.

Bravo! You got immediately to the heart of the matter. You said it better than I did. This is the essential thing WHATEVER the formalities of the explanation of nature happen to be.

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, for example, "jacobson equation of state"

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.

Notice the careful language: suggests that it MAY
It could well be extremely appropriate to quantize the GR equation Diracly! Or it might not be so appropriate. The important thing is not the formalities or the heuristics used to arrive. The important thing is what you said.

As a reminder of the current goings on in Loop research reformulation-wise I'll quote my earlier post #19:

The reformulation of Loop now being explored is complex, and some parts seem still tentative.
I see three main initiatives:

A. Immirzi-less BH entropy.
Bianchi and others find S = A/4. The coefficient of area no longer depends on Immirzi parameter γ. So gamma is unclamped. arxiv:1204.5122 arxiv:1205.5325

B. un-Diracly quantizing GR.
Jacobson proposed a new goal. Find the correct quantum "molecules" of spacetime geometry for which Einstein's GR equation is the thermodynamic equation of state.
It could turn out that the Spinfoam description of geometric evolution already provides the correct degrees of freedom, and GR is simply the equation of state of spinfoam.
So that instead of quantizing GR Diracly, one has quantized it un-Diracly.
arxiv:1204.6349 arxiv:1205.5529

C. The sign of the tetrad--could one detect a region of "antispacetime"?
One possible crude picture of spacetime geometry is that of a partially coherent swarm of tetrads. Like flocking birds or shoals of fish, these tetrads tend to be oriented coherently with their neighbors. But in principle, divisions might occur: there could appear patches with opposite orientation. The set-up described in the May paper "Discrete Symmetries in Covariant LQG" arxiv:1205.0733 allows for this to happen. The usual Holst action is modified in a significant way---by introducing the sign of the tetrad, a symbol s which can be +1, 0, or -1 depending on the sign of the determinant of the tetrad.
Since fermions couple to the tetrad, phase can evolve in either of two senses and a double slit experiment can in principle detect reversed geometry by a shift of the interference pattern.

Just a tip, in case anyone is unfamiliar with using ARXIV to get current research papers: For instance if you want to read a copy of the May 2012 paper just mentioned Discrete Symmetries in Covariant LQG arxiv:1205.0733 , then all you need to do is paste " arxiv:1205.0733 " into google. You don't need the quotes. Merely click on google's first hit to get the abstract summary, and from there, the full PDF text.

 

[tom.stoer]

1) The theory must have consistent quantizations w/o anomalies etc.
I think that (due to the unsettled problems regarding H or the second-class constraints / the PI measure) this is still work in progress, but I am optimistic that these issues can be clarified quite soon. Whether we will have one unique theory or whether this will result in a larger class of theories is still unclear to me.

2) There must be a subset of quantum theories for which GR is recovered in a certain limit.
I am optimistic that this is a more or less universal property of a large class of LQG theories.

3) These theories should predict genuine quantum-gravity effects beyond GR and beyond the semiclassical limit which are testable in principle.

4) There must be a non-empty subset of theories for which these genuine quantum-gravity effects are testable in practice and agree with nature.
I am afraid that this problem (which is a problem for all theories dealing with 'quantum gravity') could be an insurmountable obstacle. It is unclear to me whether CMB effects are sufficient to distinguish between different QG approaches.

 

[Dickfore]

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, for example, "jacobson equation of state"

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.

Notice the careful language: suggests that it MAY
It could well be extremely appropriate to quantize the GR equation Diracly! Or it might not be so appropriate. The important thing is not the formalities or the heuristics used to arrive. The important thing is what you said.

I don't know if a wide audience of people in the LQG community is familiar with the fact, but the equation for sound is quantied, albeit in condensed systems (solids and liquids, plasma), and not gases. The bosonic quasiparticles corresponding to these collective modes of excitations are called phonons, plasmons, depending on the system.

These quasiparticles play a significant role in determining the properties of the system. Not only do they determine the heat capacity due to lattice vibrations (motion of ions), but one can make an effective theory where the electrons interact with them. A consequence of this interaction in metals is resistivity to charge transport, or, more exotically, Cooper pairing to form a new superconducting state.

 

[atyy]

I don't know if a wide audience of people in the LQG community is familiar with the fact, but the equation for sound is quantied, albeit in condensed systems (solids and liquids, plasma), and not gases. The bosonic quasiparticles corresponding to these collective modes of excitations are called phonons, plasmons, depending on the system.

These quasiparticles play a significant role in determining the properties of the system. Not only do they determine the heat capacity due to lattice vibrations (motion of ions), but one can make an effective theory where the electrons interact with them. A consequence of this interaction in metals is resistivity to charge transport, or, more exotically, Cooper pairing to form a new superconducting state.

Yes, Jacobson made an error there. He corrected himself later, citing the same examples you mention. However, the examples from condensed matter support his general point "in spirit": the quasiparticles are emergent properties of more fundamental degrees of freedom, as in string theory.

Here's Jacobson's later remarks http://arxiv.org/abs/gr-qc/0308048
"This led me at first to suggest that the metric shouldn’t be quantized at all. However I think this is wrong. Condensed matter physics abounds with examples of collective modes that become meaningless at short length scales, and which are nevertheless accurately treated as quantum fields within the appropriate domain. (Consider for example the sound field in a Bose-Einstein condensate of atoms, which loses meaning at scales below the so-called “healing length”, which is still several orders of magnitude longer than the atomic size of the fundamental constituents.) Similarly, there exists a perfectly good perturbative approach to quantum gravity in the framework of low energy effective field theory[2]. However, this is not regarded as a solution to the problem of quantum gravity, since the most pressing questions are non-perturbative in nature: the nature and fate of spacetime singularities, the fate of Cauchy horizons, the nature of the microstates counted by black hole entropy, and the possible unification of gravity with other interactions."

 

[marcus]

Thanks both Dickfore and Atyy for these interesting points relating to the Jacobson quote. Since we just turned a page, I will copy the quote from his 1995 paper to make it clear what you refer to:

...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, for example, "jacobson equation of state"

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.

Notice the careful language: suggests that it MAY
It could well be extremely appropriate to quantize the GR equation Diracly! Or it might not be so appropriate. The important thing is not the formalities or the heuristics used to arrive. The important thing is what you said...

It must provide a testable theoretical prediction different from GR.

 

[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:
$$\alpha = \frac{e^2}{\hbar \, c}$$
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 ($\hbar \rightarrow 0$), 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.