# Reformulation of Loop gravity in progress, comment?

1. May 9, 2012

### 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 HΓ 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.
Bianchi's Colloquium talk 30 May at Perimeter, in case it provides something of relevance to this topic:
http://pirsa.org/12050053

Last edited: May 9, 2012
2. May 9, 2012

### Dickfore

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

3. May 9, 2012

### 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:

This link is slow (old Stanford/SLAC system) but still working:
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.

Last edited by a moderator: May 6, 2017
4. May 9, 2012

### Dickfore

Are these works published in some peer-reviewed journals?

5. May 9, 2012

### marcus

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

6. May 9, 2012

### 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:

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?

7. May 9, 2012

### marcus

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!

8. May 9, 2012

### Dickfore

I meant the publishers, sorry for the confusion.

9. May 9, 2012

### 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.
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.

Last edited by a moderator: May 6, 2017
10. May 10, 2012

### 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.

Last edited: May 10, 2012
11. May 10, 2012

### tom.stoer

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

12. May 11, 2012

### marcus

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

One can leave the internal Minkowski space alone and simply reverse the single timelike leg of the foursome.
So et → -et 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 ei 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

Last edited: May 11, 2012
13. May 12, 2012

### MTd2

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.

14. May 12, 2012

### 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]=∫eIΛeJΛ( ∗ + s/γ) FI J

The first term is just the original tetrad action
ST[e] = ∫eIΛeJΛ ∗ FI 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
∫eIΛeJΛ (s/γ) FI 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 SEH 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 ST 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 SEH 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 ST 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.

Last edited: May 12, 2012
15. May 13, 2012

### 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.

Last edited: May 13, 2012
16. May 14, 2012

### 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:
which also contains some links to related papers by 't Hooft.

17. May 14, 2012

### 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/ [Broken]

Last edited by a moderator: May 6, 2017
18. May 15, 2012

### 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 [Broken] (#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

Last edited by a moderator: May 6, 2017
19. Jun 8, 2012

### 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.

Last edited: Jun 8, 2012
20. Jun 9, 2012

### 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.

Last edited: Jun 10, 2012