Can Holometer Null Result falsify LQG?

[Edward Wij]

Google and even article searches here have no hits of whether null results of the Holometer can falsify Loop Quantum Gravity. First see first what is the Holometer:

http://holometer.fnal.gov/

It is supposed to measure if the Planck scale is discrete or continuous. And results would be forthcoming soon. If it has null results. Would it prove space is continuous and even maybe falsify Loop Quantum Gravity? If not, why won't it since LQG is about the discreteness of space and time?

Or how is the Holometer discreteness experiment related to the discreteness of the Planck scale related to LQG?

 

[Breo]

What? Never heared about this.

That link lack of information and also is out of date since August.

Can anyone tell more about the current state of the project?

By the way spacetime is discrete :p

 

[julian]

By the way spacetime is discrete :p

To put the cat among the pigeons - just because you quantize something that doesn't mean observables must have a discrete spectrum, usually there is a compactness assumption. In the book "Approaches to quantum gravity" Livine says:

"Indeed, the compactness of the SU(2) gauge group is directly responsible for the discrete spectra of areas and volumes, and therefore is at the origin of most of the successes of LQG: what happens if we drop this assumption?"

"The theory is derived from the original first order GR formulation in a particular (partial) gauge fixing, the time gauge, which breaks the local Lorentz invariance down to a local SU(2) gauge invariance...Nevertheless, it appears as the result of a gauge fixing."

 

[marcus]

Julian notes that what is meant by "discreteness" is that certain observables have a discrete spectrum.
It is really important to realize that in LQG context discreteness refers to the results of MEASUREMENTS. If you measure an area the outcomes are discrete. Just like if you measure the energy levels of a hydrogen atom, the levels are a discrete set of energies.

The book "Approaches to QG" edited by Dan Oriti is a rather old book. Although it did not come to market until 2009, the chapters tend to date around 2007 or earlier. Livine's chapter dates back to 2006! (http://arxiv.org/abs/gr-qc/0608135) It would be good to check and see if there is any follow up discussion in the more recent literature. One paper that might be relevant is this
http://arxiv.org/abs/1012.1739
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
(Submitted on 8 Dec 2010)
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. ... This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.
Comments: 6 pages, 1 figure.

Since Livine's 2006 essay quite a lot of work has gone into reformulating LQG. What Etera Livine talks about in a chapter of Oriti's book most likely is NOT the same theory as the EPRL formulation that he himself was collaborating on in 2008-2009. The EPRL formulation (L stands for Livine) took prominence 2009-2010 or so.

 

[marcus]

... If not, why won't it since LQG is about the discreteness of space and time?...

I don't know how you picture discreteness of a geometry theory. Some people have the naive idea of LQG that it treats space or spacetime as made up of little hard balls.
So they think LQG is falsified by this or that.
But you probably realize that LQG does not picture space as made up of discrete "points". that would not be Lorentz covariant! Space is not a material.
LQG (and its ancestor Einstein GR) is about geometry and that means geometric measurements. As with any quantum theory there is an observer who can measure---angles, areas, volumes etc.---in this case geometric quantities, geometric observables.

We are talking about a web of interrelated quantum observables---about how nature responds to (geometric in this case) measurement. not about a collection of little round pebbles or some other kind of discrete material assemblage---little tetrahedral bricks, or balls and sticks. Measurements are interactions with nature and the results can have discrete spectra. Like hydrogen levels.

Since 2009-2010 when LQG was reformulated in the EPRL version (Engle Pereira Rovelli Livine) a lot of work has gone into checking that some of the geometric observables are operators with discrete spectrum. I don't know the current status of that. BTW some of the latest formulations use a noncompact group like SL(2, C).
There is work by Wolfgang Wieland, also by Thiemann&Lanery. I'm not on top of that, can't give exact references. Sorry to be vague.
Anyway AFAIK the theory is still Lorentz covariant and still has geometric observables with discrete spectrum, but its work in progress, continues to evolve.

 

[julian]

A free quantum particle has a continuous spectrum whereas a particle trapped by a coulomb potential (hydrogen atom) has a discrete spectrum. Being bound by such a potential is a form of compactness.

In my quote I'm referring to the introduction of chapter 14. In Livine et al's formalism of covariant loop quantum gravity the question is raised about the area operator having a continuous spectrum. It is kind of disconcerting.

Thanks for the reference to Rovelli, I have heard of it but haven't looked at it. I will now.

I'm going through Rovelli/Vidotto at the moment to better understand EPRL. I'm interested to see how it relates to Livine et al's formulation (which I think was a difficult program to complete). Given that L stands for Livine he will be able to see it from both perspectives.

On "So they think LQG is falsified by this or that."...Rovelli addresses issues about discreteness of the area spectrum and non-violation of Lorentz invariance in his book "Quantum gravity" page 316. Since then I know proof of the theory being Lorentz invariant have been made, I'm yet to read the papers but will now.

I wasn't saying necessarily that Lorentz covariance conflicts with discreteness of geometric operators...cat - pigeons.

 

[Edward Wij]

I don't know how you picture discreteness of a geometry theory. Some people have the naive idea of LQG that it treats space or spacetime as made up of little hard balls.
So they think LQG is falsified by this or that.
But you probably realize that LQG does not picture space as made up of discrete "points". that would not be Lorentz covariant! Space is not a material.
LQG (and its ancestor Einstein GR) is about geometry and that means geometric measurements. As with any quantum theory there is an observer who can measure---angles, areas, volumes etc.---in this case geometric quantities, geometric observables.

We are talking about a web of interrelated quantum observables---about how nature responds to (geometric in this case) measurement. not about a collection of little round pebbles or some other kind of discrete material assemblage---little tetrahedral bricks, or balls and sticks. Measurements are interactions with nature and the results can have discrete spectra. Like hydrogen levels.

Since 2009-2010 when LQG was reformulated in the EPRL version (Engle Pereira Rovelli Livine) a lot of work has gone into checking that some of the geometric observables are operators with discrete spectrum. I don't know the current status of that. BTW some of the latest formulations use a noncompact group like SL(2, C).
There is work by Wolfgang Wieland, also by Thiemann&Lanery. I'm not on top of that, can't give exact references. Sorry to be vague.
Anyway AFAIK the theory is still Lorentz covariant and still has geometric observables with discrete spectrum, but its work in progress, continues to evolve.

But that was I think what Lee Smolin was thinking especially when he proposed the gamma ray bursts test that test the discreteness of space similar to the holometer. If you will recall Lee Smolin article "Atoms of Space and Time".. http://www.phys.lsu.edu/faculty/pullin/sciam.pdf
There was a way to test it.. from gamma ray bursts and comparing them at the detector.. quoting: "The discrete nature of
space causes higher-energy gamma rays to travel slightly faster than lower-energy ones. The difference is tiny, but its
effect steadily accumulates during the rays’ billion-year voyage. If a burst’s gamma rays arrive at Earth at slightly
different times according to their energy, that would be evidence for loop quantum gravity. The GLAST satellite, which is
scheduled to be launched in 2006, will have the required sensitivity for this experiment."This is very similar to the Holometer tests. I think the GLAST produced null results yet the LQG folks have different explanation.. what was it again? And would it be the same explanation that would make the Holometer possible null result inconsequential?

 

[marcus]

Jerzy Kowalski-Glikman and others tried for several years to VALIDATE Smolin's test and eventually gave up around 2006-2007. That is they tried to show that the LQG theory would actually imply some energy dependence of speed of light as Smolin had GUESSED it might. A good bit of the attempt was done at Perimeter under Smolin's urging I would suppose, and Perimeter support. Kowalski-Glikman was at Perimeter for part of that time. Now he is in Poland, at Wroclaw I believe. Excellent guy! Doing other QG research. No longer trying to show that LQG predicts so and so. gamma ray burst etc etc.

GLAST was called GLAST when Smolin was guessing about a possible test but then it was renamed Fermi-LAT, around the tine it was launched.

I suppose basically a general rule is don't read anything about QG that is more than 5 years old. It is a fast-moving field

 

[marcus]

Wij, just to be clear. LQG does not imply energy dependent speed of gammaray photons. So when Fermi-LAT (the former GLAST) did not find dispersion (the technical term for energy dependent speed) it did not make any trouble for LQG.

However there may be OTHER types of quantum gravity with OTHER types of discreteness, which do violate Lorentz invariance and predict energy-dependence of speed. And Fermi-LAT and other similar results may make trouble for those theories. But those others may be dead-letter anyway. Old versions of this or that, no longer currently worked on. I don't know.

 

[julian]

I said "In Livine et al's formalism of covariant loop quantum gravity the question is raised about the area operator having a continuous spectrum. It is kind of disconcerting." I meant to say that he DOES get a continuous area spectrum! Not just that the question is raised. And this is disconcerting.

 

[marcus]

why disconcerting?
Livine's chapter dates back to 2006! (http://arxiv.org/abs/gr-qc/0608135)
At that time what we now call "covariant LQG", namely EPRL spin foam formulation, did not exist.
2006 was over 8 years ago, the field progresses, this does not seem disconcerting.
the thing that is mildly disconcerting is that you are reading old stuff and talking as if you were discussing current research

Oh! I remember! there was something else going back to like 2003 that was ALSO called "covariant LQG"! It involved someone called Alexandrov. One has to be careful not to confuse the old theory which no one has worked on for a long time with the newer theory. It was too good a name not to be recycled.
Yes, back around 2003 when Etera was writing dissertation and stuff he co-authored a paper about the old Alexandrovian CLQG. Maybe several papers.
That is potentially quite a confusion, the old theory was not at all similar to EPRL spin foam theory. AFAIK Alexandrov has not worked on it for many years. Or Etera. Or anybody else. But it has the same name!
If that is what the chapter is about, best just to forget about it. Simple confusion of having the same name for two technically different things.

Look and see if there is reference to Alexandrov papers in the bibliography. Then you know that the chapter is about something else--not current.

Yes! I looked. that chapter has references to a bunch of paper from over 10 years back like this:
...
[13] S. Alexandrov, E.R. Livine, SU(2) Loop Quantum Gravity seen from Covariant Theory, Phys.Rev. D67 (2003) 044009, [arXiv:gr-qc/0209105]
[14] E.R. Livine, Boucles et Mousses de Spin en Gravité Quantique, PhD Thesis 2003, Centre de Physique Theorique CNRS- UPR 7061 (France), [arXiv:gr-qc/0309028]
[15] S. Alexandrov, Z. Kadar, Timelike surfaces in Lorentz covariant loop gravity and spin foam models, Class.Quant.Grav. 22 (2005) 3491-3510, [arXiv:gr-qc/0501093]

 

[julian]

I know they are two different theories, they aim to achieve the same thing - a Lorentz covariant formulation. With the older version, I'm concerned that the dynamics is dictated by the Barrett-Crane model as this has been shown to not get out the correct propagator. In this older version, it appears that reintroducing the Immirzi ambiguity has something to do with recovering a discrete spectrum. Is a key difference between the BC spinfoam and the newer spinfoams to do with incorporation of the Immirzi parameter? It has been a while.

I did say to put the cat among the pigeons...so don't take it too seriously :).

 

[julian]

What do you think of the comment in Rovelli/Vidotto on page 238

"The idea that propagation can be affected by quantum gravity - considered and then partially discarded some years ago because of the proof that the theory is Lorentz invariant - is not necessarily wrong, as Lorentz-invariant corrections to the propagator are possible. This is also a direction to explore. For this, one needs to study higher-order corrections to the graviton propagator computed in Bianchi et al (2009): Bianchi and Ding (2012). Is there a Plank correction to the form of the classical propagator?"

If having an energy dependent speed of light violates Lorentz invariance, what should we be looking for from such Lorentz-invariant corrections?

 

[julian]

Just looked at the first page of "Lorentz covariance of loop quantum gravity" by Rovelli and there are references to papers by Alexandrov.

References back to 1987.

 

[marcus]

Just looked at the first page of "Lorentz covariance of loop quantum gravity" by Rovelli and there are references to papers by Alexandrov.

Makes sense that there would be! In Livine's 2006 article there had been no reformulation and the references make clear that the article was talking about the old Alexandrovian CLQG. In the 2010 the EPRL reformulation had already occurred and it was being called CLQG. So the term had a new meaning. There was no chance of confusion and it's good practice to refer to antecedents. Let's not get bogged down in a history of nomenclature :)
Is it clear that the EPRL (aka Covariant LQG) established by Engle Pereira Rovelli Livine around 2009 is a different animal from the old Alexandrovian CLQG worked on circa 2002 and 2003 by Alexandrov and Livine, and discussed in the 2006 article? Interestingly when it went into the book as chapter 14 the title acquired a question mark,
the title became "Covariant LQG?". It sounds like Livine was signaling he no longer supported the earlier work and that there was a gap to be filled--that earlier initiative hadn't quite worked out---so what to do? And later he was himself one of those who responded to the implied challenge.

I personally admire Sergei Alexandrov and think the earlier (2002-2003) work was valuable and instrumental in bringing about progress---but is a formulation which is very different from what we now mean when we say Covariant Loop Quantum Gravity (look at Rovelli&Vidotto "Introduction to CLQG" textbook).

 

[marcus]

...

"The idea that propagation can be affected by quantum gravity - considered and then partially discarded some years ago because of the proof that the theory is Lorentz invariant - is not necessarily wrong, as Lorentz-invariant corrections to the propagator are possible. This is also a direction to explore. For this, one needs to study higher-order corrections to the graviton propagator computed in Bianchi et al (2009): Bianchi and Ding (2012). Is there a Plank correction to the form of the classical propagator?"

If having an energy dependent speed of light violates Lorentz invariance, what should we be looking for from such Lorentz-invariant corrections?

Why shouldn't some researchers look for "higher-order corrections to the graviton propagator"? We should have an open mind. Maybe "propagation can be affected" in various ways which do not show up in the SPEED of propagation, or specifically effect photons.

You ask "what should we be looking for?" well it sounds like an interesting research area---Lorentz invariant corrections to the graviton propagator---maybe there are some PhD thesis topics here. There are different aspects of graviton propagation, indeed we don't understand gravitational waves completely, certainly not at quantum level (!) but even at the classical level. Even the experimental/observational experience is not clear. "What should we be looking for?" Many things are possible, simply go ahead and learn more about the (CLQG) graviton propagator, be open to surprises. Is that a fair paraphrase?

BTW the CLQG graviton propagator is not the familiar perturbative QG or effective QG one. Some readers may not realize. It is in the context of the General Covariant theory, so there can be no fixed flat background to "propagate on". As I recall the covariant graviton propagator appeared around 2008 and was one of the things that guided the development of CLQG---it sparked use of the boundary formalism. that could certainly be a fruitful research area for some people. it is still new and relatively unexplored. So from my non-expert perspective what Rovelli Vidotto say about that certainly seems reasonable.

 

[Edward Wij]

markus.. as an enthusiast or researcher of quantum gravity.. have you come across any ideas or papers about the Planck scale being solid and matter being the emptiness or holes in the solidity.. akin to water passing thru clothes?

 

[julian]

The point of the holometer, according to the link, is to determine: "whether it [space] always jitters by a tiny amount, carrying all matter with it, due to quantum-geometrical fluctuations." I'm not sure what the experimental arrangement is, but I'm reminded of a cautionary note by Rovelli:

"Some objections are based on the intuition that the position of the matter defining the surface could be subjected to quantum fluctuations, preventing the possibility of defining a sharp surface. This objection is incorrect...it is only the gravitational field in the location determined by the matter, or, the other way around, the location of the matter in the gravitational field, that have physical reality. The two do not form independent sets of degrees of freedom subjected to independent quantum fluctuations."

in http://fr.arxiv.org/pdf/gr-qc/9806079 page 7. The diffeomorphism invariance of GR means that if you "carry" (over the spacetime manifold) the matter field and gravitational field together, the new configuration is physically identical to the original configuration - this is why they can only be located with respect to one another.

Oh and yep the old and new theories are different animals. At the time of the new spinfoam models I wrote up some notes on the FK paper. I recognise objects from that paper that are in the Rovelli/Vidotto book - SU(2) coherent states .

"Lorentz covariance of Loop Quantum Gravity" is a neat paper. They are using the then "recent developments in spinfoam theory". As well using "aspects and results" of Alexandrov and Liveine formalism, "that are of direct value for LQG, disentangling them from Alexandrov's attempts to find alternative models".

 

[julian]

To say space stands still or jitters is naive. It implies that space is an entity with independent physical reality, and it is not. The main lesson of GR, as Rovelli says all the time, is that, well spacetime (which includes space) IS NOT an entity with independent physical reality. Physical spatial/temporal localization, in a relational sense, requires the introduction of matter. So you have to be careful about what it is you are supposed to be observing.

 

[Edward Wij]

To say space stands still or jitters is naive. It implies that space is an entity with independent physical reality, and it is not. The main lesson of GR, as Rovelli says all the time, is that, well spacetime (which includes space) IS NOT an entity with independent physical reality. Physical spatial/temporal localization, in a relational sense, requires the introduction of matter. So you have to be careful about what it is you are supposed to be observing.

This paragraph causes me hours of reading with regards to Einstein hole arguments but googling "hole argument loop quantum gravity" doesn't produce any hits. Is LQG about space an entity with independent physical reality or just relational, but the spin networks appear to be an entity so what is really the hole arguments with regards to LQG? Can someone please clarify?

 

[julian]

Just about to turn in...Have you looked at Rovelli's book "Quantum Gravity"? There is on online draft at http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

 

[Edward Wij]

Just about to turn in...Have you looked at Rovelli's book "Quantum Gravity"? There is on online draft at http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Thanks. It may take me a week to read it. Can you give a one paragraph abstract or summary. So is loop quantum gravity spacetime an entity or relational or is it a hybrid or combination.. an entity that is relational?

 

[marcus]

Just about to turn in...Have you looked at Rovelli's book "Quantum Gravity"? There is on online draft at http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

Edward Wij, this is a very good suggestion! You were asking about the "hole argument". As I recall, Rovelli has quite a substantial section of an early chapter of that book which is devoted to the "hole argument".
It played a role in Einstein's deliberation before 1915 about whether to accept that his theory would be general covariant, or "diffeomorphism invariant".

Reading the early chapters of Rovelli's "Quantum Gravity" will certainly help put things in perspective for you. You seem to have some desire for philosophical perspective---you ask "is spacetime an entity or is it relational" . The book's first one or two chapters makes clear that the answer is relational, if you are using the word as Rovelli does in the book.
You asked about "spin network". That is not an ENTITY that is a way of describing the quantum state of geometry as a network of geometric measurements, or as a network of geometric relations.
Rather than an entity it is a finite and simple way of representing information about the geometry (the geometry is the same as the gravitational field).

 

[Edward Wij]

Edward Wij, this is a very good suggestion! You were asking about the "hole argument". As I recall, Rovelli has quite a substantial section of an early chapter of that book which is devoted to the "hole argument".
It played a role in Einstein's deliberation before 1915 about whether to accept that his theory would be general covariant, or "diffeomorphism invariant".

Reading the early chapters of Rovelli's "Quantum Gravity" will certainly help put things in perspective for you. You seem to have some desire for philosophical perspective---you ask "is spacetime an entity or is it relational" . The book's first one or two chapters makes clear that the answer is relational, if you are using the word as Rovelli does in the book.
You asked about "spin network". That is not an ENTITY that is a way of describing the quantum state of geometry as a network of geometric measurements, or as a network of geometric relations.
Rather than an entity it is a finite and simple way of representing information about the geometry (the geometry is the same as the gravitational field).

Thanks. Lee Smolin sci-am article "Atoms of

Edward Wij, this is a very good suggestion! You were asking about the "hole argument". As I recall, Rovelli has quite a substantial section of an early chapter of that book which is devoted to the "hole argument".
It played a role in Einstein's deliberation before 1915 about whether to accept that his theory would be general covariant, or "diffeomorphism invariant".

Reading the early chapters of Rovelli's "Quantum Gravity" will certainly help put things in perspective for you. You seem to have some desire for philosophical perspective---you ask "is spacetime an entity or is it relational" . The book's first one or two chapters makes clear that the answer is relational, if you are using the word as Rovelli does in the book.
You asked about "spin network". That is not an ENTITY that is a way of describing the quantum state of geometry as a network of geometric measurements, or as a network of geometric relations.
Rather than an entity it is a finite and simple way of representing information about the geometry (the geometry is the same as the gravitational field).

Long google and PF archives searches produced no hits for "experimental tests of general covariance" or "experimental tests of diffeomorphism invariance". Do you have a list of such tests already done and to be done?

Or are they in principle untestable.. and the reasons for that? If such is so. Then relational in the hole arguments are not yet proven? I'm still thinking of the superstrings spacetime. Recall the Planck scale spacetime where the superstrings are embedded are not known. What if the superstrings spacetime is the one that supports background independence and our spacetime being produced by the strings gravitons are just second order or secondary. This means our spacetime doesn't have to be relational. What is the extent of tests already done to tell which is which? And what are the current thoughts of this?

 

[julian]

On spin networks I suggest having a look at sections"1.2.1 Why loops?" and "1.2.2 Quantum space: spin networks". Rovelli talks about "the position of a loop state is relevant only with respect to other loops states, and not with respect to the background." and "Only a finite displacement of a loop carrying the loop state across another loop produces a physically different state". He explains why this allows a loop basis to be viable due to diffeomorphism invariance. The theory "admits an orthonormal basis of spin network states, which are formed by finite linear combinations of loop states." These combinatorial structures are relevant to describe the quantum gravitational field. You are told that they are eigenstates of the area and volume operators, and given the intuition that the edges carry quantum of area and the node quantum volume...

...However, it is NOT physical entity of itself as is explained on page 7 of the paper http://fr.arxiv.org/pdf/gr-qc/9806079 where Rovelli points out that the area operator is "invariant under SU(2) gauge transformations, but not under three or four dimensional diffeomorphisms. Therefore, strictly speaking it is not an observable of the theory, and we cannot directly give its spectrum physical meaning. The failure of A(Σ) to be diff-invariant is a consequence of the fact that the area of an abstract surface defined in terms of coordinates is not a diff invariant concept."

"In fact, physical measurable areas in general relativity correspond to surfaces defined by physical degrees of freedom, for instance matter (the area of the surface this table) or the gravitational field itself (the area of an event horizon)."

 

[julian]

Long google and PF archives searches produced no hits for "experimental tests of general covariance" or "experimental tests of diffeomorphism invariance". Do you have a list of such tests already done and to be done?

Or are they in principle untestable.. and the reasons for that? If such is so. Then relational in the hole arguments are not yet proven? I'm still thinking of the superstrings spacetime. Recall the Planck scale spacetime where the superstrings are embedded are not known. What if the superstrings spacetime is the one that supports background independence and our spacetime being produced by the strings gravitons are just second order or secondary. This means our spacetime doesn't have to be relational. What is the extent of tests already done to tell which is which? And what are the current thoughts of this?

In Roger Penrose The Road to Reality, A Complete Guide to the Laws of Physics, section (19.6):

“ ... Gravitation is not to be regarded as a force; for, to an observer who is falling freely (such as our astronaut A), there is no gravitational force to be felt. Instead, gravitation manifests itself in the form of spacetime curvature. Now, it is important, if this idea is to work, that there be no ‘preferred coordinates’ in the theory. For, if a certain limited class of coordinate systems were taken to be Nature’s preferred choices, then these would define “natural observer systems” with respect to which the notion of a “gravitational force could be reintroduced, and the central role of the principle of equivalence would be lost.”

"The point is, rather, the more subtle one that such special coordinates should not have a physical role to play, and that the equations of the theory should be such that their most natural expression does not depend on any particular choice of coordinates.”

The Hole argument is based on this. So I guess any experiment looking for violation of the equivalence principle...Kind of like doing experiments looking for signs of the Eather violating the principle of SR. Also the fact that Einstein spent a couple of years looking for a particular choice in which the equations of the theory take their most natural form and failed...is also a good reason to believe.

String theory - arh Smolin's paper "The case for background independence" http://fr.arxiv.org/pdf/hep-th/0507235 - might be helpful at some point.

 

[julian]

I said that you need to introduce matter to get physical spatial/temporal localisation. But actually in the pure gravity case, you can use some degrees of freedom of the gravitational field itself to what's called "deparametrise" the other gravitational degrees of freedom, but you don't get point-like localisation only localisation up to a surface I think. There is also the case of asymptotically flat spacetimes where diffeomorphisms reduce to Poincare transformations at asymptotic infinity, in which case the 9 Poincare charges are diff-invariant, possibly used to describe black holes - these are also non-local observables.

 

[Edward Wij]

I read the summary of LQG in Wikipedia. At the end there is this sentence "An alternative criticism is that general relativity may be an effective field theory, and therefore quantization ignores the fundamental degrees of freedom".

May I know what is the meaning of it.. what are the fundamental degrees of freedom in case GR is an effective field theory? Does superstring theory treat GR as an EFT? If both LQG and superstrings are not effective field theory of GR. What are the candidate Quantum Gravity theories that threat GR as EFT?

 

[Edward Wij]

I read the summary of LQG in Wikipedia. At the end there is this sentence "An alternative criticism is that general relativity may be an effective field theory, and therefore quantization ignores the fundamental degrees of freedom".

May I know what is the meaning of it.. what are the fundamental degrees of freedom in case GR is an effective field theory? Does superstring theory treat GR as an EFT? If both LQG and superstrings are not effective field theory of GR. What are the candidate Quantum Gravity theories that threat GR as EFT?

I think the above fundamental degrees of freedom is referring to strings or other stuff wherein general relativity doesn't need to be quantized.

Anyway here is a more challenging question. From Electroweak theory, we know Symmetry occurs first.. then Symmetry breaking. Could anyone give an example where it is the reverse.. that is.. where there is initially no symmetry then symmetry occurs? I'm thinking about General Relativity Equivalence Principle. Is it possible at early universe Spacetime is not symmetric and Equivalence Principle can be violated.. then after phase transition, spacetime becomes symmetric and EP rules. Would anyone give any papers that have explored these issues?