A friend of mine from St. John's College, who was recently accepted to a physics doctoral program at Penn State, asked me what my opinion of Loop Quantum Gravity is. I replied be email, and then I decided, why not tell the world!

Now, Loop Quantum Gravity is the main rival to String Theory as an attempt to quantize gravity, although it only commands about a tenth of the resources that String Theory does. The people who work on it tend to have more of a General Relativity background than a Particle Physics background, and this tends to influence what types of problems they are trying to solve.

**Warning: Unlike my other physics posts, I have made no attempt to make my commentary here accessible to non-physics people. **(Yes, that means every other time I wrote a physics post and nobody understood it, * I* was the one to blame for not making it accessible enough!)

Einstein's theory of general relativity is *background free*, meaning that it does not start with any absolute background space or time, but instead allows the spacetime geometry to be dynamically constructed from the evolution of the metric. A theory of quantum gravity ought to be similar---it ought to be expressed in a way which doesn't depend on the prior specification of any spacetime metric. I think this is really important, but no one really knows how to do this. There are many ideas, but they all have various difficulties.

In principle, I think the idea of LQG---to build spacetime out of a discrete, quantum structure---is a very elegant and moving idea. (I first got interested in quantum gravity by reading the online writings of John Baez, who used to work on LQG.) Also, the LQG people have a very beautiful quantization of space at one time, in terms of spin networks. Essentially, by doing a step-by-step quantization of GR at one time (minus the dynamics), making only a few arbitrary choices, they were able to obtain spin networks. I'm sure you [*i.e. the friend I was writing to---AW*] know what these are, but let me assure you that they are beautiful and have some deep connections to geometrical ideas.

The next step in the construction of LQG is to decide what the dynamics are. Technically, this is done either (A) by choosing a "Hamiltonian constraint" in parallel with the Hamiltonian formulation of GR, or (B) in the spin-foam formalism, by postulating some sort of sum over histories assigning an action to each spin foam. It is here which we encounter the major problem: There is no agreement over how to implement the dynamics! There are many ideas, but no consensus on what to do. Implementing dynamics seems to involve some arbitrary choices. Some of the proposed solutions seem to me obviously wrong (e.g. see Smolin's criticism of Thiemann's Hamiltonian constraint: arXiv:gr-qc/9609034). There is also a serious danger that by choosing the wrong dynamics, one breaks the diffeomorphism invariance of the theory. In the Hamiltonian approach this manifests itself in so-called "anomalies in the constraint algebra", while in the spin foam approach it is unclear whether the inner product obtained from the sum over histories really has the necessary gauge invariance. I summarized these problems in passing, with citations, in the Introduction to this article of mine: arxiv:1201.2489.

Thus---even leaving aside the critical hard problem of whether and how a continuum spacetime can emerge from a discrete description (a problem aggravated by the fact that it is difficult to see how any discrete model of spacetime besides causal sets could possibly preserve Lorentz invariance, see arXiv:gr-qc/0605006)---I would say that LQG really doesn't exist yet as a well-defined theory. Unless you consider dynamics to be an unimportant part of a theory. And finding sensible dynamics is a really hard problem, perhaps impossible.

Yet, despite the lack of dynamics, there's no end of papers where people do specific applications, like count black hole entropy, or even attempt to do quantum cosmology (basically by truncating the theory to a finite number of degrees of freedom, and then quantizing those degrees of freedom in a way which is "loopy" in spirit). But all of these things are totally provisional until one can embed them in an actual theory with dynamics. People used to be really interested in solving these hard problems, but I feel like a lot of them have now given up and are seeking more limited goals. This is a shame, since I think progress can only come by facing the hard issues head on. And maybe by showing some flexibility in how the theory is formulated.

Once one has the dynamics, again one can say nothing about the real world until one has identified the correct vacuum state. An arbitrarily constructed "weave" state that happens to look like some Riemannian geometry doesn't cut it. You have to figure out how to identify the *right* vacuum state---the one with lowest energy (once you figure out how to define that!). Many deep questions here! I think most people in LQG are asking all the wrong questions.

One can put too much emphasis on quantizing gravity---really that's backwards, we need the classical theory to emerge from the quantum theory, not vice versa. When people calculate discrete area and volume spectra for spin network edges and vertices, they've got things backwards. These are just some operators at the Planck scale. The really interesting question is not, how much "area" is associated with each spin, but how many of each type of spin crosses a given area of the vacuum state (if such a thing even exists).

I despise the ignorant bigotry which most string theorists show towards LQG, even though LQG barely exists as a theory. Their contempt is undeserved. The LQG people are trying to do something genuinely harder---to reconstruct spacetime from first principles. We don't know how to formulate string theory except by means of strings propagating in some background spacetime, or via dualities like AdS/CFT. Since the theory has gravitons, with a diffeomorphism gauge symmetry, it's clear to me there has to be some background free formulation of string theory, but no one has any idea what this would look like. And most string theorists don't even understand why it is important.

Personally (and unexpectedly for me) I've found that as someone who studies black hole theormodynamics, I can interface better with string theorists than with LQG people---the ones who are really interested in fundamental concepts, like Don Marolf and others at UCSB, for example---even though I don't really consider myself a string theorist. This may be a bit of a conceit at this point, since I've now written multiple papers on AdS/CFT. My heart is more strongly devoted to the types of ideas LQG people explore, but my mind

recognizes that they really haven't made all that much progress.

Dear Aron: Why does a continuum spacetime have to emerge from a discrete description? GR uses the continuum, but maybe that's the problem. If GR switched to a discrete description, we remove the infinity of points from in between the quanta being described. GR would still work as an extremely good approximation. But the insistence on using the Infinitessimal (A Dangerous Idea! - Amir Alexander) brings a huge issue to light. If spacetime is, at the absolute heart, quantized - then describing it as a continuum, by adding an infinity of points that just aren't there, will give you error.

Roy,

When I said that a continuum description would have to emerge from the discrete description, I actually meant that it would emerge as a good approximation, just like you say above. I didn't mean that there would

reallybe a continuum of points, but just that at much larger distance scales than the Planck length, it would be effectivelyas ifthere was a continuum, from the point of view of macroscopic observers.GR describes spacetime as a continuum, and it passes very stringent experimental tests. But that doesn't mean that the true theory has to have a continuum, but only that it has to approximate to GR in the situations where we can do experimental measurements.

Great Post ;)

Great post! Although I find it odd that "background free" -ness in GR and LQG supports spacetime relationism, but when people take about 4-D spacetime as a whole (for example when we say gravity is the curvature of spacetime) they are making statements which are clearly about spacetime substantivism.

David,

Thanks for the compliment. Personally, I think that "relationalism" and "spacetime substantism" aren't really opposites. Relationalism means that the "positions" of fields and matter are defined only in relation to each other. But why can't the spacetime metric (or whatever microscopic degrees of freedom constitute it) be itself one of the "matter fields" which is in relationship to other things? I think that's the situation in GR.

You're welcome Aron, although when you say "ignorant bigotry which most string theorists show towards LQG" I immediately think, 'hey why not use the proper term': Lubos Molt . . . (^^,) just kidding

@ David and Aron,

Interesting blog and comments. Although, my knowledge of String theory and LQG is quite laymanish, I will try to defend Motl’s blog little bit. I agree completely that some of the roughest language in physics blogs is found on his blog and such discussions should be civil. But his knowledge of theoretical physics is very thorough and he gives detailed answers to questions. I can’t believe the number of hours he must be spending on typing in a day!! I think, eventually the best theory will win as it always has. So I am not losing any sleep over it!! Anyway, I think, on LQG he may be essentially right. GR is so successful that if some theory violates Lorentz invariance and ignores dynamical connection between space time and matter-energy, it deserves to be struck out, even if there is no alternative.

Aron,

We have exchanged comments on religious issues. But I promise, this will be straight physics!

It is interesting to see that your heart is in LQG but your mind is in ST. Is this because you suspect that a final theory will be mixture of two? As I understand, the main argument for ST is its consistency, natural incorporation of all interactions etc. Do you believe, it is the only game in town? If supersymmetry is not found in the current run of LHC, would you still use some of its ideas, assuming that eventually it will be right at Planck energy?

Kashyap, I was only joking. Generally, I agree with Lubos Motl, on foundations of physics, because I happen to like Consistent Histories very much (some of the string theory is above my understanding ). But I know him for his 'take no prisoners' approach to defending string theory. So I was immediately reminded of him from Aron's comment.

Although, Im a lot less confident than Motl about the Histories approach, I find its answer to the Aharonov-Vaidman three-box paradox is pretty shocking. But I think Aron said he may do a post on Everett many worlds in the future, so maybe that would be a more appropriate place.

David,

I am surprised that you think Lubos is in favor of consistent history approach. As far as I can tell, he is firmly a "shut up and calculate" and Copenhagen person. Mostly he thinks that no interpretation is necessary and all these people (including the famous ones like Weinberg and t' Hooft) who are thinking about interpretations, are _______!! Yes. I will be interested in knowing about Aron's favorite interpretation. In general, I do read interpretation debates, very often for weird reasons like my religion and metaphysics! Ha,ha!! One thing for which there is unanimous agreement is that QM is weird and counterintuitive, which is fine with me!

Well this really is getting far away from LQG so I wont say anything more other than your take on Lubos is wrong. First the Consistent Histories approach is a modern variant of the Copenhagen interpretation, it's been amended to allow quantum cosmology. It sort of ends up looking like a single universe Everett interpretation. So there's no contradictions in saying you believe in both Copenhagen and Consistent Histories. Here's two quotes from him: "People behind Consistent Histories usually admit that their interpretation - my favorite one - is just a refinement of the probabilistic Copenhagen interpretation"

http://physics.stackexchange.com/questions/3862/is-the-consistent-histories-interpretation-of-qm-a-many-worlds-interpretation

and

"The most correct interpretation, consistent histories, was picked by 0 percent of the participants. What a pack of. . ." http://motls.blogspot.co.uk/2013/01/poll-about-foundations-of-qm-experts.html

I think Aron likes QBism.

David,

Yes. Discussion of interpretations is going too far away from the blog subject of LQG. Aron may not want to spend his bits on it now. But let me say little bit any way. I have not studied consistent histories. So your opinion that consistent histories is a modern variant of Copenhagen may very well be right. But according to the survey of people who make their living by studying these things (see, Sean Carroll’s blog on “most embarrassing graph in modern physics”) consistent histories 0%. Copenhagen 42% and MWI 18%. Lubos may be upset that MWI got more votes than consistent histories! Anyway, the whole field is confused now and you can find just about any opinion. Lubos’ contempt of the whole field of foundations of QM and philosophy is well-known. I trust Lubos’ opinion on theoretical physics, but on other matters, sometimes you have to take it with a ton of salt!!

David,

Sorry. After writing the above comment, I realized that you (and Lubos and Sean) are referring to the same survey. Of course, this does not change any thing. What Sean calls embarrassing , Lubos calls ------!

Kashyap,

I think string theory should be regarded as tentative unless and until it makes a sufficiently specific prediction which is confirmed by actual experimental evidence. In the meantime, I think it is valuable as a mathematical toy model which incorporates various ideas, whether or not it is the correct theory of nature...

Also, from the theoretic point of view string theory as we currently have it, apart from its role in certain dualities, is defined only by a perturbative expansion about a backgroud spacetime metric. The final theory, if it to be like GR, must be formulated in a way which is independent of an

a priorispecification of the spacetime metric.LQG is attempting this more ambitious approach, but it cannot yet recover a continuum spacetime geometry. So people are building the bridge from both sides, but there is no guarantee at all that they will meet in the middle!

Aron,

Thanks. Some more questions. Is your current research completely different from either ST or LQG? What is your opinion on Ashtekar's work? Is it promising? I am trying to get some idea on various current models of QG.

I can't help but over read this and I would recommend Lee Smolins book "three roads to quantum gravity" he talks about LQG and String stuff and CDT and in chapter three why he likes Consistent Histories ;)

David,

Thanks for the suggestion. But I am turned off completely by Smolin's LQG which violates

Lorentz invariance and has problems with classical GR. So I will not spend money to buy his book!!!

Some time later I will try to understand CDT and perhaps try to find Smolin's book in library! But in the meantime ST is ok with me even without any experimental proof !

kashap,

My research focusses on black hole thermodynamics, which is probably going to be relevant regardless of whether ST, LQG, both, or neither turns out to be correct. That's one of the reasons I picked the research topic: I don't want all my work to go to waste if I bet on the wrong horse!

However, some of my work on gravity and black holes connects to AdS/CFT, which is usually regarded as a string theory topic. I actually suspect that

anyconsistent theory of quantum gravity should obey the holographic principle and therefore (if the cosmological constant is negative) an analogue of AdS/CFT. But the actually worked out examples are all from string theory.I agree that LQG

probablyviolates Lorentz invariance, but I don't think we can know for sure until somebody constructs the appropriate dynamics! And Lorentz violation is an issue with CDT as well. (As well as my own personal nutty model described here.) If you want a discrete model of spacetime which has Lorentz symmetry built in, you could try causal sets, although that has its own problems.By the way, this contradicts my first paragraph slightly, but if you have Lorentz violation, it turns out that this ruins BH thermodynamics. This was the subject of my first two publications!

PS I never expected the LHC to find supersymmetry.

if edward witten were to work on LQG dynamics and vaccuum state do you think he could solve it? would it appeal to other physicists?

what if,

Presumably if Ed had a good idea of how to solve the problems with LQG, he would have published them. There are a bunch of people already working on LQG, I assume it appeals to them, or they'd be working on something else.

what is ed wittens opinion of lqg and other string theorists? ive heard ed witten is the smartest man alive but hes never worked on lqg ever

Dear Aron,

Do you think Christians will have to change much about their theological beliefs if LQG or String Theory turns out to be true?

Andrew,

No, I don't think there would be all that much change. We already know that the universe is, most of the time, well-described by a set of mathematical rules. Why should things become any different just because the precise form of those rules changes?

There is a possible effect on certain specific arguments for the existence of God. Potentially, learning the correct theory of quantum gravity might make the Fine Tuning Argument (that God chose the laws of physics in order to produce life) stronger or weaker. For example, String theory has potential ways to produce a giant Multiverse, which is the most popular rival explanation.

Similarly, once we understand String theory or LQG better than we now do (so really this goes beyond your question) it might give us a better understanding of early universe cosmology, and that might (or might not) explain the low entropy intitial conditions of the universe. It also might (or might not) make it more or less likely that the universe had a beginning, something which is strongly correlated with Theism in many people's minds (though not mine), and is traditionally regarded as a Christian doctrine (Gen 1:1). Of course, Science

alreadyrequires us to interpret various aspects of Genesis as symbolic rather than literal, so there may be some room for flexibility here.Apart from this single issue, the worst case scenario seems to be that we lose a couple arguments for the existence of Theism (but there are other arguments are unaffected, such as this type of Cosmological Argument). The best case scenario is that those arguments get strengthened.

It's important to realize that God's existence does not depend on our ability to argue for his existence in particular ways. There are lots of arguments for Theism, and we shouldn't expect them all to pan out in the end. That's okay, as long as we have other ways of coming to know God. Myself, the primary reason that I am a Christian is the historical death and resurrection of Jesus Christ. I don't see how the historical evidence for miracles and so on would be affected in any way by progress in fundamental physics.

Hope this is clear.

Thanks Aron, very helpful !! :)

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