The Road Less Traveled… To Quantum Gravity

An interview with theoretical physicist Lee Smolin.

In 2001, Lee Smolin, one of the main thinkers in , published the popular science book, in which he laid out his hopes and vision for the future of the field.

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In this book, Lee — always the optimist — made the prediction that

“We shall have the basic framework of the quantum theory of gravity by 2010, 2015 at the outside.”

When I visited Perimeter Institute some weeks ago I figured time had come to revisit this prediction.

Sabine: Thanks for sharing your thoughts with us! So, what are the “Three roads” that the book title is referring to?

Lee: The thee roads were loop quantum gravity, string theory and the right theory, which I was arguing might have elements of one or even both of the first two, but would incorporate other ideas which are still missing.

Are we there yet? Where are we?

“To be there” would be not just to have a consistent quantum theory of gravity, but to have tested experimental predictions made by that theory and have had some confirmation of those predictions. We are not there.

But we are a lot further along towards that goal then we were when I wrote 3 roads in 2000.

As I will explain, we may already “have the basic framework of the quantum theory of gravity”. But it is too soon to know this with any assurance. So, strictly speaking, I was not wrong, but I also did not ask for enough.

We do have several different theories which have been intensively developed. Each has definite successes. Each also has well understood defects, or points on which they are stuck, which make it difficult to believe that they are the whole story.

I’ll detail these in a minute, after which I’ll make the case that one may be the basic framework for quantum gravity.

But first, I want to mention that we have something at least as important, which is a domain of experiment which has opened up where serious hypotheses about quantum gravity have been tested. These include high energy astrophysical observations as well as some cosmological observations. So far no quantum gravity phenomena have been identified but, remarkably, some very plausible ideas have already been ruled out. These include the hypothesis that Lorentz invariance is broken to leading order in the ratio of energies to the Planck energy.

Here is my very brief accounting of the strengths and weaknesses of the various approaches to quantum gravity.

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Image credit: © WGBH Educational Foundation, via .

String theory advantages:

  • Naturally unifies gravity, gauge fields and fermions perturbatively.
  • Consistent and finite up to two loops (going beyond to a full proof of finiteness is still an open problem despite progress understanding higher genus amplitudes.)
  • Provides examples of Ads/CFT conjecture when the cosmological constant is negative.
  • Accounts for the entropy of extremal and near extremal black holes.

String theory disadvantages:

  • no proof of finiteness past genus two.
  • no background independent formulation or non-perturbative definition.
  • AdS/CFT doesn’t work when cosmological constant is positive, as in nature.
  • Landscape problem, due to the vast number of compactifications.
  • it is hard to stabilize all the moduli that must be fixed in a compactification.
  • In spite of that, there is still no version that reproduces the standard model; generic compactifications that include the standard model also include exotic states that are not seen.
  • no accounting of entropy of generic, non-extremal black holes.
  • requires supersymmetry and extra dimensions (at unspecified scales), which so far are not seen.
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Image credit: Manny Lorenzo, via .

Loop quantum gravity advantages:

  • Generic method for quantizing diffeomorphism invariant gauge field theories, including general relativity coupled to various kinds of matter fields.
  • The path integral sum over spins is ultraviolet finite, and also infrared finite for non-zero cosmological constant.
  • The emergence of general relativity from the semiclassical approximation of the path integral is understood.
  • It accounts for the entropy of generic black hole and cosmological horizons.
  • It makes robust predictions for discrete quantum geometry.
  • There are many successes of method on models in 2+1 and 1+1 dimensions as well as topological field theories.
  • Applied to cosmological models, it gives robust predictions of a bounce replacing the cosmological singularity.

Loop quantum gravity disadvantages:

  • So far nothing robust to say about unification or origin of standard model (but there are suggestions such as extended Plebanski and graviweak unification.)
  • No clean results yet on summing over triangulations in the path integral.
  • Renormalization or course graining hard to define.
  • No robust predictions yet for quantum gravity phenomenology such as breaking or deformation of lorentz invariance.
  • No quantum positive energy theorem.
  • There are open issues regarding chiral fermions in the Hamiltonian theory.
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Image credit: 5-cell (4-simplex), relevant for CDT, by Wikipedia user .

Causal dynamical triangulations advantages:

  • Sums over triangulations can be computed, leading to emergence of spacetime.
  • Dimensional reduction discovered.

Causal dynamical triangulations disadvantages:

  • It appears to be in universality class of Horava-Lifshitz theory, which is distinct from general relativity because of extra degrees of freedom.
  • It has nothing to say about unification.

Causal sets (pure version) advantages:

  • Elegant definition with few assumptions and strong motivation.

Causal sets (pure version) disadvantages:

  • hard to show low dimensional spacetime emerging (but this can be shown in inpure versions such as energetic causal sets.)
  • It has nothing to say about unification.

Asymptotic safety advantages:

  • It gives a perturbative resolution of non-renormalizability.

Asymptotic safety disadvantages:

  • There are known asymptotic theories that have problems with positivity and unitarity. Not known if there are any versions which avoid these fatal difficulties.

My view is that, of all of these, the strongest case can be made for loop quantum gravity.

String theory starts of with some attractive features. But in general, it requires extraneous hypothesizes such as supersymmetry and extra dimensions, for which there is no observational evidence. These vastly complicate the theory by the incorporation of large numbers of extraneous degrees of freedom that are not seen in nature as well as long lists of additional parameters to describe how supersymmetry is broken and the extra dimensions are compactified. These add tremendous arbitrariness and complications that have no payoff for explaining anything in nature.

There are features of string theory that involve elegant mathematics, but these mostly apply to the study of unphysical model systems such as compactifications that only break the supersymmetry down to N=2 or N=4 or higher. The physically relevant cases of breaking to N=1 or N=0 are not so elegant. The tradition of mathematical physics is full of elegant mathematical models which don’t describe nature, string theory seems to yield a great many models of this kind.

Finally, the persistent open issues which stand in the way of taking string theory as a fundamental theory are long standing and there is no reason to believe progress can be made on them. Indeed, few have even worked on them over the last decade. These issues include the problem of ultraviolet finiteness, the lack of a background independent formulation, and the landscape problem, which prevents the theory from making any predictions.

Of course, given that we don’t really know what string theory is, it remains possible that new principles will emerge which solve these issues while giving an entree to experiment. In this regard I am intrigued by the recent work on metastrings, by Freidel et al, which tie them to the principle of relative locality.

On the other hand, loop quantum gravity assumes only features of nature that are well established: which are the principles of general relativity and quantum mechanics. Beyond these, it makes only a few technical assumptions that appear to be necessary to consistently marry these principles to each other. It yields a beautiful and robust description of quantum geometry, which allows the Einstein equations to be represented quantum mechanically. There are good indications that general relativity is indeed the semiclassical limit.

Two other approaches also assume only the principles of general relativity and quantum theory: causal dynamical triangulations and asymptotic safety. Each yields a picture of quantum geometry, unfortunately there is reason in each case to believe that it yields an unphysical theory, in asymptotic safety an unstable theory, and in causal dynamical triangulations a theory without the full spacetime diffeomorphism invariance of general relativity.

This is not to ignore the open issues of loop quantum gravity, these are challenging, but there is no reason of principle to suggest they are not solvable.

What was it that made you so optimistic back then and what was it that didn’t go according to plan?

I was very optimistic because both string theory and loop quantum gravity had developed into significantly stronger and more compelling theories in the decade between 1990 and 2000. These include the introduction of path integral techniques in loop quantum gravity, which address dynamics much better than the previously studied hamiltonian dynamics, as well as an understanding of how to treat horizons leading to computations of the black hole entropy. Simultaneously, string theory went through its duality and M theory revolutions. Both sets of developments were exhilarating. It was very plausible to me at that time that string theory and loop quantum gravity were just different sides of the same phenomena. Each expresses the duality of quantum gauge fields and extended objects-loops or field lines. String theory does that in a fixed non-dynamical background, loop quantum gravity does it in a deeper, background independent way.

At the same time we had the beginnings of work on quantum gravity phenomenology and it was plausible that within a decade or so we would detect the discrete structure of space predicted by loop quantum gravity through violations or deformations of lorentz invariance.

Since then, in my view, progress on string theory related to quantum gravity has been slower, while there has been steady progress in understanding loop quantum gravity. But neither has made any contact with experiment. But note that there have been near misses such as BICEP.

What would convince you that a theory of quantum gravity is the right theory of quantum gravity?

A robust prediction tested and confirmed by an experiment.

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Image credit: Perimeter Institute for Theoretical Physics, 2012. Via .

Where do you think should the community direct its efforts now?

I believe strongly that we should encourage new ideas and new research programs. We should support and promote people who have their own high risk/high payoff ideas and who follow their own compasses-valley crossers in the landscape of ideas rather than hill climbers. We should give incentives to people to change their research direction and seek new directions and discourage people who follow long standing established research programs and do “me-too” science. This was of course the point of my .

While we’re all still waiting on quantum gravity both theoretically and experimentally, we’re also convinced . It’s just a matter of getting there, which may prove to be either right around the corner or off at the far reaches of the great energy desert.

Update (6/12): Lee Smolin has the following addition to make to this article.

If I can add a thought, I should have emphasized that, in my view, all the standard approaches are lacking two important pieces of the puzzle. The first is that I believe that quantum theory requires a completion, in a deeper theory that allows a complete description of individual processes. I see no other way to resolve the measurement problem. This may not invalidate one the approaches to quantum gravity based on conventional quantum theory, so long as they are understood as a theory of small subsystems of the universe. Extending the description to the universe as a whole will, I am convinced, require new principles. Similarly, I am convinced that time needs to be described as fundamental and irreversible, for reasons I have set out in detail in my last two books, Time Reborn and the Singular Universe. Part of this is the mandate that if the landscape problem is to be solved, laws must have an evolutionary dynamics of their own. One of the reasons I remain interested in loop quantum gravity, is that I believe it may provide a framework and ontology for microscopic physics, within which these radical reconfigurations of time and quantum theory can be situated. As evidence for this I can offer the fact that certain spin foam models invented by Wolfgang Wieland can be read as energetic causal sets, as developed with Marina Cortes.

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