Phenomenological Quantum Gravity

Participants of the 2012 conference on 
Experimental Search for Quantum Gravity.

The search for quantum gravity and a theory of everything captures the public imagination like no other area in theoretical physics. It aims to answer three questions that every two-year old could ask if they would just stop being obsessed with cookies for a minute: What is space? What is time? And what is matter? We know that the answers we presently have to these questions are not fundamentally correct; they are merely approximately correct. And we want to know. We really really want to know. (The cookies. Are out.)

Strictly speaking of course physics will not tell you what reality is but what reality is best described by. Space and time are presently described by Einstein’s theory of general relativity; they are classical entities that do not have quantum properties. Matter and radiation are quantum fields described by the standard model. Yet we know that this cannot be the end of the story because the quantum fields carry energy and thus gravitate. The gravitational field thus must be compatible with the quantum aspects of matter sources. Something has to give, and it is generally expected that a quantization of gravity is necessary. I generally refer to ‘quantum gravity’ as any approach to solve this tension. In a slight abuse of language, this also includes approaches in which the gravitational field remains classical and the coupling to matter is modified.

Quantizing gravity is actually not so difficult. The problem is that the straight-forward, naive, quantization does not give a theory that makes sense as a fundamental theory. The result is said to be non-renormalizable, meaning it is a good theory only in some energy ranges and cannot be taken to describe the very essence of space, time, and matter. There are meanwhile several other, not-so-naïve, approaches to quantum gravity – string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and a handful of others. The problem is that so far none of these approaches has experimental evidence.

This really isn’t so surprising. To begin with, it’s a technically hard problem that has kept some of the brightest minds on the planet occupied for decades. But besides this, returns on investment have diminished with the advent of scientific knowledge. The low hanging fruits have all been picked. Now we have to develop increasingly more complex experiments to find new physics. This takes time, not to mention effort and money. With that, progress slows.

And quantum gravity is a particularly difficult area for experiment. It’s not just a weak force, it’s weaker than the weak force! This grammatical oxymoron is symptomatic of the problem: Quantum effects of gravity are really, really tiny. Most of the time when I estimate an effect, it turns out to be twenty or more orders of magnitude below experimental precision. I’ve sometimes joked I should write a paper on “50 ways one cannot test quantum gravity”, just to make use of these estimates. It’s clearly not a low hanging fruit, and we shouldn’t be surprised it takes time to climb the tree.

Some people have claimed on occasion that the lack of a breakthrough in the area is due to sociological problems in the organization of knowledge discovery. There are indeed problems in the organization of knowledge discovery today. We use existing resources inefficiently, and I do think this hinders progress. But this is a problem which affects all of academia and is not special to quantum gravity.

I think the main reason why we don’t yet know which theory describes gravity in the quantum regime is that we haven’t paid enough attention to the phenomenology.

One reason phenomenological quantum gravity hasn’t gotten much attention so far is that it has long been believed experimental evidence for quantum gravity is inaccessible to experiment (a belief promoted prominently by Freeman Dyson). The more relevant reason is though that in the field of theoretical physics it’s a very peculiar research topic. In all other areas of physics, researchers share either a common body of experimental evidence and aim to develop a good theory. Or they share a theoretical framework and aim to explore its consequences. Phenomenological quantum gravity has neither a shared theory nor a shared set of data. So what can the scientist do in this situation?

Methodology

The phenomenology of quantum gravity proceeds by the development of models that are specifically designed to test for properties of the yet-to-be-found theory of quantum gravity. These phenomenological models are normally extensions of known theories and are developed with the explicit aim of testing for general features. These models do not aim to be fundamental theories on their own.

Examples of such general properties that the fundamental theory might have are: violations or deformations of Lorentz-invariance, additional space-like dimensions, the existence of a minimal length scale or a generalized uncertainty principle, holography, space-time fluctuations, fundamental discreteness, and so on. I discuss a few examples below. If we develop a model that can be constrained by data, we will learn what properties the fundamental theory can have, and which it cannot have. This in turn can serve as guidance for the development of the theory.

In practice, these phenomenological models quantify deviations from general relativity and/or quantum field theory. One expects that the only additional dimensionful scale in these models is the Planck scale, which gives a ‘natural’ range for the expected size of effects in which all dimensionless constants are of order one. The aim is then to find an experiment that is sensitive to this natural parameter range. Since most of these models do not actually deal with quanta of the gravitational field, I prefer to speak more generally of “Planck scale effects” being what we are looking for.

Example: Lorentz-invariance violation

The best known example that demonstrates that effects are measureable even when they are suppressed by the Planck scale are violations of Lorentz-invariance. You expect violations of Lorentz-invariance in models for space-time that make use of a preferred frame that violates observer-independence, for example some regular lattice or condensate that evolves with some special time-slicing.

Such violations of Lorentz-invariance can be described by extensions of the standard model that couple to a time-like vector field and these couplings change the predictions of the standard model. Even though the effects are tiny, many of them are measureable.

The best example is maybe vacuum Cherenkov-radiation: the spontaneous emission of a photon by an electron. This process is normally entirely forbidden which makes it a very sensitive probe. With Lorentz-invariance violation, an electron above a certain energy will start to lose energy by radiating photons. We thus should not receive electrons above this threshold from distant astrophysical sources. From the highest energies of electrons of astrophysical origin that we have measured we can thus derive a bound on the possible violation of Lorentz invariance. This bound is today already (way) beyond the Planck scale, which means that the natural parameter range is excluded.

This shows that we can constrain Planck scale effects even though they are tiny.

Now this is a negative result in the sense that we have ruled out certain properties. But from this we have learned a lot. Approaches which induce such violations of Lorentz-invariance are no longer viable.

Example: Lorentz-invariance deformation

Deformations of Lorentz-invariance have been suggested as symmetries of the ground state of space-time. In contrast to violations of Lorentz-invariance, they do not single out a preferred frame. They generically lead to modifications of the speed of light, which can become energy-dependent.

I have explained a great many times that I think these models are flawed because they bring more problems than they solve. But leaving aside my criticism of the model, it can be experimentally tested. The energy dependence of the speed of light is tiny – a Planck scale effect – but the measurable time-difference adds up over the distance that photons of different energies travel. This is why highly energetic photons from distant gamma ray bursts are presently receiving a lot of attention as possible probes of quantum gravitational effects.

The current status is that we are just about to reach the natural parameter range expected for a Planck scale effect. It is presently a very active research area.

Example: Decoherence induced by space-time foam

If space-time undergoes quantum fluctuations that couple to all matter fields, this may induce decoherence in quantum mechanical oscillations. We discussed this previously in this post. In oscillations of neutral Kaon systems, we are presently just about to reach Planck scale sensitivity.

Misc other examples

There is no lack of creativity in the community! Some other examples of varying plausibility that we have discussed on this blog are Craig Hogan’s quest for holographic noise, Bekenstein’s table-top experiment that searches for Planck-length discreteness, massive quantum oscillators testing Planck-scale modified commutation relations, and searches for evidence for a generalized uncertainty in tritium decay. There is also a vast body of work on leftover quantum gravitational effects from the early universe, captured in various models for string cosmology and loop quantum cosmology, and of course there are cosmic (super) strings. There are further proposed tests for the idea that gravity is just classical (still a little outside the natural parameter range), and suggestions to look for dimensional reduction.

This is not an exhaustive list but just to give you a sense of the breadth of the topics.

Demarcation issues

What counts and what doesn’t count as phenomenological quantum gravity is inevitably somewhat subjective. I do for example not count the beyond the standard model physics of grand unification, though, if you believe in a theory of everything, this might be relevant for quantum gravity. I also don’t count applications of AdS/CFT because these do not describe gravitational systems in our universe, though arguably they are examples for some quantized version of gravity. I also don’t count general modifications of quantum theory or general relativity, though these might of course be very relevant to the problem. I don’t label these phenomenological quantum gravity mostly for practical reasons, not for ideological ones. One has to draw the line somewhere.

Endnote

I often get asked which approach to quantum gravity I believe in. When it comes to my religious affiliation, I’m not only an atheist, I was never Christianized. I have never belonged to any church and I have no intention to join one. The same can be said about my research in quantum gravity. I don’t belong to any church and have never been Christianized. I have on occasion erroneously been called a string theorist and I have been mistaken for working on loop quantum gravity. Depending on the situation, that can be amusing (on a conference) or annoying (in a job interview). For many people it still seems to be hard to understand that the phenomenology of quantum gravity is a separate research area that does not built on the framework of any particular approach.

The aim of my work is to identify the most promising experiments to find evidence for quantum gravity. For that, we need phenomenological models to quantify the effects, and we need to understand the models that we have (for me that includes criticizing them). I follow with interest the progress in various approaches to quantum gravity (presently I’m quite excited about Causal Sets) and I try to develop testable phenomenological models based on these developments. On the practical side, I organize conferences and workshops to bring together theoreticians with experimentalists who have an interest in the topic to stimulate exchange and the generation of new ideas.

What I do believe in, and what I hope the above examples illustrate, is that it is possible for us to find experimental evidence for quantum gravity if we ask the right questions and look in the right places.