A useful analogy to illustrate the meaning of a low-energy effective theory of gravity is to compare with hydrodynamics. The fluid equations of hydrodynamics are only approximate and do not describe the individual, complicated and chaotic motion of molecules. For most fluid applications the detailed behavior of the molecules is in fact completely irrelevant. We need to look at very detailed properties of a fluid, e.g. through a strong microscope, to see the individual molecules. We can see signs of the molecules when we observe the Brownian motion of a dust particle on the fluid, but what we observe is apparent statistical and chaotic Brownian behavior rather than the precise microscopic behavior of all individual molecules.
The analogy with hydrodynamics is probably more than just an analogy, as we have good reasons to believe that gravitational theories also consist of complicated microscopic chaotic building blocks. In contrast to the situation with fluids, we do not have a suitable microscope to see those, as the required energies are well beyond reach. We can however see statistical features of the chaotic building blocks in suitable gravitational low-energy computations, similar to the average diffusion that a Brownian particle experiences. The entropy of a black hole, for example, provides us with a fairly precise estimate of the statistical entropy of the building blocks. This leads to a suggestive picture where low-energy gravity is a theory which is able to uncover coarse-grained, statistical properties of the building blocks, but is unable to recover the individual building blocks.
In CanISeeQG we collect evidence for this perspective on what a gravitational theory is and try to make precise, quantitative predictions based on this perspective. A possible and not unlikely outcome is that gravity is the theory in nature which is maximally good at hiding its quantum features from observation, which would have interesting conceptual but also philosophical implications.
So far, various projects which are part of CanISeeQG have led to partial but important progress in this direction. One objective was to make the analogy between hydrodynamics and gravity more precise and to import some of the known results from hydrodynamics into the gravitational realm. Gravity has certain universal features, and one first needs to quantify the types of hydrodynamical systems which have similar universal IR behavior. This is currently under investigation, inspired by the universal behavior of black hole horizons.
As part of another objective, we have been able to greatly clarify to what extent gravity captures statistical features of the underlying microscopic theory. If gravity perceives only statistics, it will also in suitable circumstances perceive statistical correlations without there being any actual correlations. We proposed that such perceived statistical correlations are represented in gravitational theories by non-trivial geometric solutions of the field equations that typical resemble wormholes. We have been able to substantiate this claim in various concrete examples. To leading order, purely Gaussian correlations are the most important ones, but we also found examples where higher correlations are important. This series of papers has also led to follow-up work by other authors who have added further important details to this picture.
It is tempted to speculate that what is eventually needed is a generalization of statistical mechanics where the input is just a set of experimental/computational data and the output is a description of a system with maximal uncertainty compatible with the inputs given. Statistical mechanics is very much like this, where the input is the measured energy plus precise knowledge of the Hamiltonian, and the output is the canonical ensemble. Here, we would also only have approximate knowledge of the Hamiltonian, and the result will possibly involve a classical statistical average over quantum mechanical density matrices. An initial attempt to develop this formalism has led to interesting preliminary results with intriguing connections to random matrix theory and the so-called eigenstate thermalization hypothesis on which we hope to report soon.
While such a statistical picture yields a compelling picture of classical gravitational physics, most of the relevant computations are performed in spacetimes with rigid boundaries and involve operator insertions on those rigid boundaries. The translation of the results to observers which are not part of the rigid boundary involves a second step which sometimes goes under the name of “bulk reconstruction”. Bulk reconstruction, especially for observers who fall into black holes, has a notorious yet subtle ambiguity whose technical name is the “frozen vacuum problem.” We are currently exploring various new ideas on how to deal with this ambiguity using ideas from quantum information theory. The combination of this ongoing work, if successful, together with the statistical interpretation of low-energy gravity (which also involves substantial ongoing work) would go a long way towards realizing the overall goal of CanISeeQG.
