Panel Discussion

To turn LQG into a predictive theory, it will be essential to understand how to extract universal features from the dynamics of quantum geometry, and cleanly separate them from contingent/practical choices that have been made in the construction of the formalism (e.g. ambiguities related to the choice of variables, quantization map, kinematical vacuum, Hamiltonian constraint etc.). To reach this goal, it would be highly desirable to develop convincing toy-models explaining how a smooth space-time structure could potentially emerge from the dynamics of quantum geometry (what the Ising model is to the theory of magnetization: a simple theory that captures the key mechanism driving the phase transition of interest).

What’s essential:

i) that we couple to matter

ii) that we make clear the conceptual assumptions and benefits of LQG, i.e. if it is not THE theory of quantum gravity (which it isn’t) then why is it still useful to consider it?

It will be essential to the future of LQG to develop formal and phenomenological aspects of the theory in constant dialogue, based on a coherent philosophy of what the underlying theory is.

To take seriously suggestion of the approach that physics is discrete at the Planck scale and that there are way more degrees of freedom in the UV than those naively expected from purely canonical methods. Even when this is not always clear in present analysis, it should play a central role in the future: specially in discussions about black hole formation and evaporation, cosmology, and phenomenology.

To take seriously suggestion of the approach that physics is discrete at the Planck scale and that there are way more degrees of freedom in the UV than those naively expected from purely canonical methods. Even when this is not always clear in present analysis, it should play a central role in the future: specially in discussions about black hole formation and evaporation, cosmology, and phenomenology.

Thinking of quantum gravity as the straightforward result of quantizing (by canonical, covariant or other methods) the gravitational field means requiring that the fundamental degrees of freedom of the universe remain the same as in the classical theory, just turned into quantum ones, and that the same is true for their dynamics. On the other hand, both the classical degrees of freedom we are used to (e.g. the metric or the gravitational connection) and the properties and dynamics they satisfy could be approximate, collective or otherwise emergent only. That they are recovered in some approximation is necessary to have a viable theory, but we simply do not know whether they should be part of the very definition of the fundamental theory. On the other hand, insisting on them being part of the fundamental theory could be an obstacle in defining it and/or in gaining control over it. In particular, it may make the continuum approximation harder to study, the true fundamental degrees of freedom harder to identify, if different, and the very emergence of spacetime as we know it mysterious. Moreover, sticking to a too-rigid conceptual and/or mathematical framework (e.g. canonical or covariant quantization of GR) could make it harder to learn from other approaches to quantum gravity, to import their insights and results into ours. The classical continuum theory and its structures should be useful reference points, to be kept within sight, but not more. Quantizing them gives precious insights on what could be part of the fundamental picture, but not more. We need conceptual and mathematical flexibility to predispose ourselves to find out what works toward our goal (understanding what a quantum spacetime is and how the classical world emerges out of it), and to be ready to question our assumptions (including our very basic ones) whenever doing so may help. What to maintain and what to leave behind in the process is ambiguous, and this is both necessary and good: we need to explore different choices and different paths; as many as possible, in fact.

An essential feature to the future developments of quantum gravity to me is to identify possible phenomenology, which includes (but is not limited to) low-energy tests of the quantum nature of gravity. This could shed light on what the (quantum?) nature of the gravitational field is, and on deep conceptual problems related to the nature of space, time, and causality at the interface of gravity and quantum theory.

To apply the theory to the real world. Go from mathematical physics to physics. There are open issues and variants, but we have a theory. And it is a very good theory, the best on the market. The problem is to see if it works, what we can do with it: find support in observations. Cosmology, dark matter, black holes...