Information Theoretic Foundations for Physics
Recent developments reveal a deep connection between entanglement entropy and the emergence of space time and gravity. In anti-de Sitter space gravity appears to be derived from the first law of thermodynamics for entanglement entropy, which in the large radius limit obeys an area law. Based on insights from string theory, we propose a generalisation of these results to flat space and de Sitter space. In the latter case, the vacuum entanglement entropy has an additional contribution that scales like the volume of the bulk space time.
Remote talk by teleconference
In science, we often see new advances and insights emerging from the intersection of different ideas coming from what appeared to be disconnected research areas. The theme of my seminar will be an ongoing collision between the three topics listed in my title which has been generating interesting new insights into a variety of fields, eg, condensed matter physics, quantum field theory and quantum gravity.
The second law of thermodynamics appears to be a universal law of physics. This universality suggests that entropy and with it information theory is part of the foundations of physics.
Classical and quantum theories are very different, but the gap between them may look narrow particularly if the notion of classicality is broadened. For example, if we do not impose all the classical assumptions at the same time, hidden variable theories reproduce the results of quantum mechanics. If a quantum system is restricted to Gaussian states, evolution and measurements, then classical phase space mechanics with a finite resolution fully reproduces its behavior.
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. This is an expression of Leibniz's principles of sufficient reason and the identity of the indiscernible.
To make precise the sense in which nature fails to respect classical physics, one requires a formal notion of "classicality". Ideally, such a notion should be defined operationally, so that it can be subjected to a direct experimental test, and it should be applicable in a wide variety of experimental scenarios, so that it can cover the breadth of phenomena that are thought to defy classical understanding.
I will discuss my work (in progress) to formulate General Relativity as an operational theory which includes probabilities and also agency (knob settings). The first step is to find a way to discuss operational elements of GR. For this I adapt an approach due to Westman and Sonego. I assert that all directly observable quantities correspond to coincidences in the values of scalar fields. Next we need to include agency. Usually GR is regarded as a theory in which a solution is simply stated for all space and time (the Block Universe view).
It has become conventional wisdom to say that quantum theory and gravitational physics are conceptually so different, if not incompatible, that it is very hard to unify them. However, in the talk I will argue that the operational view of (quantum) information theory adds a very different twist to this picture: quite on the contrary, quantum theory and space-time are highly fine-tuned to fit to each other.