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. In this talk I take the opposite (probably more conservative) approach: I assume that the dynamics of relational degrees of freedom form the foundation of physics. Physical information is an emergent phenomenon. This approach has an interesting consequence: Typical (initial) data for a gravitationally dominated universe leads to the spontaneous emergence of a gravitational arrow of time for the universe as a whole. This primary gravitational arrow of time generates secondary thermodynamic arrows of time in sufficiently isolated subsystems of the universe, which coincide with the gravitational arrow of time. This coincidence explains the universality of the second law of thermodynamics. I will also explain why a recent criticism by Zeh is due to a fundamental misunderstanding of this framework and compare the gravitational arrow of time with work by Carrol and Guth who consider an apparently similar setting but without gravity.

Weakly isolated horizons (WIHs) have played a key role in state counting calculations for black hole entropy from Loop Quantum Gravity which is rooted in a first order formulation of gravity. In principle, imposing WIH boundary conditions should not restrict the additional Lorentz gauge freedom of a first order description. However, we will argue that the requirement of a well defined variational principle may actually do so, shedding some light on an old controversy surrounding this subject.

In contrast to relativity, quantum theory has evaded a commonly accepted apprehension, in part because of the lack of physical statements that fully characterize it. In an attempt to remedy the situation, we summarize a novel reconstruction of the explicit formalism of quantum theory (for arbitrarily many qubits) from elementary rules on an observer’s information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and define S’s state as O’s “catalogue of knowledge” about S; no ontic assumptions are necessary. From the rules, one can derive, among other things, the state spaces, the unitary group, the von Neumann evolution and show that the binary questions correspond to Pauli operators. The reconstruction also offers new structural insights in the form of novel informational charges and informational complementarity relations which define the state spaces and the unitary group. This reconstruction permits a new perspective on quantum theory. (Based on arXiv:1412.8323 and arXiv:1511.01130.)

The talk will focus on issues connected with the quantization of initial data for vacuum general relativity on null hypersurfaces. After a brief review of a classical canonical formulation of general relativity in terms of unconstrained null data, I will present recent joint work with Andreas Fuchs bearing on the quantization of the main null initial data. We note that the Poisson brackets of these data are almost the same in cylindrically symmetric gravity as in the full theory, and we use a non-linear and non-local change of variables to transform the Poisson brackets in the cylindrically symmetric case into a form that has a known quantization. Note that the talk deals with putting the classical theory in a quantizable form. Very little will be said about the quantum theory itself.