Scientific Series

A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. Two fundamental challenges to any such approach are, at the conceptual level, the role of time in the emergent context and, technically, the fact that the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics and quantum field theory to the problem. We initiate a study of such problems using spin systems as toy models for emergent geometry and gravity. These are models of quantum networks with no a priori geometric notions. In this talk we present two models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This is essentially a Hubbard model on a dynamical lattice. We will see that regions of high connectivity behave like analogue black holes. Particles in their vicinity behave as if they are in a Schwarzchild geometry. Time permitting, I will show our study of the entanglement entropy of the system, which suggests particle localization near these traps.

There is now a consensus that gamma-ray bursts involve extraordinary power outputs, and highly relativistic dynamics. The trigger is probably a binary merger or collapse involving compact objects. The most plausible progenitors, ranging from NS-NS mergers to various hypernova-like scenarios, eventually lead to the formation of a black hole with a debris torus around it. The various modes of energy extraction from such systems are discussed.

Today there is robust observational evidence of dark and compact objects in X-ray binary systems with a mass of 5-20 $M_\odot$ and in galactic nuclei with a mass of $10^5 - 10^9$ $M_\odot$. The conjecture is that all these objects are the Kerr black holes predicted by General Relativity, as they cannot be explained otherwise without introducing new physics. However, there are no directs observational evidences. In this talk, I discuss how the Kerr black hole hypothesis can be tested with present and future X-ray data and the current constraints on the nature of this objects.

This is a very informal talk about some of the issues associated with the notion of "macroscopic realism" (MR) and its relation to quantum mechanics (QM). After a brief discussion of the motivation for attempts to modify QM at some point between the level of the atom and that of our own direct experience, and a survey of some candidate experimental systems, I will discuss attempts to quantify the notion of "macroscopic distinctness", the use of temporal Bell inequalities to discriminate between the predictions of QM and those of MR, the related concept of "noninvasive measurement" and existing and possible ways to implement it. I will also comment briefly on the relation between Bell-EPR experiments and those on MR.

Continuous-variable SICPOVMS seem unlikely to exist, for a variety of reasons. But that doesn't rule out the possibility of other 2-designs for the continuous-variable Hilbert space L2(R). In particular, it would be nice if the coherent states -- which form a rather nice 1-design -- could be generalized in some way to get a 2-design comprising *Gaussian* states. So the question is: "Can we build a 2-design out of Gaussian states?". The answer is "No, but in a very surprising way!" Like coherent states, Gaussian states have a natural transitive symmetry group. For coherent states, it's the Heisenberg group. For Gaussian states, it's the affine symplectic group -- the Heisenberg group plus squeezings and rotations. And this group acts irreducibly on the symmetric subspace of L2(R) x L2(R)... which, by Schur's Lemma, implies that the Gaussian states *should* be a 2-design. Yet a very simple explicit calculation shows that they are not! The resolution is fascinating -- it turns out that the "symplectic twirl" involves an integral that does not quite converge, and this provides a loophole out of Schur's Lemma. So, in the end, we: (1) Show that Gaussian 2-designs do not exist, (2) Demonstrate a major stumbling block to *any* symplectic-covariant 2-designs for L2(R), (3) Gain a pretty complete understanding of *one* of the [formerly] mysterious discrepancies between discrete and continuous Hilbert spaces.

String theory should give a well-defined answer to the following question: What is the state of matter in the limit of infinite energy density? We use results obtained from the understanding of black hole entropy to conjecture this equation of state, noting that the maximum entropy state in string theory has vastly more entropy than the states used in traditional approaches to early Universe Cosmology. The evolution of the Universe with this equation of state can be obtained in closed form.

A serious shortcoming of spinfoam loop gravity is the absence of matter. I present a minimal and surprisingly simple coupling of a chiral fermion field in the framework of spinfoam quantum gravity. This result resonates with similar ones in early canonical loop theory: the naive fermion hamiltonian was found to be just the extension of the simple

It is argued that the correct quantization of a scalar field theory in de Sitter spacetime involves a de Sitter invariant state which is not the Bunch-Davies vacuum. A novel but natural de Sitter invariant alternative exists and it is suggested that this and is the prefered state for scalar field theories. The argument is based on the exact solution of an interacting scalar field theory.

Cosmic inflation has given us a remarkably successful cosmological phenomenology. But the original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize. I review the status of "eternal inflation" with an eye on the roles various infinities have (both helpful and unhelpful) in our current understanding. I then discuss attempts to construct an alternative cosmological framework that is truly finite, using ideas about equilibrium and dark energy. I report some recent results that point to observable signatures.

The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of $Tr\phi^n$ (for all $n$) operators. We show that at low energies independently of the dimensionality $D$ the Hamiltonian system in question reduces to the {\it integrable} effective theory. The obtained Hamiltonian system describes large wavelength KdV type (Burger--Hopf) equation with an external potential and is related to the effective theory obtained by Das and Jevicki for the matrix quantum mechanics.