Scientific Series

The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework. I will also explain how this might be the ideal setting to attempt a proof of the Bousso entropy bound, or to incorporate the associated holographic principle in a quantization of gravity.

Lee Smolin has argued that one of the barriers to understanding time in a quantum world is our tendency to spatialize time. The question is whether there is anything in physics that could lead us to mathematically characterize time so that it is not just another funny spatial dimension. I will explore the possibility(already considered by Smolin and others) that time may be distinguished from space by what I will call a measure of Booleanity. The Bell-Kochen-Specker Theorem shows that the statistics of quantum systems (unlike that of classical systems) do not in general permit of a Boolean substructure. I will outline reasons for thinking that time is the dimension in which the Booleanity of spacetime (considered as a quantum system) varies, while space is characterized by constant Booleanity. I will not be able to give a mathematically complete characterization of the Booleanity of a region of spacetime, since that would require nothing less than knowing how to quantize spacetime; however, I will argue that something like this is needed if one is to make any sense of an ontological distinction between past, present, and future in terms of modern physics. I will also briefly consider possible objections to this view arising from the relativity of simultaneity, which (on its usual interpretation) apparently places all events on an equal ontological footing. In order to get around this we need a generalized conception of simultaneity that treats Einstein's notion of simultaneity as a special case, and which allows for equivalence classes of spacelike separate events distinguished by covariant quantities such as action, phase, and (as I will argue) any reasonable measure of Booleanity.

We are currently in the throes of a potentially huge paradigm shift in physics. Motivated by recent developments in string theory and the discovery of the so-called \'string landscape\', physicists are beginning to question the uniqueness of fundamental theories of physics and the methods by which such theories might be understsood and investigated. In this colloquium, I will give a non-technical introduction to the nature of this paradigm shift and how it developed. I will also discuss some of the questions to which it has led, and the nature of the controversies it has spawned.

I will show the calculation of the probability distribution for the volume of the Universe after slow-roll inflation both in the eternal and the non-eternal regime. Far from the eternal regime the probability distribution for the number of e-foldings, defined as one third of the logarithm of the volume, is sharply peaked around the number of e-foldings of the classical inflaton trajectory. At the transition to the eternal regime this probability is still peaked (with the width of order one e-foldings) around the average, which however gets twice larger at the transition point. As one enters the eternal regime the probability for the volume to be finite rapidly becomes exponentially small. In addition to developing techniques to study eternal inflation, these results allow us to establish the quantum generalization of the recently proposed bound on the number of e-foldings in non-eternal regime: the probability for slow-roll inflation to produce a finite volume larger than Exp[S_dS/2], where S_dS is the de Sitter entropy at the end of the inflationary stage, is smaller than the uncertainty due to non-perturbative quantum gravity effects. The existence of such a bound provides a consistency check for the idea of de Sitter complementarity.

Recent experimental results seem to require a dramatic change in our view of the dark matter sector. In this talk I will describe the reasons for this change and the ingredients required to describe the new data. I will present possible field theories that give rise to such phenomena and delineate the resulting collider signatures.

In this talk I discuss methods to determine hydrodynamical dispersion relations from an extra-dimensional gravity dual wherein the metric is supported by scalar fields. Such a setup may eventually be used as a model of the strongly coupled plasma created in heavy ion collisions. I examine examples of both the shear and sound modes. The shear mode is analyzed using the black hole membrane paradigm; a calculation of the shear viscosity is reviewed, and then the calculation is extended to the next hydrodynamical order. All results agree with those found using the AdS/CFT prescription. The sound mode is analyzed by examining the quasi-normal modes of the dual black hole. The relevant gauge invariant equations are derived, and a special case solution of these equations is discussed.

Using 2-dimensional CGHS black holes, I will argue that information is not lost in the Hawking evaporation because the quantum space-time is significantly larger than the classical one. I will begin with a discussion of the conceptual underpinnings of problem and then introduce a general, non-perturbative framework to describe quantum CGHS black holes. I will show that the Hawking effect emerges from it in the first approximation. Finally, I will introduce a mean field approximation to argue that, when the back reaction is included, future null infinity is `long enough\' to capture full information contained in pure states at past null infinity and that the S-matrix is unitary. There are no macroscopic remnants.

In recent years, the analysis of boolean functions has arisen as an important theme in theoretical computer science. In this talk I will discuss an extension of the concept of a boolean function to quantum computation. It turns out that many important classical results in the theory of boolean functions have natural quantum analogues. These include property testing of boolean functions; the Goldreich-Levin algorithm for approximately learning boolean functions; and a theorem of Friedgut, Kalai and Naor on the Fourier spectra of boolean functions. The quantum generalisation of this theorem uses a quantum extension of the hypercontractive inequality of Bonami, Gross and Beckner. This talk is based on joint work with Tobias Osborne.

According to general relativity, space-time ends at singularities and classical physics just stops. In particular, the big bang is regarded as The Beginning. However, general relativity is incomplete because it ignores quantum effects. Through simple models, I will illustrate how the quantum nature of space-time geometry resolves the big bang singularity. Quantum physics does not stop there. Indeed, quantum space-times can be vastly larger than what general relativity had us believe, with unforeseen physical effects in the deep Planck regime.

Quantum entanglement has two remarkable properties. First, according to Bell\'s theorem, the statistical correlations between entangled quantum systems are inconsistent with any theory of local hidden variables. Second, entanglement is monogamous -- that is, to the degree that A and B are entangled with each other, they cannot be entangled with any other systems. It turns out that these properties are intimately related.

Understanding dynamics of strongly coupled quantum field theories is an important problem in both condensed matter physics and high energy physics. In condensed matter systems, interacting quantum field theories can arise either at a critical point, or in a finite region of a parameter space. In the former case, massless modes arise as a result of fine tuning of external parameters, while, in the latter case, massless modes are protected by topology and/or symmetry. In this talk, I will discuss two examples in 2+1 dimensions (one for each case) where one can understand strong coupling physics nonperturbatively. In the first example, a lattice model which describes a superconducting phase transition will be discussed. In this model, a superconformal symmetry dynamically emerges at the quantum critical point and one can predict non-trivial critical exponents using the enlarged symmetry, even though there is no underlying supersymmetry in the microscopic model. In the second example, I will discuss about a 2+1 dimensional non-relativistic quantum field theory which is dual to a gravitational theory in the AdS4 background with a charged black hole. The spectral function of a fermion field exhibits an interesting non-Fermi liquid behavior, that is, all momentum points inside the Fermi surface are critical and the gapless modes are defined in a critical Fermi ball in the momentum space.