Scientific Series

Entanglement is one of the most fundamental and yet most elusive properties of quantum mechanics. Not only does entanglement play a central role in quantum information science, it also provides an increasingly prominent bridging notion across different subfields of Physics --- including quantum foundations, quantum gravity, quantum statistical mechanics, and beyond. Arguably, the property of a state being entangled or not is by no means unambiguously defined. Rather, it depends strongly on how we decide to regard the whole as composed of its part or, more generally, on the restricted ways in which we are able to observe and control the system at hand. Acknowledging the implications of such an operationally constrained point of view naturally has led to a notion of 'generalized entanglement,' which is directly based on quantum observables and offers added flexibility in a variety of contexts. In this talk, I will survey some of the main accomplishments of the generalized entanglement program to date, with an eye toward recent developments and open problems.

We know the mathematical laws of quantum mechanics, but as yet we are not so sure why those laws should be inevitable. In the simpler but related environment of classical inference, we also know the laws (of probability). With better understanding of quantum mechanics as the eventual goal, Kevin Knuth and I have been probing the foundations of inference. The world we wish to infer is a partially-ordered set ('poset') of states, which may as often supposed be exclusive, but need not be (e.g. A might be a requirement for B). In inference, a state of mind about the world degrades from perfect knowledge through logical OR, which allows for uncertain alternatives. We don't need AND, and we don't need NOT; we just need OR. This display of acceptable states of mind is [close to] a mathematical 'lattice'. We find that the OR structure by itself (!) forces the ordinary rules of probability calculus. No other rules are compatible with the structure of a lattice, so the ordinary rules are inevitable. The standard Shannon information/entropy is likewise inevitable. Taking this idea further, the OR of states of mind gives a lattice of 'Questions' that might be useful for automated learning. Disconcertingly, this lattice is very much larger (in class aleph-2), and the natural valuations on it exhibit large range. I will present this extension, and ask whether we can rationally foresee its use in practical application.

I comment on rather significant recent developments that are relevant for proposals I had presented in previous PI seminars. The Fermi/GLAST space telescope has reported observations that would naturally fit previous formalizations of Planck-scale-induced in-vacuo dispersion (but also quite a few other things). And the unexplained excess noise found at the GEO600 interferometer is just of the type that had been previously described in terms of phenomenological models of spacetime foam (but may well be caused by quite a few other things). On the pure-theory side I can finally keep my promise to show that spacetime noncommutativity is a valuable tool of exploration of nonclassicality of spacetime, allowing the derivation of discretized spectra of distance, area, volume, and also providing a completely new overall geometric picture, in which amusingly the number Pi looses some of its privileges.

The fundamental laws of physics are very simple. The world about us is very complex. Living things are very complex indeed. This complexity has led some thinkers to suggest that living things are not the outcome of physical law but instead the creation of a designer. Here I examine how complexity is produced naturally in fluids.

Holographic superconductors provide tractable models for the onset of superconductivity in strongly coupled theories. They have some features in common with experimentally studied nonconventional superconductors. I will review the physics of holographic superconductors and go on to show that many such models are to be found in the string landscape of AdS_4 vacua.

We study the entanglement dynamics and relaxation properties of a system of two interacting qubits in the two cases (I) two independent bosonic baths and (II) one common bath, at temperature $T$. The entanglement dynamics is studied in terms of the concurrence C(t) between the two spins and of the von Neumann entropy S(t) with respect to the bath, as a function of time. We prove that the system does thermalize. In the case (II) of a single bath, the existence of a decoherence-free (DFS) subspace makes entanglement dynamics very rich. We show that when the system is initially in a state with a component in the DFS the relaxation time is surprisingly long, showing the existence of semi-decoherence free subspaces. The equilibrium state in this case is not the Gibbs state. The entanglement dynamics for the single bath case is also studied as a function of temperature, coupling strength with the environment and strength of tunneling coupling. The case of the mixed state is finally shown and discussed.

s-channel resonances are predicted by many models of Physics Beyond the Standard Model and it is quite possible that such an object will be discovered in the early years of the LHC program. If this occurs, the task will be to understand its origins. A brief survey of models that predict s-channel resonances will be given, concentrating mainly on extra neutral gauge bosons (Z' 's) arising from extended gauge theories. This will be followed by a description of how to search for a Z' and the resulting Z' discovery reach of the LHC. I will describe various diagnostic measurements to study Z' 's and describe some new observables we have proposed that can distinguish between models that take advantage of the ability to tag 3rd generation fermions.

The great advances in observational cosmology in the last few years have delivered us an unprecedented amount of new data. They begin to indicate with confidence that in the past our universe underwent a phase of acceleration, called inflation, and that it is currently undergoing a similar phase, usually thought of as a consequence of a cosmological constant. I will show how inflation can be probed, using to this purpose a very general effective field theory description. In particular, I will concentrate on the new and powerful signal of the non-gaussianity of the primordial density perturbations, explaining its theoretical motivation, the techniques to look for it in the data, and the current constraints from the WMAP experiment. This signature is very important not only to identify the precise mechanism that drove inflation, but also to shed light on possible alternatives, such as the recently proposed bouncing cosmology. I will describe how these alternative theories can be consistently formulated and be predictive, and how similar theories may have interesting implications for the current acceleration of the universe. If inflation happened in our past, it might actually have been eternal. The presence of such a phase offers a new way to address the problem of the cosmological constant and of the current acceleration of the universe. This will lead us to explain in precise terms what eternal inflation is.

The cosmological constant problem is arguably the deepest gap in our understanding of modern physics. The discovery of cosmic acceleration in the past decade and its surprising coincidence with cosmic structure formation has added an extra layer of complexity to the problem. I will describe how revisiting/revising some standard assumptions in the theory of gravity can decouple the quantum vacuum from geometry, which can potentially solve the cosmological constant problem. I will then argue that a possible fascinating outcome of such a theory is to relate black hole formation to cosmic acceleration, providing a possible solution to the cosmic coincidence. A diverse range of experimental/observational probes over the next decade will tell us whether we are close to the end of this century-old mystery, which in turn could shed light on the nature of quantum gravity and black holes.

The vacuum landscape of string theory can solve the cosmological constant problem, explaining why the energy of empty space is observed to be at least 60 orders of magnitude smaller than several known contributions to it. It leads to a 'multiverse' in which every type of vacuum is produced infinitely many times, and of which we have observed but a tiny fraction. This conceptual revolution has raised tremendous challenges in particle physics and cosmology. To understand the low-energy physics we observe, and to test the theory, we will need novel statistical tools and effective theories. We must also solve a long-standing fundamental problem in cosmology: how to define probabilities in an infinite universe where every possible outcome, no matter how unlikely, will be realized infinitely many times. This 'measure problem' is inextricably tied to the quantitative prediction of the cosmological constant.

The standard cosmological model features two periods of accelerated expansion: an inflationary epoch at early times, and a dark energy dominated epoch at late times. These periods of accelerated expansion can lead to surprisingly strong constraints on models with extra dimensions. I will describe new mathematical results which enable one to reconstruct features of a higher-dimensional theory based on the behaviour of the accelerating four-dimensional cosmology. When applied to inflation, these results pose several interesting questions for the construction of concrete models. When applied to dark energy, they provide a new technique to combine measurements of dark energy parameters and constraints on variation of Newton's constant. This technique can transform near-future dark energy surveys into become powerful probes of extra dimensional physics.

Weak lensing has emerged as a powerful probe of fundamental physics such as dark energy and dark matter. After briefly reviewing the standard argument for the power of lensing, I present a variety of surprises: some quantities that are supposedly simple measures of cosmic shear are actually polluted by other effects and some quantities apparently unrelated to lensing are contaminated by lensing. These effects may lead to opportunities to strengthen the constraints lensing will place on dark energy.