Colloquium

We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. I will explain the motivation for this view, give some examples of theories of this kind and investigate general conditions for such an approach to succeed.

Conventional wisdom holds that the majority of high energy atomic nuclei ("cosmic rays") that continually rain upon the Earth originate in galactic supernova shock waves, although some different (likely extragalactic) origin must be invoked to explain the highest energy particles. Despite many decades of intensive research on the subject, only indirect clues to these ideas exist at present. Direct measurements of the spectrum and mass composition of high energy cosmic rays are needed to validate these notions, but are hampered by rapidly dwindling fluxes with energy. Indeed, there is an expectation that the cosmic nuclei should have progressively more charge (and therefore mass), on average, with increasing energy, up to the astrophysical "knee" (spectral break) in the spectrum at around 3x10^15 eV. At energies beyond the knee, only indirect measurements are possible. The CREAM (Cosmic Ray Energetics And Mass) experiment is a complex particle detector flown by high altitude balloon to directly measure the charge and energy of the cosmic rays at energies near the spectral knee. It flew successfully in Antarctica in Dec 04 / Jan 05 for a record-breaking 42 days, and again in Dec 05 / Jan 06. We will review the science and performance of the instrument in flight, and present preliminary results and discuss prospects for additional CREAM missions. The Auger experiment is the largest cosmic ray detector ever built, currently nearing completion in Argentina, covering an area of 3000 km^2. Its aim is to resolve a number of mysteries surrounding the highest energy cosmic rays, beyond 10^18 eV, whose very existence and ability to reach the Earth are difficult to understand. The rarity of the highest energy particles has precluded definitive answers to the question of their nature and origin, and indeed some controversy surrounds the existing experimental evidence. The Auger experiment will afford an order of magnitude improvement in statistics over previous efforts, as well as much improved control of systematics. We will briefly review the science of the highest energy cosmic rays and present first results obtained with the growing Auger array, and discuss plans for the future of these efforts.

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, I'll show that "for most practical purposes" one can learn a quantum state using a number of measurements that grows only linearly with n. I'll discuss applications of this result in experimental physics and quantum computing theory, as well as possible implications for the foundations of quantum mechanics. quant-ph/0608142

How should we think about quantum computing? The usual answer to this question is based on ideas inspired by computer science, such as qubits, quantum gates, and quantum circuits. In this talk I will explain an alternate geometric approach to quantum computation. In the geometric approach, an optimal quantum computation corresponds to "free falling" along the minimal geodesics of a certain Riemannian manifold. This reformulation opens up the possibility of using tools from geometry to understand the strengths and weaknesses of quantum computation, and perhaps to understand what makes certain physical operations difficult (or easy) to synthesize.

Not only general relativity but also quantum theory plays important roles in current cosmology. Quantum fluctuations of matter fields are supposed to have provided the initial seeds of all the structure of the current universe, and quantum gravity is assumed to have been essential in the earliest stages. Both issues are not fully understood, although several heuristic effects have been discussed. In this talk, implications of an effective framework taking into account the coupling of matter and gravity are discussed. This touches on interpretational issues of quantum mechanics, cosmological observations and properties of quantum gravity.

At low energy and small curvature, general relativity has the form of an effective field theory. I will describe the structure of the effective field theory, and show how it can be used to calculate low energy quantum effects.

Category theory is a general language for describing things and processes - called "objects" and "morphisms". In this language, many counterintuitive features of quantum theory turn out to be properties shared by the category of Hilbert spaces and the category of cobordisms, in which objects are choices of "space" and emorphisms are choices of "spacetime". This striking fact suggests that "n-categories with duals" are a promising language for a quantum theory of spacetime. We sketch the historical development of these ideas from Feynman diagrams to string theory, topological quantum field theory, spin networks and spin foams, and especially recent work on open-closed string theory, 3d quantum gravity coupled to point particles, and 4d BF theory coupled to strings.

Nanostructured materials continue to be the focus of intense research due to their promise of innumerable practical applications as well as advancing the fundamental understanding of these intriguing materials. From physics, to chemistry, to biology, to computer science, across the engineering disciplines and into the imagination of the general event, nanotechnology has become an extremely popular buzzword that represents both hope and hype to many people. This talk will outline and describe the exploding field of nanotechnology, including its potential for promising new applications, and for negative societal implications that cause many to fear it. Recent work in our group in the area of integration of nanoscale structures with silicon will be outlined to show the scope and approaches to building nanoscale architectures; the applications of these frameworks include molecular computing, nanoscale sensing platforms, integration of silicon with biology, and intricate structures with unforeseen properties.

A variety of physical phenomena involve multiple length and time scales. Some interesting examples of multiple-scale phenomena are: (a) the mechanical behavior of crystals and in particular the interplay of chemistry and mechanical stress in determining the macroscopic brittle or ductile response of solids; (b) the molecular-scale forces at interfaces and their effect in macroscopic phenomena like wetting and friction; (c) the alteration of the structure and electronic properties of macromolecular systems due to external forces, as in stretched DNA nanowires or carbon nanotubes. In these complex physical systems, the changes in bonding and atomic configurations at the microscopic, atomic level have profound effects on the macroscopic properties, be they of mechanical or electrical nature. Linking the processes at the two extremes of the length scale spectrum is the only means of achieving a deeper understanding of these phenomena and, ultimately, of being able to control them. While methodologies for describing the physics at a single scale are well developed in many fields of physics, chemistry or engineering, methodologies that couple scales remain a challenge, both from the conceptual point as well as from the computational point. In this presentation I will discuss the development of methodologies for simulations across disparate length scales with the aim of obtaining a detailed description of complex phenomena of the type described above. I will also present illustrative examples, including hydrogen embrittlement of metals, DNA conductivity and translocation through nanopores, and affecting the wettability of surfaces by surface chemical modification.

I will describe some recent advances in the simulation of binary black hole spacetimes using a numerical scheme based on generalized harmonic coordinates. After a brief overview of the formalism and method, I will present results from the evolution of a couple of classes of initial data, including Cook-Pfieffer quasi-circular inspiral data sets, and binaries constructed via scalar field collapse. In the latter case, preliminary studies suggest that in certain regions of parameter space there is extreme sensitivity of the resulting orbit to the initial conditions. In this regime the equal mass black holes exhibit behavior reminiscent of "zoom-whirl" particle trajectories in the test-mass limit.

Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has been generalized as our conceptions of space and time have evolved. But quantum mechanics needs to be generalized further for quantum gravity where spacetime geometry is fluctuating and without definite value. This talk will review a fully four-dimensional, sum-over-histories, generalized quantum mechanics of cosmological spacetime geometry. In this generalization, states of fields on spacelike surfaces and their unitary evolution are emergent properties appropriate when spacetime geometry behaves approximately classically. The principles of generalized quantum theory would allow for further generalization that would be necessary were spacetime not fundamental. Emergent spacetime phenomena are discussed in general and illustrated with the examples of the classical spacetime geometries with large spacelike surfaces that emerge from the `no-boundary' wave function of the universe. These must be Lorentzian with one, and only one, time direction. The question will be raised as to whether quantum mechanics itself is emergent.