Colloquium

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.

Neutrinos are the big unknown in Particle Physics. Since their very beginning they behaved strangely. However, in the last decade experiments were able to solve some of their secrets. The talk will review the current experimental status of neutrino experiments and give an outlook on future activities.

The Laser Astrometric Test of Relativity (LATOR) is a Michelson-Morley-type experiment designed to improve current tests of the Einstein’s theory of general relativity by more than four orders of magnitude. The LATOR mission uses laser interferometry between two laser sources placed on separate small spacecraft, whose lines of sight pass close by the Sun, to measure accurately the deflection of light in the solar gravity field. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (~100m) Michelson stellar optical interferometer assembled on the International Space Station (ISS). The interferometer is used to measure the angles between the two spacecraft (with accuracy of 0.1 picoradian) and for orbit determination purposes (via laser-ranging-enabled orbit determination). The three arms of the spacecraft-ISS-spacecraft triangle are monitored with laser ranging (accurate to less than 1 cm). From these three length measurements one can calculate the Euclidean value for any of the angles in this triangle. The direct interferometric angular measurement and resulting geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy. LATOR is a new fundamental physics experiment designed to test relativistic gravity at an accuracy never achieved before – probing for the first time the second-order effects in the gravitational field strength. By using independent time-series of highly accurate measurements of the Shapiro time-delay and gravitational deflection of light, LATOR will test Einstein's general theory of relativity in the most intense gravitational environment available in the solar system -- the close proximity to the Sun -- measuring gravitational deflection of light in the solar gravity with accuracy of 1 part per billion, a factor ~30,000 better than currently available (i.e. Cassini 2003 experiment). LATOR will perform series of highly-accurate tests of gravitation and cosmology in its search for cosmological remnants of scalar field in the solar system, ultimately providing addition information on the nature of dark matter and dark energy. In this talk we will discus the science, technology and mission design for the LATOR mission. The work described here was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration.