Colloquium

The graph isomorphism (GI) problem plays a central role in the theory of computational complexity and has importance in physics and chemistry as well. While no general efficient algorithm for solving GI is known, it is unlikely to be NP-complete; in this regard it is similar to the factoring problem, for which Shor has developed an efficient quantum algorithm. In this talk I will discuss our investigations of quantum particles walking on graphs and their implications for possible algorithms for GI. We find that single-particle quantum random walks fail to distinguish some nonequivalent graphs that can be distinguished by random walks with two interacting particles. The implications of these observations for classical and quantum algorithms for GI will be discussed.

I will describe a new connection between supersymmetry, geometry and computer science. An exploration of the equations of supersymmetry has revealed a geometrical sub-structure whose classification depends on self-dual error correcting codes.

Of all four forces only the weak interaction has experimentally exhibited parity violation. At the same time observations suggest that general relativity may require modification to account for dark matter and dark energy. Could it be that this modification involves gravitational parity violation? Many of the dominant approaches to quantum gravity, such as string theory and loop quantum gravity, point to an effective parity violating extension to general relativity known as Chern-Simons General Relativity (CSGR). In this colloquium I will discuss the uniqueness and phenomenological implications of parity violation in CSGR. In particular, I will discuss how CSGR can work together with inflation to generate the cosmic baryon asymmetry in a most economical fashion, through gravitational waves; and its predictions for upcoming CMB polarization experiments. I will also discuss current predictions of CSGR on binary pulsars, neutron stars and prospects for the LISA/LIGO gravitational wave detectors. While we focus on a specific theory for concreteness, some of the results presented in this colloquium can be seen as model independent.

Is there a theory yet to be discovered that underlies quantum theory and explains its structure? If there is such a theory, one of the features it will have to explain is the central role of complex numbers as probability amplitudes. In this talk I explore the physical meaning of the statement “probability amplitudes are complex” by comparing ordinary complex-vector- space quantum theory with the real-vector-space theory having the same basic structure. Specifically, I discuss three questions that bring out qualitative differences between the two theories: (i) Is information about a preparation expressed optimally in the outcomes of a measurement? (ii) Are multipartite states locally accessible? (iii) Is entanglement “monogamous”?

In 1981 Bill Unruh showed that the equation of motion for sound waves in a convergent fluid flows is given by a wave equation in an acoustic metric geometry. More importantly it is possible to set up sonic horizons in transsonic flows, and thus in principle to mimic experimentally the black-hole evaporation process. Almost 30 years later we have set up an experiment at the University of British Columbia to find out if indeed it is possible to detect (traces of) black hole radiation. We will discuss the necessary theoretical milestones, such as the effective field theory description for water to explore the robustness of Hawking radiation, and the avoidance of shock waves using surface waves rather then sound waves. In theory we should be able to detect the classical component of the thermal emission of black holes in our system and answer the ultimate question: How much do we trust our effective quantum field theory in curved spacetimes?

Gravitational waves provide a unique way to study the Universe. From 2005 to 2007, the Laser Interferometer Gravitational-wave Observatory (LIGO) took data at design sensitivity. After describing gravitational waves and how LIGO works, I will discuss the status of searches for those waves and current astronomical constraints imposed by those searches. Data taking resumed in summer 2009 with enhanced LIGO detectors and the European Virgo detectors. I will discuss plans for combined electromagnetic and gravitational observing campaigns. Finally, I will highlight the prospects for gravitational-wave astronomy with Advanced LIGO over the next decade.

Physicists have been working for banks and hedge funds on applied problems in finance for more than two decades, and recently have doing academic research as well. This talk will survey academic research by physicists and contrast it with mainstream economics. I will argue that the difference comes not from the application of alternative techniques or new mathematics, but rather from fundamental differences in what questions are considered interesting and how one should go about solving them. This will be illustrated with a simple model for how systemic risks and extreme price movements are generated by the use of leverage (buying with credit). The current financial crisis illustrates that the economy is indeed a complex system, and that new approaches are needed that properly take this into account.

According to hidden-variables theories, quantum physics is a special 'equilibrium' case of a much wider 'nonequilibrium' physics. We describe the search for that wider physics in a cosmological context. The hypothesis that the universe began in a state of quantum nonequilibrium is shown to have observable consequences. In de Broglie-Bohm theory on expanding space, relaxation to quantum equilibrium is shown to be suppressed for field modes whose quantum time evolution satisfies a certain inequality, resulting in a 'freezing' of early nonequilibrium for these particular modes. For an early radiation-dominated expansion, the inequality implies a corresponding physical wavelength that is larger than the (instantaneous) Hubble radius. These results make it possible, for the first time, to make quantitative predictions for deviations from quantum theory. We consider, in particular, corrections to inflationary predictions for the cosmic microwave background, and the possibility of finding relic cosmological particles that violate the laws of quantum mechanics. (Reference: De Broglie-Bohm Prediction of Quantum Violations for Cosmological Super-Hubble Modes, http://arxiv.org/abs/0804.4656.)

The Background Imager of Cosmic Extragalactic Polarization (BICEP) experiment is the first polarimeter developed to measure the inflationary B-mode polarization of the CMB. During three seasons of observing at the South Pole, Antarctica beginning in 2006, BICEP mapped 2% of the sky chosen to be clean of polarized foreground emission, with sub-degree resolution. In this colloquium I will present initial results derived from a subset of the data acquired during the first two years of data and discuss the unique design features of BICEP which led to the first meaningful limits on the tensor-to-scalar ratio to come from B-mode polarization. Recently, Xia, Li & Zhang (2009) have claimed a detection of parity-violating "cosmic birefringence" effects using publicly available BICEP data. I will discuss polarimetric fidelity in the light of systematic errors and how such effects are particularly pernicious for probes of cosmic parity violation. I will conclude with a discussion demonstrating how BICEP, and its successor "BICEP2" will inform future measurements of the inflationary gravitational wave background and cosmic birefringence.

I will tell how the story given in Umberto Eco's book The Search for the Perfect Language continues with modern work on logical and programming languages.(For more information, see http://www.umcs.maine.edu/~chaitin/hu.html.)