Scientific Series

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.)

We present a first-principles implementation of {\em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field. We exhibit four independent reasons for not giving into this temptation. A more likely possibility is that it can play the role of ``dark matter''. Indeed, as noted in scale invariance seems to play a role in the MOND phenomenology. Spatial boundary conditions are derived from the free-endpoint variation method and a preliminary analysis of the constraints and their propagation in the Hamiltonian formulation is presented.

Gamma-ray bursts (GRBs) -- rare flashes of ~ MeV gamma-rays lasting from a fraction of a second to hundreds of seconds -- have long been among the most enigmatic of astrophysical transients. Observations during the past decade have led to a revolution in our understanding of these events, associating them with the birth of neutron stars and/ or black holes during either the collapse of a massive star or the merger of two compact objects (e.g., a neutron star and a black hole). GRBs are particularly interesting since NS-NS and NS-BH mergers are the primary target for km-scale gravitational wave observatories such as Advanced LIGO; GRBs are also one of the most promising astrophysical sources of very high- energy neutrinos and may produce many of the neutron-rich heavy elements in nature. In this talk, I will describe the physics of these enigmatic events and summarize outstanding problems. Combined electromagnetic and gravitational-wave observations of these sources in the coming decade have the potential to produce major advances in both astrophysics and fundamental physics (tests of General Relativity and of the equation of state of dense nuclear matter).

At NIST we are engaged in an experiment whose goal is to create superpositions of optical coherent states (such superpositions are sometimes called "Schroedinger cat" states). We use homodyne detection to measure the light, and we apply maximum likelihood quantum state tomography to the homodyne data to estimate the state that we have created. To assist in this analysis we have made a few improvements to quantum state tomography: we have devised a new iterative method (that has faster convergence than R*\rho*R iterations) to find the maximum likelihood state, we have formulated a stopping criterion that can upper-bound the actual maximum likelihood, and we have implemented a bias-corrected resampling strategy to estimate confidence intervals.

The Standard model of Cosmology consists of a package of ideas that include Cold Dark Matter, Inflation, and the existence of a small Cosmological Constant. While there is no consensus about what lies beyond the Standard Model, there is a leading candidate that also includes a small package of ideas: A Landscape of connected vacua: the idea that the universe started out with a large energy density, and Coleman DeLuccia Tunneling between vacua. An additional idea that comes from string theory and black hole physics is the Holographic Principle. I will explain how the various ingredients for a "post-standard-model" standard model fit together.

Betting (or gambling) is a useful tool for studying decision-making in the face of [classical] uncertainty. We would like to understand how a quantum "agent" would act when faced with uncertainty about its [quantum] environment. I will present a preliminary construction of a theory of quantum gambling, motivated by roulette and quantum optics. I'll begin by reviewing classical gambling and the Kelly Criterion for optimal betting. Then I'll demonstrate a quantum optical version of roulette, and discuss some of the challenges and pitfalls in designing such analogues. Quantum agents have access to many more strategies than classical agents. Quantum strategies provide no advantage in classical roulette, but I'll show that a quantum agent can outperform a classical agent in quantum roulette.

The standard model of cosmology has some puzzles/problems such as the cosmological constant problem and the horizon problem which according to many stem from our lack of understanding of the very early universe. This in turn means that almost none of the theories of quantum gravity are at a stage where anything substantial can be said about observational cosmology. In the past few years Causal Set theory has proved itself different in this case where a possible solution to the Cosmological constant problem was proposed. Now some work in progress has also shown that some models of Causal Set dynamics give exponential expansion in the early universe. I hope to discuss both of these exciting prospects but this talk will mainly focus on the first proposal.

We present the first year SDSS-II Supernova Survey results and their implications for cosmology and future supernova surveys. We then discuss challenges that face next-generation surveys, such as LSST, which will deliver of order a million supernovae without spectroscopic confirmation. As a way to address these challenges, we introduce BEAMS, a statistical method to do photometric supernova cosmology, and present a preliminary application to SDSS data. Finally we highlight the importance of future surveys such as LSST, given the surprising result that we may not detect dark energy dynamics for the next decade, if the dark energy scales during matter and radiation domination.