Talks

Perhaps the earliest explicit ansatz of a truly ontic status for the density operator has been proposed in [G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol.6, 15, 127, 439, 561 (1976)]. Their self-consistent, unified quantum theory of Mechanics and Thermodynamics hinges on: (1) modifyng the ‘state postulate’ so that the full set of ontic individual states of a (strictly isolated and uncorrelated) quantum system is one-to-one with the full set of density operators (pure and mixed); and (2) complementing the remaining usual postulates of quantum theory with an ‘additional postulate’ which effectively seeks to incorporate the Second Law into the fundamental level of description. In contrast with the epistemic framework, where the linearity of the dynamical law is a requirement, the assumed ontic status of the density operator emancipates its dynamical law from the restrictive requirement of linearity. Indeed, when the ‘additional postulate’ is replaced by the dynamical ansatz of a (locally) steepest entropy ascent, nonlinear evolution equation for the density operator proposed in [G.P. Beretta, Sc.D. thesis, M.I.T., 1981, e-print quant-ph/0509116; and follow-up papers], the (Hatsopoulos-Keenan statement of the) Second Law emerges as a general theorem of the dynamics (about the Lyapunov stability of the equilibrium states). As a result, the ontic status is acquired not only by the density operator, but also by the entropy (which emerges as a microscopic property of matter, at the same level as energy), and by irreversibility (which emerges as a microscopic dynamical effect). This “adventurous scheme ... may end arguments about the arrow of time -- but only if it works” [J. Maddox, Nature, Vol.316, 11 (1985)]. Indeed, the scheme resolves both the Loschmidt paradox and the Schroedinger-Park paradox about the concept of ‘individual quantum state’. However, nonlinearity imposes a high price: the maximum entropy production (MEP) dynamical law does not have a universal structure like that of the Liouville-von Neumann equation obeyed by the density operator within the epistemic (statistical mechanics) view. Instead, much in the same way as the implications of the Second Law depend on the assumed model of a given physical reality, the MEP dynamical law for a composite system is model dependent: its structure depends on which constituent particles or subsystems are assumed as elementary and separable, i.e., incapable of no-signaling violations. See www.quantumthermodynamics.org for references.

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes, one of which could play the role of our universe. This process also leads to the production of one-dimensional branes, D-strings, and fundamental ones (F-strings), known as cosmic superstrings. In the first part of this talk, I will discuss the mechanism we have proposed in order to explain the origin of the space-time dimensionality, while in the second part I will review formation and dynamics of cosmic superstrings.

I will discuss properties of pre- and post-selected ensembles in quantum mechanics. I will also discuss the proper way to observe these properties through the use of a new type of non-disturbing measurement which I call 'weak measurement'. A number of these new experiments have already been successfully performed and others are in the planning stage. These experiments have confirmed the unique property of pre- and post-selected ensembles that I call 'weak values.' Theoretical analysis of the outcomes of these experiments have produced several very rich results. First, it has shed new light on the most puzzling features of quantum mechanics, such as interference, entanglement, etc. Secondly, it has uncovered a host of new quantum phenomena, which were previously hidden."

We use black holes to understand some basic properties of theories of quantum gravity. First, we apply ideas from black hole physics to the physics of accelerated observers to show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation $\delta Q = T \delta S$. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the energy momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum. Then, we show that the existence of semiclassical black holes of size as small as a minimal length scale l_{UV} implies a bound on a gravitational analogue of 't-Hooft's coupling $\lambda_G(l)\equiv N(l) G_N/l^2$ at all scales $l \ge l_{UV}$. The proof is valid for any metric theory of gravity that consistently extends Einstein's gravity and is based on two assumptions about semiclassical black holes: i) that they emit as black bodies, and ii) that they are perfect quantum emitters. The examples of higher dimensional gravity and of weakly coupled string theory are used to explicitly check our assumptions and to verify that the proposed bound holds. Finally, we discuss some consequences of the bound for theories of quantum gravity in general and for string theory in particular.

The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? And if the former, does it provide a complete description of the system or only a partial description? I shall address these questions here mainly from a Bohmian perspective, and shall argue that part of the difficulty in ascertaining the status of the wave function in quantum mechanics arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe, which, I argue, has a law-like character. From the wave function of the universe together with its configuration one can define the wave function of a subsystem of the universe. This, while objective, does indeed have a strong informational/subjective aspect.

The de Broglie-Bohm theory is about non-relativistic point-particles that move deterministically along trajectories. The theory reproduces the predictions of standard quantum theory given that the distribution of particle positions over an ensemble of systems, all described by the same wavefunction psi, equals the quantum equilibrium distribution |psi| squared. Numerical simulations by Valentini and Westman have illustrated that non-equilibrium particle distributions may relax to quantum equilibrium after some time. Here we consider non-equilibrium distributions and their relaxation properties for a particular class of trajectory theories, first studied in detail by Deotto and Ghirardi, that are empirically equivalent to the de Broglie-Bohm theory in quantum equilibrium. Joint work with Ward Struyve (KUL, Belgium).