Talks

The history of physics, from Galileo's spatialization of time to Einstein's block universe, and on to Julian Barbour's timeless quantum cosmology, tells a story by which time is demoted from a fundamental aspect of experience to an emergent illusion in a world held to be fundamentally timeless. The question I would like to address is, is this correct, or will the next stage in the development of physics require a rediscovery of time as a primary aspect of nature? One reason to bet on the reality of time is the strength of the argument of Pierce that laws of nature require explanation and that laws must evolve to be explained. This implies that time is prior to law, which means time cannot emerge from timeless law. This however raises a problem: is the evolution of law lawful? Are all laws effective and approximate? Is there a metalaw which governs the evolution of laws? If so, what selects the metalaw? One approach to this meta-laws dilemma is that the distinction between dynamical laws and the states they act on, which is absolute in most physical theories, is emergent. I present a simple model to illustrate this approach. This talk is partly based on joint work with Roberto Mangabeira Unger.

In his article `More is Different', P W Anderson (1972) sensitized the physics community about importance of emergence, by using concepts such as broken symmetry, emergent hierarchical structures, constructionists converse of reductionism etc. The manifestation of complexity and hierarchy in the quantum many particle systems go beyond broken symmetries. In certain quantum systems we have the opposite - emergence of new local gauge symmetries. This idea was introduced, for example, for Mott insulators, by Anderson and us in 1988. Properties such as entanglement, different possible statistics of identical particles, multi particle wave interference, vastness of Hilbert space etc;, which are unique to the world of quantum, leads to a wonderful richness in physics and mathematics, including emergent gauge symmetries, gauge fields, quantum order, holographic correspondences and continuing surprises.

This talks will focus on a particular example of emergent phenomenon in a particular system. By adding to our repertoire of emergent phenomena, it may help deepen our discussions of the topic in the abstract. The system belongs to the new family that has swept condensed matter physics and goes by the name of topological insulators, which paradoxically also includes super°uids and superconductors for these too have no low energy excitations in the bulk. While no one cared much about insulators (except while standing on one of them to change a light bulb or fuse) things changed when it was realized that insulators come in two kinds. The topological ones have gapless excitations at the edge while the others do not. The bulk topological quantum number implies a gapless edge and prevents any smooth or continuous perturbation like disorder from producing a gap. Consider the d dimensional bulk superconductor with its N-particle wavefunction ©(r1; ; ; rN). The gapless edge has d¡1 spatial dimensions and a d dimensional Euclidean spacetime. Let G(r1; ; ; rN) denote its N-point correlation functions of Heisenberg ¯eld operators. It had been noticed that quite remarkably ©(r1; ; ; rN) = G(r1; ; ; rN) for a family of superconductors and super°uids. How can a nonrelativistic thing like a wave function in the bulk equal relativistic correlation function at the edge? Ashvin Vishwanath (Berkeley) and I showed that this follows from the approximate Lorentz invariance of the Euclidean action. Our explanation along with necessary background will be furnished.

Emergent phenomena are typically described as those that cannot be reduced, explained nor predicted from their microphysical base. However, this characterization can be fully satisfied on purely epistemological grounds, leaving open the possibility that emergence may simply point to a gap in our knowledge of these phenomena. By contrast, Anderson

Effective field theories, underpinned by the resnormalization framework, are a central feature of condensed matter physics and relativistic field theory. However the phenomenon of decoherence is not so easily subsumed under this framework. Ordinary environmental decoherence may lead to very unusual effective theories, and recent ideas about intrinsic decoherence in Nature (eg., Penrose's ideas aobut gravitational decoherence) do not obviously lead to any effective field theory. I will review our ideas aobut environmental decoherence, with some examples from condensed matter physics, highlighting some of the peculiar features of these. I will then discuss what we know of intrinsic decoherence (which in some cases amounts to a breakdonw of quantum mechanics, focussing on a new path integral formulation of Penrose's ideas.

The canonical example of emergence is how thermodynamics emerges from microscopic laws through statistical mechanics. One of the vexing questions in the foundations of statistical mechanics is though how is it possible to justify thermalization in a closed system. In quantum statistical mechanics, entanglement can give the key to answer this question, provided that they are typically very entangled. Fortunately, most states in the Hilbert space are maximally entangled. Unfortunately, most states in the Hilbert space of a quantum many body system are not physically accessible. We show that the typical entanglement in physical ensembles of states is still very high.