Conference

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.

I will begin by discussing some of the strongest observational evidence for Lorentz symmetry, and the essential role that Lorentz symmetry appears to play in the consistency of black hole thermodynamics. Next I will discuss some reasons for suspecting that Lorentz symmetry may nevertheless be emergent. And finally I will discuss difficulties with the concept of emergent Lorentz symmetry, and how such difficulties might conceivably be overcome.

This paper has two aims. The first is to improve upon the diverse and often muddled philosophical characterizations of emergence by articulating reasonably precise necessary and sufficient conditions for a phenomenon to count as emergent in physics. Central to this account of emergence is the idea that emergent phenomena cannot be explained reductively. The second aim of the paper is to apply this account to the use of effective field theories in gravitational physics. Effective field theories have recently been applied to model the inspiral trajectories (and other features) of two compact, massive objects orbiting each other, with excellent predictive success. The calculational machinery has been ported from quantum field theory, but the physical interpretation is significantly different. The paper concludes that this application of effective field theories to gravitational physics is clearly not a case of emergence.

Prominent philosophers of physics, including Craig Callender and John Earman, have issued stern warnings against drawing any foundations of physics conclusions from theories obtained by taking the thermodynamic limit. Without dismissing these worries entirely, I argue that we shouldn't take them too seriously.

At the level of effective field theory it is possible to establish analogies between non-gravitational and gravitational systems. For example, first order perturbation equations in an analogue gravity model can be written as a wave equation in a curved spacetime. Perhaps the most intriguing application of analogue gravity systems is the possibility to experimentally investigate open questions in semi-classical quantum gravity, such as the black hole evaporation process. I will briefly discuss our recent black hole experiment, which demonstrates the universality of the Hawking process. If time permits, I will discuss the possibility to extend the analogue gravity programme, and outline the necessary steps towards full quantum gravity experiments.

The concepts of emergence and analogy are very closely related -- A is like B vs A is B. I will discuss this in the context of the emergence of/analogy with Hwking radiation in the arena of fluid systems, and the possibility of doing experiments in the lab. Does this mean gravity is emergent from some aether like theory? I think attempts to do that are fraught with difficulties, and will briefly discuss why I think so.