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Gravity as an Emergent Phenomenon

By Professor Sumit Das, College of Arts & Sciences Distinguished Professor (2019)

As far as we know, almost all natural phenomena stem from four fundamental interactions: electromagnetism, weak interaction, strong interaction, and gravity. The first three are governed by the laws of quantum mechanics. It is natural to think that gravity should also be governed by quantum mechanics. However ever since Einstein discovered the laws of gravity in 1915, reconciling gravity with quantum mechanics has been famously problematic.

One reason for this difficulty is the following. The other forces can be understood as processes happening in a fixed space-time background, where spatial distances and time intervals are fixed once and for all. For example, light is an electromagnetic wave which propagates in this fixed space-time. However, in the well tested theory of gravity — Einstein’s General Relativity — space- time itself is dynamical. A gravitational wave stretches or contracts space along its line of propagation. In this sense, points and distances between points are dynamical. Attempts to apply the laws of quantum mechanics naively to dynamical space-time have failed.

Recent theoretical developments have led to a radically different approach to the problem. In this approach, which originated in String Theory, the very notion of dynamical space is not fundamental. Rather, it is an emergent concept. Emergent concepts are ubiquitous in physics.

Consider, for example, water flowing through a pipe. Microscopically this a collection of molecules which are streaming along and colliding with each other and with the walls of the pipe. However, since there are a huge number of molecules, the problem of describing the motion of water in terms of molecules becomes enormously complicated. In fact, even if it is possible to do so, such a description will not be useful. Rather, it is much more useful to describe the water in terms of completely different concepts, such as density, viscosity, etc. These concepts are nonexistent at the molecular level. There is a well-known equation called the Navier Stokes equation which describes this motion. Notions like density and viscosity are examples of emergent concepts.

In this current view of gravity, smooth dynamical space itself is such an emergent concept, pretty much like a smooth density of water. At the microscopic level, physical processes are described in terms of very different concepts which can be treated in a quantum mechanical fashion. These microscopic models do not contain gravity and they are defined either in a lower dimensional fixed space, or in some cases, with no space at all. Pretty much like water, at the macroscopic level an alternative and more useful description emerges. In this description additional space dimensions emerge and the distance between points become dynamical. The equations which describe the physics in terms of these concepts are the equations of General Relativity — analogous to the Navier Stokes equation. The main challenge here is to discover the dictionary which relates the microscopic and macroscopic descriptions.

I have been involved in developing this view of emergent space and gravity from its inception. One aspect of my current research involves deciphering this dictionary. As in many other areas of physics, much progress has been made by studying toy models which capture the essential physics. Working with my UK graduate students and postdocs, and colleagues elsewhere, I have been able to understand the dictionary in a class of such models which, among other things, provide a microscopic description of black holes. This is particularly interesting since quantum processes leading to Hawking radiation from black holes have served as litmus tests for consistency of proposals for quantum gravity. These processes are manifested as chaotic behavior in these models which can be studied in a quantitative fashion, leading to a lot of recent progress in resolving puzzles related to Hawking radiation.

The second aspect of my work relates to the role of an important feature of quantum mechanics called entanglement. There is a lot of evidence that entanglement plays a major role in the emergence of smooth space-time. I have been involved in developing novel notions of entanglement which are particularly relevant to microscopic models of gravity which do not contain any a priori notion of space.

A third aspect of my work uses the connection of gravity to non-gravitational microscopic theories to learn about the microscopic theory. In most (non-gravitational) systems, it is often difficult to understand processes which are far from equilibrium. However, when these systems have equivalent gravitational descriptions, many of these processes can be quantitatively understood using the classical equations of gravity. Using this strategy, we have been able to find new universal non-equilibrium behavior in such systems near phase transitions.

The program of understanding quantum gravity using emergent space is still in its infancy, and I am sure there will be many exciting developments in the future.