Thursday, October 08, 2020

Singularities and Spinors Were Just Another Day At The Office - Twistors Are Penrose's Big Bet  |  In the 1960s, in an attempt to understand quantum gravity, physicist Roger Penrose proposed such a radical alternative. In Penrose's twistor theory, geometric points are replaced by twistors—entities that most closely resemble stretched, light ray-like shapes. Within this twistor space, Penrose discovered a highly efficient way to represent fields that travel at the speed of light, such as electromagnetic and gravitational fields. Reality, however, is composed of more than fields—any theory needs also to account for the interactions between fields, such as the electric force between charges, or, in the more complicated case of General Relativity, gravitational attraction resulting from the energy of the field itself. However, including the interactions of General Relativity into this picture has proven a formidable task.

So can we express in twistor language a full-fledged quantum gravitational theory, perhaps simpler than General Relativity, but with both fields and interactions fully taken into account? Yes, according to Neiman.

Neiman's model builds on higher spin gravity, a model developed by Mikhail Vasiliev in the 1980s and '90s. Higher spin gravity can be thought of as the "smaller cousin" of String Theory, "too simple to reproduce General Relativity, but very instructive as a playground for ideas," as Neiman puts it. In particular, it is perfectly suited for exploring possible bridges between holography and twistor theory.

On one hand, as discovered by Igor Klebanov and Alexander Polyakov in 2001, higher spin gravity, just like , can be described holographically. Its behavior within space can be captured completely in terms of a boundary at infinity. On the other hand, its equations contain twistor-like variables, even if these are still tied to particular points in ordinary space.

From these starting points, Neiman's paper takes an additional step, constructing a mathematical dictionary that ties together the languages of holography and twistor theory.

"The underlying math that makes this story tick is all about square roots," writes Neiman. "It's about identifying subtle ways in which a geometric operation, such as a rotation or reflection, can be done 'halfway.' A clever square root is like finding a crack in a solid wall, opening it in two, and revealing a new world."

Using square roots in this way has a longstanding history in math and physics. In fact, the intrinsic shape of all matter particles—such as electrons and quarks—as well as twistors, is described by a square root of ordinary directions in space. In a subtle technical sense, Neiman's method for connecting space, its boundary at infinity, and twistor space, boils down to taking such a square root again.

Neiman hopes that his proof of concept can pave the way toward a quantum of gravity that does not rely on a boundary at infinity.

"It will take a lot of creativity to uncover the code of the world," says Neiman. "And there's joy in fumbling around for it."