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Zenith Grant Awardee

Dr. Justin Khoury

Perimeter Institute


Maulik Parikh, Columbia University

Project Title

The Boundary as the Distant Stars: Mach's Principle in General Relativity

Project Summary

Whenever we accelerate we feel forces. We are flung to the side when we speed around a corner, we snap upwards when the plummet of a bungee jump is suddenly arrested, our arms fly out when we spin around.

Yet beneath these familiar observations is a profound puzzle about the nature of space and time: what does it mean to accelerate? Is acceleration relative, like motion at a constant velocity? Would an astronaut spinning alone in an empty universe experience the same forces? Einstein brilliantly recognized that acceleration and gravity were one and the same. But since gravity is the influence of matter, could acceleration too depend on matter, and thus be relative?

This tantalizing idea, known as Mach's principle, has seduced generations of physicists. Yet attempts to implement it have floundered. We will revisit it with the new insight that one must also take into account the influence of distant matter at the furthest reaches of space-time. We hope to demonstrate that an astronaut would feel exactly the same forces if, instead of him, it was this "boundary matter" that was spinning. Thus all motion would be relative; indeed, the very shape of space-time would be determined by matter.

Technical Abstract

Mach's principle is the profound claim that inertial frames are fixed by the matter in the universe. We propose a precise formulation of Mach's principle, purely within Einstein's general theory of relativity, in which matter and geometry are in one-to-one correspondence. Einstein's equations are not modified, and no selection principle is applied to their solutions. The key insight is the observation that, besides bulk matter, one can also have boundary matter. Specification of both boundary and bulk stress tensors then uniquely fixes the geometry and, thereby, the inertial frames. Our approach draws on the black hole membrane paradigm and is consistent, in asymptotically AdS space-times, with holographic duality. It generates many provocative questions, such as whether an arbitrary world-line can be made inertial by adjusting boundary matter, whether Mach's principle can be cast in terms of symmetry breaking of an even greater relativity of motion, and whether we can regard ourselves as living inside a bubble of Machian boundary matter located at our cosmological horizon.

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