Emergent Spacetime and The Origin of Gravity

TL;DR

This paper explores how electromagnetism can be geometrized in noncommutative spacetime, leading to an emergent gravity framework that offers new insights into the origin of spacetime and the cosmological constant problem.

Contribution

It demonstrates that electromagnetism in noncommutative spacetime can be geometrized, revealing gravity as an emergent phenomenon and providing a novel perspective on spacetime's origin.

Findings

Electromagnetism can be locally eliminated via coordinate transformations in NC spacetime.

Emergent gravity explains the dynamical origin of flat spacetime.

This approach offers a potential solution to the cosmological constant problem.

Abstract

We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence, the electromagnetism can be realized as a geometrical property of spacetime like gravity. We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity, dubbed as the emergent gravity. We discuss how the emergent gravity reveals a novel, radically different picture about the origin of spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity. This spacetime picture turns out to be crucial for a tenable solution of the cosmological constant problem.