Emergent Spacetime and The Origin of Gravity

Understand

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.