The space time DoF surface density as a phase-space of accelerating reference frames

TL;DR

This paper demonstrates that Padmanabhan's surface density of spacetime degrees of freedom can be understood as a projected phase space associated with an accelerating reference frame, linking it to a canonical ensemble perspective.

Contribution

It introduces a phase space construction based on an accelerating vector field, providing a new interpretation of Padmanabhan's surface density as a spatial phase space.

Findings

Padmanabhan's density is derived from a phase space related to acceleration.

The density corresponds to the projected phase space during one Euclidean time period.

This links spacetime degrees of freedom to a canonical ensemble framework.

Abstract

Padmanabhan found a definition for the surface density of space time degrees of freedom. We prove that this density can be constructed from a phase space which is derived with respect to a special space like vector field. This vector field is the direction of an accelerating vector field. After projecting this phase space along a velocity vector field, we show that Padmanabhan's surface density is actually the projected phase space during one period of the Euclidean time which is expected for a canonical ensemble. This suggests that Padmanabhan's density should be regarded as a spatial phase space which is driven by acceleration.