(1+1)-Dimensional Entropic Gravity

TL;DR

This paper explores the formulation of entropic gravity in one spatial dimension, showing that gravitational laws can be derived without area-based holography and discussing the implications for spacetime emergence.

Contribution

It demonstrates that entropic gravity can be consistently formulated in one spatial dimension, challenging previous assumptions about its ill-defined nature in this setting.

Findings

Gravitational force law derived without area dependence

Information at each point acts as an internal degree of freedom

Supports the idea of spacetime and gravity as emergent phenomena

Abstract

We consider the formulation of entropic gravity in two spacetime dimensions. The usual gravitational force law is derived even in the absence of area, as normally required by the holographic principle. A special feature of this perspective concerns the nature of temperature and entropy defined at a point. We argue that the constancy of the gravitational force in one spatial dimension implies the information contained at each point in space is an internal degree of freedom on the manifold, and furthermore is a universal constant, contrary to previous assertions that entropic gravity in one spatial dimension is ill-defined. We give some heuristic arguments for gravitation and information transfer constraints within this framework, thus adding weight to the contention that spacetime and gravitation might be emergent phenomena.