Is gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence

TL;DR

This paper investigates whether gravity is intrinsically quantum by deriving its dynamics from spacetime thermodynamics in a local Rindler frame using the equivalence principle. The central postulate—horizon entropy proportional to area—paired with a Euclidean action–entropy relation yields the Einstein–Hilbert action as the bulk term plus a surface term, connecting the gravitational coupling to a fundamental area scale $\mathcal{A}_P$ and $\hbar$. A key result is the emergence of the first-order $\Gamma-\Gamma$ Lagrangian without explicit curvature input, with the full action written as the free energy $A_{grav} = S - \beta H$, highlighting holographic and quantum aspects of gravity. The framework points toward a microscopic quantum description of spacetime via horizon entanglement and surface degrees of freedom, though it leaves the cosmological constant undetermined and invites further work on the underlying microscopic structure of spacetime.

Abstract

The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain the insight that gravity must possess a geometrical description. I show that, using the same principle of equivalence, special relativity and quantum theory in the {\it local Rindler frame} one can obtain the Einstein-Hilbert action functional for gravity and thus the dynamics of the spacetime. This approach, which essentially involves postulating that the horizon area must be proportional to the entropy, uses the local Rindler frame as a natural extension of the local inertial frame and leads to the interpretation that the gravitational action represents the free energy of the spacetime geometry. As an aside, one also obtains a natural explanation as to: (i) why the covariant action for gravity contains second derivatives of the metric tensor and (ii) why the gravitational coupling constant is positive. The analysis suggests that gravity is intrinsically holographic and even intrinsically quantum mechanical.