The weak equivalence principle and the Dirac constant: A result from the holographic principle

TL;DR

This paper links the weak equivalence principle in general relativity to a fundamental quantum constant through the holographic principle, revealing a deep connection between gravity and quantum mechanics.

Contribution

It proposes a novel equivalence between the weak equivalence principle and the dual roles of the Dirac constant within the holographic framework.

Findings

Shows the equivalence of the weak principle to Dirac constant duality

Derives a relation between Euclidean and Lorentzian actions via holography

Connects quantum uncertainty bounds with gravitational principles

Abstract

In this article, based on a recent formularization of the holographic principle proposed and investigated by the present author, we show that the weak equivalence principle in general relativity is equivalent to the equivalence between two forms of the Dirac constant, that is, the action of the spin degree of freedom in the two-dimensional Hilbert space and the lower bound in the quantum mechanical uncertainty relations. This result follows from an equation between the Euclidean and Lorentzian world-line actions of a massive particle divided by the Dirac constant, via the Wick rotation, by using the Euclidean and Lorentzian actions of a holographic tensor network, whose quantum state is classicalized by introducing the superselection rule.