Huygens-Fresnel Principle in Superspace

TL;DR

This paper introduces a novel approach to quantum gravity by applying a Huygens-Fresnel principle in superspace, aiming to bridge the gap between classical and quantum formulations through interference effects.

Contribution

It proposes a geometrodynamical formulation of gravity and a new intermediary method for quantization beyond the WKB approximation using interference in superspace.

Findings

Identifies difficulties in canonical quantum gravity approaches.

Suggests a Huygens-Fresnel inspired principle to improve quantization.

Provides a conceptual framework for interference effects in superspace.

Abstract

We first roughly present a summary of the optico-mechanical analogy, which has always been so profitable in physics. Then we put forward a geometrodynamical formulation of gravity suitable to our intentions, both formally and conceptually. We present difficulties in some approaches to canonically quantize gravity which can be amended by the idea put forward in this paper, which we introduce in the last section. It consists basically in trying to find an intermediary between the quantization step going from the classical superhamiltonian constraint to the Wheeler-DeWitt equation. This is accomplished by inputting interference beyond the WKB approximation, through a type of Huygens-Fresnel Principle (HFP) in superspace.