Amplitude for existence of spacetime points

TL;DR

This paper proposes a novel model where spacetime points have an amplitude of existence, potentially explaining gravitational effects without assuming a metric from the outset.

Contribution

It introduces a new approach to spacetime structure using amplitudes of existence, offering an alternative to metric-based descriptions.

Findings

Amplitude of existence $E(x)$ can model gravitational effects.

The model suggests a possible classical limit resembling a gravitational metric.

Provides a framework for spacetime dynamics without a predefined metric.

Abstract

This paper outlines a possibility for spacetime dynamics and structure, without postulating a metric ab initio. In this model, the closer an object is to a mass or energy source, the more paths through spacetime might be available to the object in the direction of the mass/energy, or the higher the amplitude associated with such paths. A simple possibility might be that spacetime points $x$ have an amplitude of existence $E(x)$ consistent with this. The magnitude of $E(x)$ might be greater or less than 1 at any point $x$; or the relative values of $E(x)$ might be what matters. In a classical limit, a function like $E(x)$ might give the effect of a gravitational metric.