The Possible Emergence of an Attractive Inverse-Square Law from the Wave-Nature of Particles

TL;DR

This paper proposes a wave-based particle model in finite space, suggesting that particles can attract each other via wave interactions, leading to an inverse-square law similar to gravity, derived from their wave nature.

Contribution

It introduces a model where particles as confined oscillations in a medium naturally produce an inverse-square attraction due to wave interactions.

Findings

Particles modeled as confined oscillations can attract each other.

An inverse-square acceleration law emerges from wave interactions.

The model's parameters are compared to gravitational constant G_N.

Abstract

A model of a particle in finite space is developed and the properties that the particle may possess under this model are studied. The possibility that particles attract each other due to their own wave nature is discussed. The assumption that the particles are spatially confined oscillations (SCO) in the medium is used. The relation between the SCO and the refractive index of the medium in the idealized universe is derived. Due to the plane wave constituents of SCOs, the presence of a refractive index field with a nonzero gradient causes the SCO to accelerate. The SCO locally changes the refractive index such that another SCO is accelerated towards it, and vice versa. It is concluded that the particles can attract each other due to their wave nature and an inverse-square-type acceleration emerges. The constant parameter in the inverse-square-type acceleration is used to compare with the gravitational constant $G_N$, and the possibility of non inverse-square-type behavior is preliminary discussed.