A Characteristic Particle Length

TL;DR

This paper proposes a new characteristic length scale for particles derived from quantum wavefunctions, independent of the speed of light, potentially affecting small-scale observations.

Contribution

It introduces a novel characteristic particle length based on wavefunction zeros, independent of relativistic constants, expanding understanding of quantum scales.

Findings

Derived a characteristic length  from wavefunction zeros

Proposed the length could influence observations of virus-sized objects

Established a new quantum scale unrelated to the speed of light

Abstract

It is argued that there are characteristic intervals associated with any particle that can be derived without reference to the speed of light $c$. Such intervals are inferred from zeros of wavefunctions which are solutions to the Schr\"odinger equation. The characteristic length is $\ell=\beta^2\hbar^2/(8Gm^3)$, where $\beta=3.8\dots$; this length might lead to observational effects on objects the size of a virus.