# The possibility of Scale Relativistic signatures in the Brownian motion of micro-spheres in optical traps

## TL;DR

This paper explores the potential for quantum-like signatures in the Brownian motion of micro-spheres in optical traps, suggesting that such effects could be detectable with current experimental techniques, challenging traditional distinctions between quantum and classical dynamics.

## Contribution

It proposes a novel hypothesis that macroscopic systems may exhibit quantum-like behavior under Scale Relativity, and demonstrates its potential observability in optical trap experiments.

## Key findings

- Quantum-like signatures could be present in macroscopic Brownian motion.
- Detection of such effects is feasible with current experimental setups.
- Implications for understanding structure formation in complex systems.

## Abstract

The development of a mechanics of non-differentiable paths suggested by Scale Relativity results in a foundation of Quantum Mechanics including Schr\"odinger's equation and all the other axioms under the assumption the path non-differentiability can be described as a Wiener process at the resolution-scale of observation. This naturally brings under question the possibility that the statistics of the dynamics of macroscopic systems fulfilling this hypothesis could fall under a quantum-like description with the Planck constant replaced with some other constant, possibly system specific, and corresponding to a diffusion coefficient. The observation of such a quantum-like dynamics would establish if the Scale Relativistic principle is implemented in macroscopic complex or chaotic systems. This would have major implications for the study of structure formation dynamics in various research fields. In this paper, I investigate the possibility for the detection of such an effect in the Brownian motion of a micro-sphere in an optical trap. I find that, if it exists, the observation of the transition to a quantum-like regime is within reach of modern experiments.