Scale Relativistic signature in the Brownian motion of micro-spheres in optical traps
2017
The development of mechanics of nondifferentiable paths36 suggested by Scale Relativity31,32 results in a foundation of Quantum Mechanics30,37 including Schrodinger’s equation and all the other axioms under the assumption the path nondifferentiability 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.
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