Meh Hui Teh Tuesday, December 5, 2017 2:00 PM (206 JFB)
Title: Scale Relativity: The Search of Quantum-like Signatures in Macroscopic Systems
Scale Relativity is the proposal to include resolution-scale at the fundamental level. In its application to mechanics, resolutions become relative attributes of reference frame alongside with position and motion. It opens up to the consideration of non- differentiable dynamical path and leads in a natural way to a foundation of quantum mechanics. The same development seems applicable to chaotic systems considered at times scales beyond their predictability horizon. This intriguing possibility motivates the search for quantum-like signatures in chaotic systems. I directed my focus to planetary systems since the only force involved is the gravitational force with a Keplerian 1/r potential. I expect to find quantum-like signatures with the radial positions of planets spaced in a way similar to hydrogen orbitals. I first find the Solar System to be a great compliance with such a description in two stages corresponding to the inner and outer system respectively. I then transposed the results of the Solar System analysis to the catalogue of exoplanets. I find a strong accumulation of exoplanets with orbital parameters corresponding to a principal quantum-like number n=1. Inspection of the data without restriction to the scale set by the Solar System suggests a better description with a main accumulation of exoplanets in n=2 and secondary accumulations for n ranging from 3 to 22. Although they are of low confidence level, these results are indicative that the Scale Relativity principle may be implemented in nature. Systematic effects that could be responsible for these results could not be identified nor excluded. The universality of the orbital scale of these systems is however not explained by Scale Relativity and comes as a surprise which calls for more investigation.
1. Teh, M. H., Nottale, L., LeBohec, S. (2017). Scale relativistic formulation of non- differentiable mechanics I: Application to the harmonic oscillator. https://arxiv.org/abs/1601.07778.
2. Teh, M. H., Nottale, L., LeBohec, S. (2017). Scale relativistic formulation of non-differentiable mechanics II: The Schroedinger picture. https://arxiv.org/abs/1701.00530.