Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Abstract

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in the framework of the theory of scale relativity. After having analyzed the actual status of the various postulates, rules and principles that underlie the present axiomatic foundation of quantum mechanics (in terms of main postulates, secondary rules and derived `principles'), we attempt to provide the reader with an exhaustive view of the matter, by both gathering here results which are already available in the literature, and deriving new ones which complete the postulate list.

30 pages, no figure

References in corpus (6)

• Non-differentiable variational principles
• Quantum-classical transition in Scale Relativity
• Non-Abelian gauge field theory in scale relativity
• Incompleteness of trajectory-based interpretations of quantum mechanics
• The Pauli equation in scale relativity
• Structure of Fluctuation Terms in the Trace Dynamics Ward Identity

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• The origins of macroscopic quantum coherence in high temperature super conductivity
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• Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
• Resolution-scale relativistic formulation of non-differentiable mechanics
• Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables
• Chaotic motion in classical fluids with scale relativistic methods
• The possibility of Scale Relativistic signatures in the Brownian motion of micro-spheres in optical traps
• Intrinsic quantum dynamics of particles in brane gravity
• Emergence of complex and spinor wave functions in Scale Relativity. II. Lorentz invariance and bi-spinors
• The Burgers equations and the Born rule