2015/10/31 by Ivano Tavernelli
Mathematics · Medicine · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Biofield Effects and Biophysics #Classical mechanics #Curvature #De Broglie–Bohm theory #Duality (order theory) #Geodesic #Geometry #Mathematics #Matter wave #Physics #Probability amplitude #Problem of time #Quantum #Quantum Mechanics and Applications #Quantum dissipation #Quantum dynamics #Quantum gravity #Quantum mechanics #Quantum potential #Quantum process #Relativistic quantum mechanics #Wave function #Wave–particle duality #quant-ph
paper · pdf · doi:10.1016/j.aop.2016.04.020
openalex publication_date 2016/05/11 · arxiv created 2017/08/12 · arxiv updated 2017/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.