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International Journal of Theoretical Physics

Derivation of quantum mechanics from the Boltzmann equation for the Planck aether

Friedwardt Winterberg

Published Oct 1, 1995• 21 citations
Publisher
DOI
10.1007/bf00673076

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Abstract In the Planck aether hypothesis it is assumed that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying a nonrelativistic law of motion. If described by a quantum mechanical two-component nonrelativistic nonlinear operator field equation, this model has a spectrum of particles greatly resembling the particles of the standard model, with Lorentz invariance as a derived dynamical symmetry valid in the limit of energies small com­ pared to the Planck energy. Here we show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of the Boltzmann equation for the positive and negative Planck masses, with departures from quantum mechanics suppressed by the Planck length.
This paper is concerned with the modeling and analysis of quantum dissipation and diffusion phenomena in the Schrödinger picture. We derive and investigate in detail the Schrödinger-type equations accounting for dissipation and diffusion effects. From a mathematical viewpoint, this equation allows one to achieve and analyze all aspects of the quantum dissipative systems, regarding the wave equation, Hamilton–Jacobi and continuity equations. This simplification requires the performance of “the Madelung decomposition” of “the wave function”, which is rigorously attained under the general Lagrangian justification for this modification of quantum mechanics. It is proved that most of the important equations of dissipative quantum physics, such as convection-diffusion, Fokker–Planck and quantum Boltzmann, have a common origin and can be unified in one equation.