Foundations of Physics

, Volume 41, Issue 9, pp 1437–1453 | Cite as

A Classical Explanation of Quantization

  • Gerhard GrössingEmail author
  • Johannes Mesa Pascasio
  • Herbert Schwabl


In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck’s constant h is shown to be indicative of a particle’s “zitterbewegung” and thus of a fundamental angular momentum. The latter is identified with quantum mechanical spin, a residue of which is thus present even in the non-relativistic Schrödinger theory.


Harmonic oscillator Brownian motion Langevin equation Nonequilibrium thermodynamics Quantum mechanics Spin 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Gerhard Grössing
    • 1
    Email author
  • Johannes Mesa Pascasio
    • 1
  • Herbert Schwabl
    • 1
  1. 1.Austrian Institute for Nonlinear StudiesViennaAustria

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