Abstract
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.
Similar content being viewed by others
References
Grössing, G.: The vacuum fluctuation theorem: exact Schrödinger equation via nonequilibrium thermodynamics. Phys. Lett. A 372(25), 4556–4563 (2008). arXiv:0711.4945v2
Grössing, G.: On the thermodynamic origin of the quantum potential. Physica A 388, 811–823 (2009). arXiv:0808.3539v1
Nelson, E.: Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Rev. 150(4), 1079–1085 (1966)
Fritsche, L., Haugk, M.: A new look at the derivation of the Schrödinger equation from Newtonian mechanics. Ann. Phys. (Leipz.) 12(6), 371–403 (2003)
Guerra, F., Marra, R.: Stochastic mechanics of spin-1/2 particles. Phys. Rev. D 30(12), 2579–2584 (1984)
de la Peña, L., Cetto, A.M.: The quantum dice: an introduction to stochastic electrodynamics. In: Fundamental Theories of Physics, vol. 75, Kluwer Academic, Dordrecht (1996)
Boyer, T.H.: A brief survey of stochastic electrodynamics. In: Barut, A.O. (ed.) Foundations of Radiation Theory and Quantum Electrodynamics, pp. 45–63. Plenum, New York (1980)
Haisch, B., Rueda, A., Puthoff, H.E.: Inertia as a zero-point-field Lorentz force. Phys. Rev. A 49(2), 678–694 (1994)
Grössing, G., Fussy, S., Mesa Pascasio, J., Schwabl, H.: Emergence and collapse of quantum mechanical superposition: orthogonality of reversible dynamics and irreversible diffusion. Physica A 389(21), 4473–4484 (2010). arXiv:1004.4596v1
Grössing, G.: Sub-quantum thermodynamics as a basis of emergent quantum mechanics. Entropy 12(9), 1975–2044 (2010). http://www.mdpi.com/1099-4300/12/9/1975/
Grössing, G., Fussy, S., Mesa Pascasio, J., Schwabl, H.: Elements of sub-quantum thermodynamics: quantum motion as ballistic diffusion. arXiv:1005.1058v2 (2010). To be published; based on a talk at the Fifth International Workshop DICE2010, Castiglioncello, Tuscany, September 13–17, 2010
Couder, Y., Protière, S., Fort, E., Boudaoud, A.: Dynamical phenomena: walking and orbiting droplets. Nature 437, 208–208 (2005)
Couder, Y., Fort, E.: Single-particle diffraction and interference at a macroscopic scale. Phys. Rev. Lett. 97(154), 101 (2006)
Protière, S., Boudaoud, A., Couder, Y.: Particle-wave association on a fluid interface. J. Fluid Mech. 554, 85–108 (2006)
Eddi, A., Fort, E., Moisy, F., Couder, Y.: Unpredictable tunneling of a classical wave-particle association. Phys. Rev. Lett. 102(204), 401 (2009)
Fort, E., Eddi, A., Boudaoud, A., Moukhtar, J., Couder, Y.: Path-memory induced quantization of classical orbits. Proc. Natl. Acad. Sci. USA 107(41), 17,515–17,520 (2010)
Coffey, W.T., Kalmykov, Y.P., Waldron, J.T.: The Langevin equation: with applications to stochastic problems in physics, chemistry and electrical engineering. In: World Scientific Series in Contemporary Chemical Physics, vol. 14, 2 edn., World Scientific, Singapore (2004)
Verlinde, E.P.: On the origin of gravity and the laws of Newton (2010). arXiv:1001.0785v1
Padmanabhan, T.: Thermodynamical aspects of gravity: new insights. Rep. Prog. Phys. 73, 046901 (2010). arXiv:0911.5004v2
Wallstrom, T.C.: Inequivalence between the Schrödinger equation and the Madelung hydrodynamic equations. Phys. Rev. A 49, 1613–1617 (1994)
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics: Mainly Mechanics, Radiation and Heat, vol. 1. Addison-Wesley, Reading (1966)
Esposito, S.: On the role of spin in quantum mechanics. Found. Phys. Lett. 12(2), 165–177 (1999). arXiv:quant-ph/9902019v1
Fritsche, L., Haugk, M.: Stochastic foundation of quantum mechanics and the origin of particle spin (2009). arXiv:0912.3442v1
Salesi, G.: Spin and Madelung fluid. Mod. Phys. Lett. A 11(22), 1815–1823 (1996). arXiv:0906.4147v1
Yang, C.: Modeling quantum harmonic oscillator in complex domain. Chaos Solitons Fractals 30(2), 342–362 (2006)
Recami, E., Salesi, G.: Kinematics and hydrodynamics of spinning particles. Phys. Rev. A 57(1), 98–105 (1998)
Salesi, G., Recami, E.: A velocity field and operator for spinning particles in (nonrelativistic) quantum mechanics. Found. Phys. 28(5), 763–773 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grössing, G., Mesa Pascasio, J. & Schwabl, H. A Classical Explanation of Quantization. Found Phys 41, 1437–1453 (2011). https://doi.org/10.1007/s10701-011-9556-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-011-9556-1