Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator
Abstract
1. Introduction
2. The Basis of SED
Statistics of the Stochastic Electric Field
3. The Harmonic Oscillator in SED and Its Steady State
The Steady State
4. Average Progression of a Specific Orbit
4.1. Average Change of Energy of a Specific Orbit at Moderate Times
4.2. The Energy Gain Term
4.3. The Energy Loss Term
4.4. The Energy Balance for a Specific Orbit
4.5. Renormalized Force in the Temporal Description
5. Summary: Lessons from the Harmonic Oscillator Analysis
- (1)
- The noise must be renormalized to suppress the dominance of high frequencies;
- (2)
- the damping has to be treated non-perturbatively to set the width of the resonance window;
- (3)
- the energy absorbed from the field quickly goes to its ensemble average; and
- (4)
- the energy radiation contains effects from both the classical orbit and the stochastic field.
Funding
Acknowledgments
Conflicts of Interest
References
- Allahverdyan, A.E.; Balian, R.; Nieuwenhuizen, T.M. Understanding quantum measurement from the solution of dynamical models. Phys. Rep. 2013, 525, 1–166. [Google Scholar] [CrossRef]
- Allahverdyan, A.E.; Balian, R.; Nieuwenhuizen, T.M. A sub-ensemble theory of ideal quantum measurement processes. Ann. Phys. 2017, 376, 324–352. [Google Scholar] [CrossRef]
- Cetto, A.M.; de la Peña, L. The Quantum Dice, an Introduction to Stochastic Electrodynamics; Kluwer Academic: Dordrecht, The Netherlands, 1996. [Google Scholar]
- De la Peña, L.; Cetto, A.M.; Vald’es-Hern’andez, A. The Emerging Quantum: The Physics Behind Quantum Mechanics; Springer: Berlin, Germany, 2014. [Google Scholar]
- Marshall, T.W. Random electrodynamics. Proc. R. Soc. Lond. Ser. A 1963, 276, 475–491. [Google Scholar]
- De la Peña, L.; Cetto, A. The quantum harmonic oscillator revisited: A new look from stochastic electrodynamics. J. Math. Phys. 1979, 20, 469–483. [Google Scholar] [CrossRef]
- Boyer, T.H. Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation. Phys. Rev. D 1975, 11, 790. [Google Scholar] [CrossRef]
- Santos, E. The harmonic oscillator in stochastic electrodynamics. Il Nuovo C. B (1971–1996) 1974, 19, 57–89. [Google Scholar] [CrossRef]
- Marshall, T.; Claverie, P. Stochastic electrodynamics of nonlinear systems. I. Partial in a central field of force. J. Math. Phys. 1980, 21, 1819–1825. [Google Scholar] [CrossRef]
- França, H.d.M.; Marshall, T. Excited states in stochastic electrodynamics. Phys. Rev. A 1988, 38, 3258. [Google Scholar] [CrossRef]
- Cavalleri, G. The propagator of stochastic electrodynamics. Phys. Rev. D 1981, 23, 363. [Google Scholar] [CrossRef]
- Nieuwenhuizen, T. On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics. Entropy 2016, 18, 135. [Google Scholar] [CrossRef]
- Nieuwenhuizen, T.M.; Liska, M.T. Simulation of the hydrogen ground state in stochastic electrodynamics. Phys. Scr. 2015, 2015, 014006. [Google Scholar] [CrossRef]
- De la Peña, L. Introducción a la Mecánica Cuántica; UNAM-FCE: Mexico City, Mexico, 1980. [Google Scholar]
- Puthoff, H.E. Ground state of hydrogen as a zero-point-fluctuation-determined state. Phys. Rev. D 1987, 35, 3266. [Google Scholar] [CrossRef]
- Nieuwenhuizen, T.M.; Liska, M.T. Simulation of the Hydrogen Ground State in Stochastic Electrodynamics-2: Inclusion of Relativistic Corrections. Found. Phys. 2015, 45, 1190–1202. [Google Scholar] [CrossRef]
© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Nieuwenhuizen, T.M. Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator. Atoms 2019, 7, 59. https://doi.org/10.3390/atoms7020059
Nieuwenhuizen TM. Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator. Atoms. 2019; 7(2):59. https://doi.org/10.3390/atoms7020059
Chicago/Turabian StyleNieuwenhuizen, Theodorus Maria. 2019. "Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator" Atoms 7, no. 2: 59. https://doi.org/10.3390/atoms7020059
APA StyleNieuwenhuizen, T. M. (2019). Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator. Atoms, 7(2), 59. https://doi.org/10.3390/atoms7020059