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Stochastic electrodynamics (SED) is a variant of classical electrodynamics (CED) of theoretical physics. SED consists of a set of controversial theories that posit the existence of a classical Lorentz invariant radiation field having statistical properties similar to that of the electromagnetic zero-point field (ZPF) of quantum electrodynamics (QED).
Investigations of SED have been concerned with:
- The degree to which this prescription might cause SED to mimic some behaviors traditionally considered to be the exclusive domain of quantum mechanics; and
- A possible classical ZPF-based origin for gravity, inertia and the photoelectric effect.
The reported results are subject to considerable argument. Even so, there is a fair amount of interest in SED as this suggests the possibility of anti-gravity, reactionless drives or free energy so claims for practical devices do occasionally appear. No practical devices have been publicly demonstrated or subjected to any universally agreed upon independent review.
Classical background field
The background field is introduced as a Lorentz force in the (classical) Abraham-Lorentz-Dirac equation (see: Abraham–Lorentz–Dirac force), where the classical statistics of the electric and magnetic fields and quadratic combinations thereof are chosen to match the vacuum expectation values of the equivalent operators in QED. The field is generally represented as a discrete sum of Fourier components each with amplitude and phase that are independent classical random variables, distributed so that the statistics of the fields are isotropic and unchanged under boosts. This prescription is such that each Fourier mode at frequency (f) is expected to have an energy of hf/2, equaling that of the ground state of the vacuum modes of QED. Unless cut off, the total field has an infinite energy density, with a spectral energy density (per unit frequency per unit volume) [2h/c3]f3 where h is Planck's constant. Consequently, the background field is a classical version of the electromagnetic ZPF of QED, though in SED literature the field is commonly referred to simply as 'the ZPF' without making that distinction. It should be noted that any finite cutoff frequency of the field itself would be incompatible with Lorentz invariance. For this reason, some researchers prefer to think of cutoff frequency in terms of the response of particles to the field rather than as a property the field itself.
Stochastic electrodynamics is a term for a collection of research efforts of many different styles based on the ansatz that there exists a Lorentz invariant random electromagnetic radiation. The basic ideas have been around for a long time; but Marshall (1963) and Brafford seem to have been the originators of the more concentrated efforts starting in the 1960s. Thereafter, Boyer, de la Pena and Cetto were perhaps the most prolific contributors in the 1970s and beyond. Others have made contributions, alterations and proposals concentrating on the application of SED to problems in QED. A separate thread has been the investigation of an earlier proposal by Walther Nernst attempting to use the SED notion of a classical ZPF to explain inertial mass as due to a vacuum reaction.
In 2000, Trevor Marshall derived an experimental prediction of SED dubbed "spontaneous parametric up-conversion" (SPUC) as a dual process to the well-known spontaneous parametric down-conversion (SPDC). SPUC was tested in 2009 and 2010 with positive results.
In 2010, Cavalleri et al. introduced SEDS ('pure' SED, as they call it, plus spin) as a fundamental improvement which they claim potentially overcomes all the known drawbacks to SED. They also claim SEDS resolves four observed effects that are so far unexplained by QED, i.e., 1) the physical origin of the ZPF, and its natural upper cutoff; 2) an anomaly in experimental studies of the neutrino rest mass; 3) the origin and quantitative treatment of 1/f noise; and 4) the high-energy tail (~ 1021 eV) of cosmic rays. Two double-slit electron diffraction experiments are proposed to discriminate between QM and SEDS.
Inconclusive but encouraging experiments were carried out in 2012 by Dmitriyeva and Moddel in which emissions in "... infrared was clearly observed" which they could not explain using "...conventional thermodynamic models".
In 2013 Auñon et al. showed that Casimir and Van der Waals interactions are a particular case of stochastic forces from electromagnetic sources when the broad Planck's spectrum is chosen and the wavefields are non-correlated. Addressing fluctuating partially coherent light emitters with a tailored spectral energy distribution in the optical range, this establishes the link between stochastic electrodynamics and coherence theory; henceforth putting forward a way to optically create and control both such zero-point fields as well as Lifshitz forces  of thermal fluctuations. In addition, this opens the path to build many more stochastic forces on employing narrow-band light sources for bodies with frequency-dependent responses.
In a 2014 dissertation Carlos Alberto de Oliveira Henriques measured the energy shift in the atomic levels of Xe atoms as they passed through nano-porous Casimir membranes. Some evidence of anomalous radiation were observed, however, he was not able to distinguish this radiation conclusively from the background due to said shortcomings in the detector.
Scope of SED
SED has been used in attempts to provide a classical explanation for effects previously considered to require quantum mechanics (here restricted to the Schrödinger equation and the Dirac equation and QED) for their explanation. It has also been used to motivate a classical ZPF-based underpinning for gravity and inertia. There is no universal agreement on the successes and failures of SED, either in its congruence with standard theories of quantum mechanics, QED, and gravity, or in its compliance with observation. The following SED-based explanations are relatively uncontroversial and are free of criticism at the time of writing:
The following SED-based calculations and SED-related claims are more controversial and some have been subject to published criticism:
- The ground state of the harmonic oscillator 
- The ground state of the hydrogen atom 
- De Broglie waves 
- Gravitation 
- Non-locality and tests of Bell's theorem
Zero point energy
According to Haisch and Rueda, inertia arises as an electromagnetic drag force on accelerating particles, produced by interaction with the zero-point field. In their 1998 Ann. Phys. paper (see citations), they speak of a "Rindler flux", presumably meaning the Unruh effect, and claim to have computed a nonzero "z.p.f. momentum". This computation rests upon their claim to compute a nonzero "z.p.f. Poynting vector".
These proposals for zero-point energy suggest a source of low or no cost free energy from the vacuum as well as the hope of developing a reactionless drive. NASA continues to make assessments: In the usual interpretation of vacuum energy it is not possible to use it to do work. However, SED takes a rather more literal, classical interpretation, and views the very high energy density of the electromagnetic vacuum as propagating waves, which must necessarily carry considerable energy and momentum flux, ordinarily not evident in the absence of matter, because the flux is isotropic.
- Physique synergétique (French)
- França, H. M. (2012). "The Schrödinger equation, the zero-point electromagnetic radiation and the photoelectric effect". arXiv:1207.4076.
- Marshall, T. W. (1963). "Random Electrodynamics". Proceedings of the Royal Society A 276 (1367): 475–491. Bibcode:1963RSPSA.276..475M. doi:10.1098/rspa.1963.0220.
- Boyer, Timothy H. (1975). "Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation". Phys. Rev. D 11 (4): 790–808. Bibcode:1975PhRvD..11..790B. doi:10.1103/PhysRevD.11.790.
- Boyer, T. H. (1980). "A Brief Survey of Stochastic Electrodynamics". Foundations of Radiation Theory and Quantum Electrodynamics. pp. 49–64. ISBN 0-306-40277-7.
- Boyer, Timothy H. (1985). "The Classical Vacuum". Scientific American 253 (2): 70–78. doi:10.1038/scientificamerican0885-70.
- de la Pena, L. & Cetto, A. M. (1996). The Quantum Dice: An Introduction to Stochastic Electrodynamics. Dordrecht: Kluwer. ISBN 0-7923-3818-9. OCLC 33281109. ISBN 0-7923-3818-9
- de la Pena, L. & Cetto, A. M. (2005). "Contribution from stochastic electrodynamics to the understanding of quantum mechanics". arXiv:quant-ph/0501011 [quant-ph].
- Marshall, Trevor W. (9 March 2002). "Nonlocality - The party may be over". arXiv:quant-ph/0203042 [quant-ph].
- Sun, Jinyu; Zhang, Shian; Jia, Tianqing; Wang, Zugeng; Sun, Zhenrong (2009). "Femtosecond spontaneous parametric upconversion and downconversion in a quadratic nonlinear medium". Journal of the Optical Society of America B 26 (3): 549–553. Bibcode:2009JOSAB..26..549S. doi:10.1364/JOSAB.26.000549.
- S. Akbar Ali, P. B. Bisht, A. Nautiyal, V. Shukla, K. S. Bindra, and S. M. Oak (2010). "Conical emission in β-barium borate under femtosecond pumping with phase matching angles away from second harmonic generation". Journal of the Optical Society of America B 27 (9): 1751–1756. Bibcode:2010JOSAB..27.1751A. doi:10.1364/JOSAB.27.001751.
- Giancarlo Cavalleri, Francesco Barbero, Gianfranco Bertazzi, Eros Cesaroni, Ernesto Tonni, Leonardo Bosi, Gianfranco Spavieri and George Gillies (2010). "A quantitative assessment of stochastic electrodynamics with spin (SEDS): Physical principles and novel applications.". Frontiers of Physics in China 5 (1): 107–122. Bibcode:2010FrPhC...5..107C. doi:10.1007/s11467-009-0080-0.
- Olga Dmitriyeva and Garret Moddel (2012). "Test of zero-point energy emission from gases flowing through Casimir cavities". Physics Procedia 38: 8–17. Bibcode:2012PhPro..38....8D. doi:10.1016/j.phpro.2012.08.007.
- Juan Miguel Auñon, Cheng Wei Qiu and Manuel Nieto-Vesperinas (2013). "Tailoring photonic forces on a magnetodielectric nanoparticle with a fluctuating optical source". Physical Review A 88: 043817. Bibcode:2013PhRvA..88d3817A. doi:10.1103/PhysRevA.88.043817.
- Leonard Mandel and Emil Wolf (1995). Optical Coherence and Quantum Optics. Cambridge, UK: Cambridge University Press. ISBN 9780521417112.
- E. M. Lifshitz, Dokl. Akad. Nauk SSSR 100, 879 (1955).
- "Study of atomic energy shifts induced by Casimir cavities" (PDF). 2014.
- QED-based calculations commonly implicitly adopt the SED ansatz to compute Casimir forces. See for example C. Itzykson and J-B. Zuber (2006). Quantum Field Theory. Dover Publications. ISBN 978-0-486-44568-7.
- Boyer, T. H. (1973). "Retarded van der Waals forces at all distances derived from classical electrodynamics with classical electromagnetic zero-point radiation". Physical Review A 7 (6): 1832–40. Bibcode:1973PhRvA...7.1832B. doi:10.1103/PhysRevA.7.1832.
- Boyer, T. H. (1973). "Diamagnetism of a free particle in classical electron theory with classical electromagnetic zero-point radiation". Physical Review A 21 (1): 66–72. Bibcode:1980PhRvA..21...66B. doi:10.1103/PhysRevA.21.66.
- Boyer, T. H. (1980). "Thermal effects of acceleration through random classical radiation". Physical Review D 21 (8): 2137–48. Bibcode:1980PhRvD..21.2137B. doi:10.1103/PhysRevD.21.2137.
- M. Ibison and B. Haisch (1996). "Quantum and Classical Statistics of the Electromagnetic Zero-Point Field". Physical Review A 54 (4): 2737–2744. arXiv:quant-ph/0106097. Bibcode:1996PhRvA..54.2737I. doi:10.1103/PhysRevA.54.2737.
- H. E. Puthoff (1987). "Ground state of hydrogen as a zero-point-fluctuation-determined state". Physical Review D 35 (20): 3266–3269. Bibcode:1987PhRvD..35.3266P. doi:10.1103/PhysRevD.35.3266.
- Kracklauer, A. F. (1999). "Pilot Wave Steerage: A Mechanism and Test". Foundations of Physics Letters 12 (2): 441–453. doi:10.1023/A:1021629310707.
- B. Haisch, A. Rueda, and H. E. Puthoff (1994). "Inertia as a zero-point-field Lorentz force". Physical Review A 49 (2): 678–694. Bibcode:2009PhRvA..79a2114L. doi:10.1103/PhysRevA.79.012114.
- J-L. Cambier (January 2009). "Inertial Mass from Stochastic Electrodynamics". In M. Millis; E. Davis. Frontiers of Propulsion Science (Progress in Astronautics and Aeronautics). AIAA. pp. 423–454. ISBN 9781563479564.
- A. D. Sakharov (1968). "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation". Soviet Physics Doklady 12: 1040. Bibcode:1968SPhD...12.1040S.
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- Millis, Marc G. (2007). Energy considerations of hypothetical space drives (PDF) (Report). American Institute of Aeronautics and Astronautics. AIAA–2007-5594. Retrieved January 10, 2014.
- Gribbin, John (1998). Q is for Quantum - An Encyclopedia of Particle Physics. Touchstone Books. ISBN 0-684-86315-4. OCLC 43411619.
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- Haisch, B.; Rueda, A. & Puthoff, H. E. (1994). "Inertia as a zero-point-field Lorentz force". Phys. Rev. A 49 (2): 678–694. Bibcode:1994PhRvA..49..678H. doi:10.1103/PhysRevA.49.678. PMID 9910287. on-line version from Haisch's website
- Rueda, Alfonso & Haisch, Bernard (1998). "Contribution to inertial mass by reaction of the vacuum to accelerated motion". Found. Phys. 28 (7): 1057–1108. doi:10.1023/A:1018893903079. physics/9802030
- Rueda, Alfonso & Haisch, Bernard (2005). "Gravity and the Quantum Vacuum Inertia Hypothesis". Ann. Phys. 14 (8): 479–498. arXiv:gr-qc/0504061. Bibcode:2005AnP...517..479R. doi:10.1002/andp.200510147. gr-qc/0504061
- California Institute for Physics and Astrophysics, a physics organization founded by Bernard Haisch
- H. E. Puthoff, Quantum Vacuum Fluctuations: A New Rosetta Stone of Physics?