# Stochastic electrodynamics

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In theoretical physics, **Stochastic Electrodynamics (SED)** is a variant of Classical Electrodynamics (CED) which posits 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
^{[1]}

There is not universal agreement on the success of these endeavors.

## The 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 is expected to have an energy of , equaling that of the ground state of the vacuum modes of QED. Unless cutoff, the total field has an infinite energy density, with a spectral energy density (per unit frequency per unit volume) proportional to where 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.

## Brief history

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 (for reviews see Boyer 1975, 1980, 1985) and de la Pena & Cetto (1996, 2005) were perhaps the most prolific contributors to SED 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)^{[2]} as a dual process to the well-known spontaneous parametric down-conversion (SPDC). SPUC was tested in 2009 and 2010 with positive results.^{[3]}^{[4]}

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 (~ eV) of cosmic rays. Two double-slit electron diffraction experiments are proposed to discriminate between QM and SEDS^{[5]}

## 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 not 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 Casimir force
^{[6]} - The Van der Waals force
^{[7]} - Diamagnetism
^{[8]} - The Unruh effect
^{[9]}

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
^{[10]} - The ground state of the hydrogen atom
^{[11]} - de Broglie waves
^{[12]} - Inertia
^{[13]} - Gravitation
^{[14]} - Non-locality and tests of Bell's theorem
^{[15]}

## The work of Haisch and Rueda

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"*.

## Zero Point Energy Details

The proposals of Haisch and Rueda for zero point energy might ultimately provide no cost "energy from the vacuum", thereby solving many current problems in contemporary human society. Others ^{[16]} claim that the work of Haisch, Rueda, and Puthoff holds out hope of developing a reactionless drive. NASA continues to make assessments:^{[17]}^{[18]} In the usual interpretation of vacuum energy it is not possible to use it to do work.^{[19]} 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.

## Fictional References

Arthur C. Clarke describes a "SHARP drive" (for Sakharov, Haisch, Rueda and Puthoff) in his 1997 novel "3001: The Final Odyssey". This follows speculation in (non-technical) papers by Haisch and Rueda on the control of inertia using SED principles.

## See also

- Casimir effect
- Vacuum energy
- Zero-point energy
- Andrei Sakharov
- Harold E. Puthoff
- Physique synergétique Template:Fr

## Notes and in-line references

- ↑ http://arxiv.org/pdf/1207.4076.pdf
- ↑ Trevor W. Marshall, 2000, "Nonlocality - The party may be over", http://arxiv.org/abs/quant-ph/0203042
- ↑ Jinyu Sun, Shian Zhang, Tianqing Jia, Zugeng Wang, and Zhenrong Sun, 2003, "Femtosecond spontaneous parametric upconversion and downconversion in a quadratic nonlinear medium.", http://www.opticsinfobase.org/abstract.cfm?URI=josab-26-3-549
- ↑ 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.", http://www.opticsinfobase.org/abstract.cfm?URI=josab-27-9-1751
- ↑ Giancarlo Cavalleri, Francesco Barbero, Gianfranco Bertazzi, Eros Cesaroni, Ernesto Tonni, Leonardo Bosi, Gianfranco Spavieri and George Gillies, "A quantitative assessment of stochastic electrodynamics with spin (SEDS): Physical principles and novel applications.", http://www.springerlink.com/content/56g7l52656544387/
- ↑ QED-based calculations commonly implicitly adopt the SED ansatz to compute Casimir forces. See for example C. Itzykson and J-B. Zuber,
*Quantum Field Theory*, Dover Publications, 2006. ISBN 978-0-486-44568-7 - ↑ T. H. Boyer (1973), "Retarded van der Waals forces at all distances derived from classical electrodynamics with classical electromagnetic zero-point radiation", Physical Review A, Vol. 7 No. 6, 1832-40.
- ↑ T. H. Boyer (1973), "Diamagnetism of a free particle in classical electron theory with classical electromagnetic zero-point radiation", Physical Review A, Vol. 21 No. 1, 66-72.
- ↑ T. H. Boyer (1980), "Thermal effects of acceleration through random classical radiation", Physical Review D, Vol. 21 No. 8, 2137-48.
- ↑ M. Ibison and B. Haisch (1996), "Quantum and Classical Statistics of the Electromagnetic Zero-Point Field", Physical Review A, Vol. 54 No. 4, 2737-44.
- ↑ H. E. Puthoff (1987), "Ground state of hydrogen as a zero-point-fluctuation-determined state", Physical Review D, Vol. 35, No. 20, 3266-9.
- ↑ Kracklauer, A. F., Foundations of Physics Letters, Vol. 12 No. 2, 441-453 (1999)
- ↑ B. Haisch, A. Rueda, and H. E. Puthoff (1994), "Inertia as a zero-point-field Lorentz force", Physical Review A, Vol. 49 No. 2, 678–694.§J-L. Cambier (2009), "Inertial Mass from Stochastic Electrodynamics", in M. G. Millis
*et al*: Frontiers of Propulsion Science. pages 423-454, American Institute of Aeronautics & Astronautics, Reston, ISBN 1-56347-956-7 - ↑ A. D. Sakharov (1968), "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation", Soviet Physics Doklady Vol. 12, 1040.
- ↑ SED is not absolutely excluded by Bell inequality experiments due to the detection efficiency loophole. Experiments by G. Brida
*et al*, Physics Letters A Vol. 299 No. 2, 121 and G. Brida*et al*, Journal of Modern Optics Vol. 11 No. 3, 1757 however, agree perfectly with Quantum Mechanics but are at variance with SED. SED has also been tested on the basis of the theoretical proposals: A. Casado*et al.*, http://arxiv.org/abs/quant-ph/0202097; Journal of the Optical Society of America B Vol. 14 (1997) 494; Physical Review A, Vol. 55 (1997) 3879, Physical Review A, Vol. 56 (1997) 2477, Journal of the Optical Society of America B Vol. 15 (1998) 1572, European Physics Journal Vol. D11 (2000) 465, and Vol. D13 (2001) 109; Dechoum et al., Journal Modern Optics Vol. 47 (00) 1273. - ↑ G. A. Robertson, P. A. Murad and E. Davis (2008), "New frontiers in space propulsion sciences", Vol. 49
- ↑ M. Millis
*Assessing potential propulsion breakthroughs*(2005) - ↑ M. Millis
*Energy considerations of hypothetical space drives*(2007) - ↑ {{#invoke:citation/CS1|citation |CitationClass=book }}

## References

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|CitationClass=conference }} ISBN 0-306-40277-7

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|CitationClass=journal }} on-line version from Haisch's website

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|CitationClass=book }} ISBN 0-7923-3818-9

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|CitationClass=journal }} physics/9802030

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|CitationClass=journal }} gr-qc/0504061

- Template:Cite arXiv, a review paper

## External links

- 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?