# Stochastic electrodynamics

Stochastic electrodynamics (SED) extends classical electrodynamics (CED) of theoretical physics by adding the hypothesis of a classical Lorentz invariant radiation field having statistical properties similar to that of the electromagnetic zero-point field (ZPF) of quantum electrodynamics (QED).

## Key ingredients

Stochastic electrodynamics combines two conventional classical ideas – electromagnetism derived from point charges obeying Maxwell's equations and particle motion driven by Lorentz forces – with one unconventional hypothesis: the classical field has radiation even at T=0. This zero-point radiation is inferred from observations of the (macroscopic) Casimir effect forces at low temperatures. As temperature approaches zero, experimental measurements of the force between two uncharged, conducting plates in a vacuum do not go to zero as classical electrodynamics would predict. Taking this result as evidence of classical zero-point radiation leads to the stochastic electrodynamics model.

## 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 originated the more concentrated efforts that started in the 1960s. Thereafter Timothy Boyer, Luis de la Peña and Ana María Cetto were perhaps the most prolific contributors in the 1970s and beyond. Others have made contributions, alterations, and proposals concentrating on applying 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 2010, Cavalleri et al. introduced SEDS ('pure' SED, as they call it, plus spin) as a fundamental improvement that they claim potentially overcomes all the known drawbacks of 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 (~ 10$^{21}$ eV) of cosmic rays. Two double-slit electron diffraction experiments are proposed to discriminate between QM and SEDS.
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.

## 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 motivated 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 Van der Waals force
* Diamagnetism
* The Unruh effect
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
* Inertia
* Gravitation