Stochastic quantum mechanics (or the stochastic interpretation) is an

interpretation of quantum mechanics An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraord ...

. The modern application of stochastics to

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

involves the assumption of spacetime stochasticity, the idea that the small-scale structure of spacetime is undergoing both metric and topological fluctuations (

John Archibald Wheeler John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in e ...

's "

quantum foam Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroye ...

"), and that the averaged result of these fluctuations recreates a more conventional-looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics is due to persistent

vacuum fluctuation In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...

. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it as it is usually considered.

Stochastic mechanics

The first relatively coherent stochastic theory of quantum mechanics was put forward by Hungarian physicist Imre Fényes who was able to show the

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the ...

could be understood as a kind of

diffusion equation The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's la ...

for a

Markov process A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

Louis de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave na ...

felt compelled to incorporate a stochastic process underlying quantum mechanics to make particles switch from one

pilot wave In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets qua ...

to another. Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by

Edward Nelson Edward Nelson (May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical ...

and is called stochastic mechanics. This was also developed by Davidson, Guerra, Ruggiero and others.

Stochastic electrodynamics

Stochastic quantum mechanics can be applied to the field of electrodynamics and is called

stochastic electrodynamics 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 statisti ...

(SED). SED differs profoundly from

quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...

(QED) but is nevertheless able to account for some vacuum-electrodynamical effects within a fully classical framework. In classical electrodynamics it is assumed there are no fields in the absence of any sources, while SED assumes that there is always a constantly fluctuating classical field due to

zero-point energy Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...

. As long as the field satisfies the

Maxwell equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. T ...

there is no a priori inconsistency with this assumption. Since Trevor W. Marshall originally proposed the idea it has been of considerable interest to a small but active group of researchers.

Stochastic mechanics

Stochastic electrodynamics

See also

References

Notes

Papers

Books