**Stochastic quantum mechanics** (or the **stochastic interpretation**) is an interpretation of quantum mechanics.

The modern application of stochastics to quantum mechanics 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's "quantum foam"), 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. 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.

The first relatively coherent stochastic theory of quantum mechanics was put forward by Hungarian physicist Imre Fényes ^{ [1] } who was able to show the Schrödinger equation could be understood as a kind of diffusion equation for a Markov process.^{ [2] }^{ [3] }

Louis de Broglie ^{ [4] } felt compelled to incorporate a stochastic process underlying quantum mechanics to make particles switch from one pilot wave to another.^{ [5] } Perhaps the most widely known theory where quantum mechanics is assumed to describe an inherently stochastic process was put forward by Edward Nelson ^{ [6] } and is called **stochastic mechanics**. This was also developed by Davidson, Guerra, Ruggiero and others.^{ [7] }

Stochastic quantum mechanics can be applied to the field of electrodynamics and is called stochastic electrodynamics (SED).^{ [8] } SED differs profoundly from quantum electrodynamics (QED) but is nevertheless able to account for some vacuum-electrodynamical effects within a fully classical framework.^{ [9] } 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. As long as the field satisfies the Maxwell equations there is no a priori inconsistency with this assumption.^{ [10] } Since Trevor W. Marshall^{ [11] } originally proposed the idea it has been of considerable interest to a small but active group of researchers.^{ [12] }

**Quantum gravity** (**QG**) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as in the vicinity of black holes or similar compact astrophysical objects where the effects of gravity are strong.

In cosmology, the **cosmological constant** is the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity. It is closely associated to the concepts of dark energy and quintessence.

The **de Broglie–Bohm theory**, also known as the **pilot wave theory**, **Bohmian mechanics**, **Bohm's interpretation**, and the **causal interpretation**, is an interpretation of quantum mechanics. In addition to a wavefunction on the space of all possible configurations, it also postulates an actual configuration that exists even when unobserved. The evolution over time of the configuration is defined by a guiding equation that is the nonlocal part of the wave function. The evolution of the wave function over time is given by the Schrödinger equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992).

**Zero-point energy** (**ZPE**) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions, and force fields, whose quanta are bosons. All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy; however, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.

**Vacuum energy** is an underlying background energy that exists in space throughout the entire Universe. Its behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.

**Quantum foam** or **spacetime foam** is the fluctuation of spacetime on very small scales due to quantum mechanics. The idea was devised by John Wheeler in 1955.

**Edward Nelson** 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 logic, he was noted especially for his internal set theory, and views on ultrafinitism and the consistency of arithmetic. In philosophy of mathematics he advocated the view of formalism rather than platonism or intuitionism. He also wrote on the relationship between religion and mathematics.

In quantum field theory, the **quantum vacuum state** is the quantum state with the lowest possible energy. Generally, it contains no physical particles. **Zero-point field** is sometimes used as a synonym for the vacuum state of an individual quantized field.

**Stochastic electrodynamics** (**SED**) is an extension of the de Broglie–Bohm interpretation of quantum mechanics, with the electromagnetic zero-point field (ZPF) playing a central role as the guiding pilot-wave. The theory is a deterministic nonlocal hidden-variable theory. It is distinct from other more mainstream interpretations of quantum mechanics such as QED, a stochastic electrodynamics of the Copenhagen interpretation and Everett's many-worlds interpretation. SED describes energy contained in the electromagnetic vacuum at absolute zero as a stochastic, fluctuating zero-point field. The motion of a particle immersed in this stochastic zero-point radiation generally results in highly nonlinear, sometimes chaotic or emergent, behaviour. Modern approaches to SED consider the quantum properties of waves and particles as well-coordinated emergent effects resulting from deeper (sub-quantum) nonlinear matter-field interactions.

**Ana Maria Cetto** is a Mexican physicist.

**Mendel Sachs** was an American theoretical physicist. His scientific work includes the proposal of a unified field theory that brings together the weak force, strong force, electromagnetism, and gravity.

**Einstein–Cartan–Evans theory** or **ECE theory** was an attempted unified theory of physics proposed by the Welsh chemist and physicist **Myron Wyn Evans**, which claimed to unify general relativity, quantum mechanics and electromagnetism. The hypothesis was largely published in the journal *Foundations of Physics Letters* between 2003 and 2005. Several of Evans' central claims were later shown to be mathematically incorrect and, in 2008, the new editor of *Foundations of Physics*, Nobel laureate Gerard 't Hooft, published an editorial note effectively retracting the journal's support for the hypothesis.

A **quantum vacuum thruster** is a theoretical system hypothesized to use the same principles and equations of motion that a conventional plasma thruster would use, namely magnetohydrodynamics (MHD), to make predictions about the behavior of the propellant. However, rather than using a conventional plasma as a propellant, a QVT would interact with quantum vacuum fluctuations of the zero-point field.

In theoretical physics, **stochastic quantization** is a method for modelling quantum mechanics, introduced by Edward Nelson in 1966, and streamlined by Parisi and Wu.

**Stochastic thermodynamics** is an emergent field of research in statistical mechanics that uses stochastic variables to better understand the non-equilibrium dynamics present in microscopic systems such as colloidal particles, biopolymers, enzymes, molecular motors and many other types of systems.

**Peter Walden Milonni** is an American theoretical physicist who deals with quantum optics, laser physics, quantum electrodynamics and the Casimir effect.

* The Quantum Vacuum: An Introduction to Quantum Electrodynamics* is a physics textbook authored by Peter W. Milonni in 1993. The book provides a careful and thorough treatment of zero-point energy, spontaneous emission, the Casimir, van der Waals forces, Lamb shift and anomalous magnetic moment of the electron at a level of detail not found in other introductory texts to quantum electrodynamics.

**Luis Fernando de la Peña-Auerbach** known as **Luis de la Peña** is a Mexican physicist, born in Mexico City in 1931. He is a researcher of the Institute of Physics and professor of the Faculty of Sciences of the National Autonomous University of Mexico (UNAM) and is a member of the Science Advisory Council of the Presidency of Mexico.

**Imre Fényes** was a Hungarian physicist who was the first to propose a stochastic interpretation of quantum mechanics.

**Georges Lochak** is a French physicist known for his work on magnetic monopoles.

- ↑ See I.Fényes ( 1946 , 1952 )
- ↑ Davidson (1979) , p. 1
- ↑ de la Peña & Cetto (1996) , p. 36
- ↑ de Broglie (1967)
- ↑ de la Peña & Cetto (1996) , p. 36
- ↑ See E.Nelson ( 1966 , 1985 , 1986 )
- ↑ de la Peña & Cetto (1996) , p. 36
- ↑ de la Peña & Cetto (1996) , p. 65
- ↑ Milonni (1994) , p. 128
- ↑ Milonni (1994) , p. 290
- ↑ See T. W.Marshall ( 1963 , 1965 )
- ↑ Milonni (1994) , p. 129

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