Bohmian mechanics

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 the wavefunction, it also postulates an actual configuration of particles exists even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. 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).
The theory is deterministic and explicitly nonlocal: the velocity of any one particle depends on the value of the guiding equation, which depends on the configuration of the system given by its wave function; the latter depends on the boundary conditions of the system, which, in principle, may be the entire universe.
The theory results in a measurement formalism, analogous to thermodynamics for classical mechanics, that yields the standard quantum formalism generally associated with the Copenhagen interpretation. The theory's explicit non-locality resolves the "measurement problem", which is conventionally delegated to the topic of interpretations of quantum mechanics in the Copenhagen interpretation.
The Born rule in Broglie–Bohm theory is not a basic law. Rather, in this theory, the link between the probability density and the wave function has the status of a hypothesis, called the "quantum equilibrium hypothesis", which is additional to the basic principles governing the wave function.
The theory was historically developed in the 1920s by de Broglie, who, in 1927, was persuaded to abandon it in favour of the then-mainstream Copenhagen interpretation. David Bohm, dissatisfied with the prevailing orthodoxy, rediscovered de Broglie's pilot-wave theory in 1952. Bohm's suggestions were not then widely received, partly due to reasons unrelated to their content, such as Bohm's youthful communist affiliations. De Broglie–Bohm theory was widely deemed unacceptable by mainstream theorists, mostly because of its explicit non-locality. Bell's theorem (1964) was inspired by Bell's discovery of Bohm's work; he wondered whether the theory's obvious nonlocality could be eliminated. Since the 1990s, there has been renewed interest in formulating extensions to de Broglie–Bohm theory, attempting to reconcile it with special relativity and quantum field theory, besides other features such as spin or curved spatial geometries.The Stanford Encyclopedia of Philosophy article on quantum decoherence groups "approaches to quantum mechanics" into five groups, of which "pilot-wave theories" are one (the others are the Copenhagen interpretation, objective collapse theories, many-worlds interpretations and modal interpretations).
There are several equivalent mathematical formulations of the theory, and it is known by a number of names. The de Broglie wave has a macroscopic analogy termed Faraday wave.

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