De Broglie–Bohm theory

Scientific Theory
Name	De Broglie–Bohm theory
Type	Realist (causal) interpretation of quantum mechanics
Author(s)	Louis de Broglie (1927), David Bohm (1952), Jean Pierre Vigier (stochastic version)
Keywords	pilot wave, causal interpretation, quantum potential, hidden variables, determinism, non-locality
Year	1927; 1952

The de Broglie–Bohm theory — also called the pilot-wave theory, the causal interpretation, or Bohmian mechanics — is a formulation of quantum mechanics in which particles are real objects with definite positions and trajectories at all times, guided by a physically real wave. It reproduces every experimental prediction of standard quantum mechanics while dispensing with wave-function collapse, irreducible randomness, and any special role for the observer.

Its importance to the critical tradition documented on this wiki is not that it is proven correct, but that it exists and works. The Copenhagen interpretation's central claims — that nature is inherently probabilistic and that particles have no definite properties until measured — are shown by this theory to be interpretive choices rather than conclusions forced by the evidence.

Origins

Louis de Broglie presented an early version of the pilot-wave idea at the 1927 Solvay Conference, where a particle is accompanied and directed by a real wave. Meeting heavy criticism, and unable at the time to answer objections concerning many-particle systems, he set the approach aside.

In 1952, working in exile in Brazil, David Bohm independently reconstructed and completed the theory in two papers, giving it a consistent treatment for systems of many particles and for the measurement process itself. Bohm's work prompted de Broglie to return to the programme, which he developed further as his theory of the double solution. His assistant Jean Pierre Vigier went on to build a stochastic variant, in which quantum behaviour emerges from fluctuations of an underlying subquantum medium.

How the theory works

The theory keeps the ordinary Schrödinger equation and adds one further ingredient: a guidance equation specifying how the wave function determines particle velocities. Equivalently, the particle moves under the classical forces plus a quantum potential derived from the wave function.

Two consequences follow:

• The theory is deterministic. Given the initial positions and the wave function, all subsequent motion is fixed. The statistical predictions of quantum mechanics are recovered because those initial positions are distributed according to the Born rule — a state of "quantum equilibrium" — so the observed randomness reflects our ignorance of initial conditions rather than any indeterminism in nature.
• There is no collapse. Measurement is an ordinary physical interaction between system and apparatus. The outcome recorded is determined by the actual pre-existing configuration, so nothing needs to be said about observers, consciousness, or a boundary between quantum and classical realms.

In the double-slit experiment the account is unambiguous: the particle passes through one slit, while its guiding wave passes through both and produces the interference pattern that steers the particles. The paradoxes of wave–particle duality dissolve, at the price of admitting a real wave in addition to the particle.

Non-locality

The theory is explicitly non-local: in a many-particle system the guiding wave depends on the instantaneous configuration of all particles, so distant events can influence one another immediately. This is the feature most often cited against it.

Proponents regard the objection as misplaced, because Bell's theorem subsequently established that any theory reproducing quantum predictions must be non-local. Bohm's theory does not introduce non-locality; it makes visible what the standard formalism conceals. Bell himself made this point repeatedly, and was prepared to accept a preferred frame of reference to accommodate it — see John Stewart Bell.

Reception

For decades the theory was absent from textbooks and rarely taught, and it remains a minority position. The usual objections are that it is superfluous, since it makes no predictions differing from standard quantum mechanics; that its non-locality sits uncomfortably with relativity; and that its particle positions are an unobservable addition.

Critics of the orthodoxy reply that "superfluous" is a strange charge against the only formulation that states clearly what is supposed to be happening; that non-locality is a demonstrated feature of nature rather than a defect of this theory; and that the theory's long neglect owed much to von Neumann's flawed impossibility proof and to the professional standing of its author after his political persecution. See David Bohm and Quantum mechanics.

Support and development from researchers on this wiki

Related material catalogued here includes Jean-Pierre Vigier and the Stochastic Interpretation of Quantum Mechanics, Classical Interpretation of Quantum Mechanics, On the Interpretation of Quantum Mechanics and Measurement Theory via Hidden Variables Not Subject to Bell's Theorem. Further material is indexed under Category:Quantum Theory.

See also

• David Bohm
• Louis de Broglie
• Jean Pierre Vigier
• John Stewart Bell
• Hidden variable
• Quantum mechanics
• Category: Quantum Theory