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, remains a non-mainstream attempt to interpret quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave–particle duality, instantaneous wave function collapse and the paradox of Schrödinger's cat but introducing nonlocality.

The de Broglie–Bohm pilot wave theory is one of several equally valid interpretations of (non-relativistic) quantum mechanics. An extension to the relativistic case has been developed since the 1990s.

In his 1926 paper,Max Born suggested that the wave function of Schrödinger's wave equation represents the probability density of finding a particle. From this idea, de Broglie developed the pilot wave theory, and worked out a function for the guiding wave. Initially, de Broglie proposed a double solution approach, in which the quantum object consists of a physical wave (u-wave) in real space which has a spherical singular region that gives rise to particle-like behaviour; in this initial form of his theory he did not have to postulate the existence of a quantum particle. He later formulated it as a theory in which a particle is accompanied by a pilot wave. He presented the pilot wave theory at the 1927 Solvay Conference. However, Wolfgang Pauli raised an objection to it at the conference, saying that it did not deal properly with the case of inelastic scattering. De Broglie was not able to find a response to this objection, and he and Born abandoned the pilot-wave approach. Unlike David Bohm years later, de Broglie did not complete his theory to encompass the many-particle case. The many-particle case shows mathematically that the energy dissipation in inelastic scattering could be distributed to the surrounding field structure by a yet-unknown mechanism of the theory of hidden variables.

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