Pilot wave theory
Its more modern version, the de Broglie–Bohm theory, interprets quantum mechanics as a deterministic theory, and avoids issues such as wave function collapse, and the paradox of Schrödinger's cat by being inherently nonlocal.
The de Broglie–Bohm pilot wave theory is one of several interpretations of (non-relativistic) quantum mechanics.
Louis de Broglie's early results on the pilot wave theory were presented in his thesis (1924) in the context of atomic orbitals where the waves are stationary.
He further suggested that since the equation described waves in configuration space, the particle model should be abandoned.
Following these results, de Broglie developed the dynamical equations for his pilot wave theory.
[6] 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.
[7] He later formulated it as a theory in which a particle is accompanied by a pilot wave.
De Broglie presented the pilot wave theory at the 1927 Solvay Conference.
[8] 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 abandoned the pilot-wave approach.
Unlike David Bohm years later, de Broglie did not complete his theory to encompass the many-particle case.
[7] 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.
[clarification needed] In 1932, John von Neumann published a book,[9] part of which claimed to prove that all hidden variable theories were impossible.
In 1952, David Bohm, dissatisfied with the prevailing orthodoxy, rediscovered de Broglie's pilot wave theory.
[12][13] The de Broglie–Bohm theory itself might have gone unnoticed by most physicists, if it had not been championed by John Bell, who also countered the objections to it.
In 1987, John Bell rediscovered Grete Hermann's work,[14] and thus showed the physics community that Pauli's and von Neumann's objections only showed that the pilot wave theory did not have locality.
So what one sees around oneself are also the positions of nearby things, not their wave functions.
A collection of particles has an associated matter wave which evolves according to the Schrödinger equation.
[16] The theory brings to light nonlocality that is implicit in the non-relativistic formulation of quantum mechanics and uses it to satisfy Bell's theorem.
[17] Couder, Fort, et al. claimed[18] that macroscopic oil droplets on a vibrating fluid bath can be used as an analogue model of pilot waves; a localized droplet creates a periodical wave field around itself.
They proposed that resonant interaction between the droplet and its own wave field exhibits behaviour analogous to quantum particles: interference in double-slit experiment,[19] unpredictable tunneling[20] (depending in a complicated way on a practically hidden state of field), orbit quantization[21] (that a particle has to 'find a resonance' with field perturbations it creates—after one orbit, its internal phase has to return to the initial state) and Zeeman effect.
[22] While attempts to reproduce these experiments have shown some aspects to be questionable[23] and the interpretation with respect to quantum mechanics has been challenged,[24] work on the concept has continued with some success.
is the potential associated with the quantum force (the particle being pushed by the wave function), is integrated along precisely one path (the one the electron actually follows).
[12] where the velocity field is determined by the “guidance equation” According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities (unlike standard quantum mechanics, which postulates no physical particle or wave entities, only observed wave-particle duality).
The pilot wave guides the motion of the point particles as described by the guidance equation.
Ordinary quantum mechanics and pilot wave theory are based on the same partial differential equation.
The main difference is that in ordinary quantum mechanics, the Schrödinger equation is connected to reality by the Born postulate, which states that the probability density of the particle's position is given by
Pilot wave theory considers the guidance equation to be the fundamental law, and sees the Born rule as a derived concept.
[27][28][29][30][31][32] Lucien Hardy[33] and John Stewart Bell[16] have emphasized that in the de Broglie–Bohm picture of quantum mechanics there can exist empty waves, represented by wave functions propagating in space and time but not carrying energy or momentum,[34] and not associated with a particle.
[35][36][37] In contrast, the many-worlds interpretation of quantum mechanics does not call for empty wave functions.
