| pilot wave theory | |
|---|---|
| Name | Pilot wave theory |
| Era | 20th century |
| Schools tradition | Quantum mechanics interpretations |
| Main interests | Quantum foundations, determinism |
| Notable figures | Louis de Broglie, David Bohm |
pilot wave theory
Pilot wave theory is an interpretation of quantum phenomena proposing that particles have definite trajectories guided by a physical wave. Originating with Louis de Broglie in the 1920s and developed by David Bohm in 1952, it provides a deterministic alternative to the standard Copenhagen interpretation and bears on debates in quantum foundations and the interpretation of the wave function.
Pilot wave ideas trace to Louis de Broglie's 1927 proposal at the Fifth Solvay Conference that matter waves guide point-like particles, presented alongside early formulations by Erwin Schrödinger and Werner Heisenberg. De Broglie's concept lost favor during the rise of the Copenhagen interpretation, but was revived when David Bohm published a detailed nonlocal formulation in 1952 (often called Bohmian mechanics). Key historical antecedents include de Broglie's 1923 doctoral thesis and the subsequent experimental development of electron diffraction at Davisson–Germer experiment. Institutional contexts influencing reception included leading centers such as University of Cambridge, Princeton University, and the Niels Bohr Institute.
Pilot wave theory posits two ontological elements: the configuration of particles and the guiding wave (the wave function). For a single particle, the particle position x(t) evolves by the guidance equation derived from the phase S of the wave function ψ = R exp(iS/ħ), giving velocity v = (1/m)∇S. The wave evolves according to the Schrödinger equation, a partial differential equation central to nonrelativistic quantum mechanics. For an N-particle system the theory uses a wave on configuration space, ψ(x1,...,xN,t), and the guidance equations are nonlocal, connecting to Bell's theorem and the notion of quantum nonlocality. The theory reproduces the Born rule distribution |ψ|^2 under the assumption of quantum equilibrium, a statistical postulate analogous to equilibrium in classical statistical mechanics and treated in studies by Antony Valentini and others. Mathematical treatments often employ tools from Hamiltonian mechanics, functional analysis, and the theory of stochastic processes when considering relaxation to equilibrium.
Unlike the Copenhagen interpretation which treats the wave function as a complete description and invokes collapse, pilot wave theory is explicitly deterministic and denies fundamental collapse: measurement outcomes reflect particle positions and the evolving wave. It is empirically equivalent to standard quantum mechanics in quantum equilibrium for nonrelativistic systems, reproducing predictions for double-slit experiment, Stern–Gerlach experiment, and spectroscopy. Key conceptual contrasts involve ontology (particles + wave versus wavefunction-only), the role of measurement, and explicit nonlocality emphasized by John Bell. Pilot wave formulations avoid the measurement problem by assigning definite properties, but face different challenges when addressing quantum field theory and relativistic covariance.
Many-body generalizations treat the wave on high-dimensional configuration space, enabling application to condensed matter physics models and quantum chemistry methods. Relativistic extensions attempt to reconcile pilot-wave ideas with special relativity; proposals include particle-based models with preferred foliation of spacetime and field ontology approaches where fields are the beables (see work by Detlef Dürr and collaborators). In quantum field theory contexts, pilot-wave approaches model quantum fields as configuration variables (e.g., scalar field configurations) or introduce particle creation and annihilation mechanisms; contributors include Ward Struyve and Sheldon Goldstein. Applications explored include foundations of quantum information experiments, analysis of semiclassical limits, numerical trajectory methods in molecular dynamics, and conceptual analyses of decoherence.
Pilot wave theory yields the same statistical predictions as standard quantum mechanics in quantum equilibrium, so direct experimental discrimination is challenging. Proposed tests target scenarios where quantum equilibrium might be violated, as argued by Antony Valentini, potentially imprinting signals in cosmology or relic non-equilibrium in the cosmic microwave background. Other experimental discussions involve precision interferometry (e.g., advanced double-slit variants), weak measurement reconstructions of Bohmian trajectories, and analogue experiments in fluid dynamics such as the walking droplet systems studied by Yves Couder's group, which display pilot-wave-like behavior at macroscopic scales. While these hydrodynamic analogues illuminate possible mechanisms, they do not demonstrate microscopic pilot-wave physics for electrons or photons; mainstream experimental confirmation remains consistent with standard quantum mechanics.
Pilot wave theory informs debates on realism, determinism, and nonlocality in philosophy of science and physics. It exemplifies a realist ontology by positing particle positions as "beables" (a term introduced by John Bell), and challenges common readings of complementarity and indeterminism. Discussions engage with criteria such as explanatory depth, parsimony, and empirical equivalence; advocates argue that pilot wave theory restores a clear account of measurement and avoids ill-defined notions of collapse, while critics highlight issues with manifest Lorentz invariance and the ontological status of configuration space. The theory continues to be influential in work on quantum foundations, prompting research at institutions including University of Oxford, Rutgers University, and University of Vienna, and in conferences on the foundations of quantum mechanics.
Category:Interpretations of quantum mechanics Category:Quantum mechanics