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Journal of Physics Conference Series

Configuration Space Interference in Hong-Ou-Mandel-Type Experiments: A de Broglie–Bohm Analysis

Christopher Dewdney

Published Mar 1, 2026• 0 citations
Publisher

Abstract

Abstract This paper examines how quantum mechanics, interpreted through the de Broglie–Bohm (deBB) framework, can reveal a deeper underlying reality in configuration space. Rather than proposing new predictions, the aim is to clarify how deBB theory provides a coherent, realist account of massive particle, Hong–Ou–Mandel (HOM)-type correlations—often regarded as uniquely quantum. It is suggested that in this interpretation, configuration space is not simply a mathematical convenience but the fundamental arena in which quantum processes unfold. Observable non local behaviour in space and time arises as a projection of local configuration-space dynamics. The analysis illustrates the explanatory power of the deBB approach and supports the view that the configuration-space wave function carries ontological significance.

DOI
10.1088/1742-6596/3189/1/012012

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Abstract This paper examines how quantum mechanics, interpreted through the de Broglie–Bohm (deBB) framework, can reveal a deeper underlying reality in configuration space. Rather than proposing new predictions, the aim is to clarify how deBB theory provides a coherent, realist account of massive particle, Hong–Ou–Mandel (HOM)-type correlations—often regarded as uniquely quantum. It is suggested that in this interpretation, configuration space is not simply a mathematical convenience but the fundamental arena in which quantum processes unfold. Observable non local behaviour in space and time arises as a projection of local configuration-space dynamics. The analysis illustrates the explanatory power of the deBB approach and supports the view that the configuration-space wave function carries ontological significance.
In many-particle quantum mechanics the wave function is irreducibly defined on configuration space. In the de Broglie–Bohm theory this fact is made explicit: both the wave function and the actual motion are naturally described as evolving in configuration space, while the familiar three-dimensional motions of particles arise only as projections of this higher-dimensional dynamics. In this paper we argue that configuration space should be regarded as the fundamental arena of quantum dynamics. On this view, the nonlocal correlations observed in ordinary three-dimensional space are not mysterious dynamical influences but direct consequences of local evolution in configuration space. This perspective is developed and illustrated through a detailed analysis of momentum measurement and which-way detection in the iconic two slit experiment, in the two-particle interferometry experiment of Horne–Shimony–Zeilinger and in the Einstein–Podolsky–Rosen experiment.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes to the claim of standard interpretation on the completeness of description of the state of quantummechanical system, that description in Bohmian mechanics is completed by defining positions of the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation for the introduction of a new theory that can describe dubious axiomatic requirements of standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically more general and conceptual elaborate formulation. Along with the historical overview, a note is given about the main properties of the theory, such as the issue of nonlocality and hidden variables. The aim of this paper is to present and explain the main ideas and properties of the theory as well as to give a systematic overview of present and historical mathematical construction of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of quantum-mechanical picture, showcasing examples of the equivalency of the description of a free particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing of the interpretations is presented: the double-slit experiment, with a detailed examination of the Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment. The graphs of trajectories for given examples are obtained.
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the usual dBB interpretation applied to all wave functions, in particular to particles in bound states whose wave function is defined in a 3N-dimensional configuration space in which N is the number of particules. We show that the current criticisms of the dBB interpretation do not apply to this weak interpretation and that, furthermore, there are theoritical and experimental reasons to justify the weak dBB interpretation. Theoretically, the main reason concern the continuity existing for such particles between quantum mechanics and classical mechanics: we demonstrate in fact that the density and the phase of the wave function of a single-particle (or a set of identical particles without interaction), when the Planck constant tends to 0, converges to the density and the action of a set of unrecognizable prepared classical particles that satisfy the statistical Hamilton-Jacobi equations. As the Hamilton-Jacobi action pilots the particle in classical mechanics, this continuity naturally concurs with the weak dBB interpretation. Experimentally, we show that the measurement results of the main quantum experiments (Young's slits experiment, Stern and Gerlach, EPR-B) are compatible with the de Broglie-Bohm weak interpretation and everything takes place as if these unbounded particles had trajectories. In addition, we propose two potential solutions to complete the dBB weak interpretation.
It is argued that in Bohmian mechanics the effective wave function of a subsystem of the universe does not encode the influences of other par-ticles on the subsystem. This suggests that the ontology of Bohmian mechanics does not consist only in Bohmian particles and their posi-tions. It is nonetheless pointed out that since the wave function in configuration space may represent the state of ergodic motion of non-Bohmian particles in three-dimensional space, the ontology of Bohmian mechanics may still consist only in particles. Bohmian mechanics, which is also called the de Broglie-Bohm theory, is a realistic alternative to standard quantum mechanics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete realistic description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. It has been a hot topic of debate how to interpret the wave function in the theory. Recently Esfeld et al (2013) further developed the nomological interpretation of the wave function, as suggested by Dürr, Goldstein and Zangh̀ı (1997), Goldstein and Teufel (2001) and Goldstein and Zangh̀ı (2012). They argued that the ontology of Bohmian mechanics consists only in Bohmian particles and their positions, and in particular, the effective wave function of a subsystem of the universe encodes the influences of other particles in the universe on the subsystem. In this note, we will argue that this interesting view may be problematic. The Bohmian law of motion is expressed by two equations, a guiding equation for the configuration of particles in three-dimensional space and the Schrödinger equation, describing the time evolution of the wave function, which enters the guiding equation. The law can be formulated as follows: dQ(t) dt = vΨ(t)(Q(t)). (1)
Abstract David Bohm published his “Suggested Interpretation of Quantum Theory in Terms of Hidden Variables” some twenty five years after Louis de Broglie first presented his similar Pilot Wave theory of quantum mechanics. In the following 30 years what became known as the de Broglie–Bohm approach to quantum theory was to a large extent ignored within the physics community. Even David Bohm himself became somewhat disillusioned with the lack of impact of his interpretation of quantum theory and he directed his interest elsewhere. But some 27 years after Bohm had published his interpretation of quantum theory, interest was rekindled in part by new, detailed calculations that demonstrated clearly and graphically, exactly how his interpretation explained quantum phenomena in terms of well defined individual particle trajectories. These computations encompassed two-slit interference, quantum tunnelling, neutron interferometry, Wheeler’s delayed choice experiment, orbital and intrinsic angular momentum, quantum measurement and Einstein–Podolsky–Rosen nonlocal correlations for orbital angular momentum, intrinsic angular momentum and correlated particle interferometry. Since then, the acceptance of the validity of de Broglie–Bohm theory has steadily grown, as has the interest in the consequences of the approach. For my contribution to the current celebratory volume I was asked to provide a personal review specifically of this novel work within its historical context of the last quarter of the twentieth century.
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maximally realistic causal quantum mechanics in n−n-n−dimensional configuration space \cite{Roy-Singh1995}. Phase space Bell inequalities and 'Marginal Theorems' \cite{Auberson2002} play a crucial role.