We develop an explicit configuration-space formulation of EPR-Bell experiments within the framework of de Broglie-Bohm theory, in which joint measurement outcomes arise from a deterministic mapping from initial particle configurations to outcome pairs. This construction induces a partition of the hidden-variable configuration space into domains associated with the different measurement outcomes. Using a reduced-dimensional Stern-Gerlach model, we derive the structure of these domains and identify the corresponding separatrices that define their boundaries. We show that Bell correlations emerge from the geometry of these partitions: the domain boundaries depend nonlocally on the measurement settings, while the marginal outcome distributions remain invariant, providing a direct dynamical realization of no-signaling. Analytical results are supported by numerical simulations, which exhibit quantitative agreement with the predicted domain structure as a consequence of the underlying partition of configuration space induced by the measurement dynamics. This approach provides an explicit configuration-space representation of nonlocal correlations in Bohmian mechanics, linking trajectory dynamics, measurement processes, and statistical predictions within a unified framework.

Relativistic extensions of de Broglie-Bohm theory postulate a preferred foliation of space-time, an additional structure essential for defining simultaneous configurations on Minkowski space-time, but conventionally believed to be empirically undetectable at quantum equilibrium. In this paper, we outline an experimental protocol for empirically detecting the preferred foliation, which is assumed to be flat for simplicity. Building on the arrival-time distributions for spin-1/2 particles predicted by Das and Dürr, we show that in an EPRB-type experiment with spacelike-separated spin and arrival-time measurements, the observed arrival-time statistics will depend crucially on the temporal order of these measurements relative to the preferred foliation of space-time. This dependence offers a potential experimental signature of the preferred foliation postulated by relativistic Bohmian models. Moreover, it implies the possibility of superluminal signaling.

We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell's equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie-Bohm theory for an effective massive particle describing a photon in this cavity. This work is part of a critical analysis of recent experiments by Sharoglazova et al. carried out with a view to refuting the de Broglie-Bohm theory. Furthermore, the consequences of our analysis for microphotonics go far beyond these experiments. In particular, extensions that take into account photon spin and stochastic aspects associated with radiative or absorption losses are considered. From the point of view of symmetries and probability current, here the effective photon behaves like a spin-1/2 particle.

In their recent paper [Nature 643, 67 (2025)], Sharaglazova et al. report an optical microcavity experiment yielding an "energy-speed relationship" for quantum particles in evanescent states, which they infer from the observed population transfer between two coupled waveguides. The authors argue that their findings challenge the validity of Bohmian particle dynamics because, according to the Bohmian guiding equation, the velocities in the classically forbidden region would be zero. In this note, we explain why this claim is false and the experimental findings are in perfect agreement with Bohmian mechanics. We also clarify why the operationally defined speeds reported in the paper are unrelated to particle velocities in the sense described by Bohmian mechanics. In contrast to other recent replies, our analysis relies solely on the standard Bohmian guidance equation for single particles.

In this work celebrating the centenary of quantum mechanics, we rewiev the principles of de Broglie Bohm theory, also known as pilot-wave theory and Bohmian mechanics. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of current Bohmian theory and perhaps quantum mechanics itself.

This paper examines the physical meaning of the wave function in Bohmian mechanics (BM), addressing the debate between causal and nomological interpretations. While BM postulates particles with definite trajectories guided by the wave function, the ontological status of the wave function itself remains contested. Critics of the causal interpretation argue that the wave function's high-dimensionality and lack of back-reaction disqualify it as a physical entity. Proponents of the nomological interpretation, drawing parallels to the classical Hamiltonian, propose that the wave function is a "law-like" entity. However, this view faces challenges, including reliance on speculative quantum gravity frameworks (e.g., the Wheeler-DeWitt equation) and conceptual ambiguities about the nature of "nomological entities". By systematically comparing BM to Hamilton-Jacobi theory, this paper highlights disanalogies between the wave function and the classical action function. These differences, particularly the wave function's dynamical necessity and irreducibility, support a sui generis interpretation, where the wave function represents a novel ontological category unique to quantum theory. The paper concludes that the wave function's role in BM resists classical analogies, demanding a metaphysical framework that accommodates its non-local, high-dimensional, and dynamically irreducible nature.

In this chapter we discuss the Einstein Podolsky Rosen theorem and its strong relation with Bell's theorem. The central role played by the concept of beable introduced by Bell is emphasized. In particular we stress that beables involved in EPR and Bell theorems are not limited to hidden supplementary variables (e.g., like in the de Broglie-Bohm (dBB) pilot-wave theory) but also include the wave function. In full agreement with Bell this allows us the reformulate the EPR and Bell results as strong theorems concerning nonlocality for quantum mechanics itself and not only for hidden-variables approaches as it is often mistakenly assumed. Furthermore, we clarify some repeated ambiguities concerning `local-realism' and emphasize that neither realism nor determinism nor counterfactual definiteness are prerequisites of EPR and Bell theorems.

In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delayed wave and an advanced wave (known as antisymmetric waves) are capable of following quantum trajectories predicted by the de Broglie–Bohm theory (also known as Bohmian mechanics). Our theory reproduces the main results of orthodox quantum mechanics and unlike Bohmian theory, is local in the Bell sense. We show that this is linked to the superdeterminism and past–future (anti)symmetry of our theory.

In this work we develop a model based on the double solution theory of de Broglie in order to reproduce the famous Landau levels splitting in a constant magnetic field.

In this work, we analyze recent proposals by Das and Dürr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by Goldstein Tumulka and Zanghì (GTZ) of these same proposals, and show that each protagonist is both right and wrong. In detail, we show that DD’s predictions are indeed measurable in principle, but that they will not lead to violations of the no-signalling theorem used in Bell’s theorem, in contradiction with some of Das and Maudlin’s hopes.

In this note, we discuss a historical point regarding Schrödinger's discovery of the famous quantum wave equation in 1926 following de Broglie's fundamental works published in 1923-1925 regarding the introduction of matter waves. Drawing on the work of historians and personal analysis, we show that de Broglie was very close to the discovery of the Schrödinger equation (at least for the stationary one-electron problem).

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry.

The aim of this article is to discuss the preferred basis problem in relational quantum mechanics (RQM). The issue is at the heart of quantum mechanics and we first show that the mathematical formalism of RQM is immune to recent critics concerning consistency. Moreover, we also analyse the notion of interaction in RQM and provide a for all practical purposes reading of RQM comparing it with Bohmian mechanics.

In this work we develop a time-symmetric soliton theory for quantum particles inspired from works by de Broglie and Bohm. We consider explicitly a non-linear Klein–Gordon theory leading to monopolar oscillating solitons. We show that the theory is able to reproduce the main results of the pilot-wave interpretation for non interacting particles in a external electromagnetic field. In this regime, using the time symmetry of the theory, we are also able to explain quantum entanglement between several solitons and we reproduce the famous pilot-wave nonlocality associated with the de Broglie-Bohm theory.

We discuss a recent work by J.~Lawrence et al.[arxiv.org/abs/2208.11793] criticizing relational quantum mechanics (RQM) and based on a famous nonlocality theorem Going back to Greenberger Horne and Zeilinger (GHZ). Here, we show that the claims presented in this recent work are unjustified and we debunk the analysis.

We assess the analysis made by Bohr in 1935 of the Einstein Podolsky Rosen paradox/theorem. We explicitly describe Bohr's gedanken experiment involving a double-slit moving diaphragm interacting with two independent particles and show that the analysis provided by Bohr was flawed. We propose a different protocol correcting Bohr's version that confirms EPR dilemma: Quantum mechanics is either incomplete or non-local.

In order to celebrate this double birthday the journal Foundations of Physics publishes a topical collection `Pilot-wave and beyond' on the developments that have followed the pioneering works of Louis de Broglie and David Bohm on quantum foundations. This topical collection includes contributions from physicists and philosophers debating around the world about the scientific legacy of Bohm and de Broglie concerning the interpretation and understanding of quantum mechanics. In these forewords we give a general review of the historical context explaining how de Broglie and Bohm developed their interpretations of quantum mechanics. We further analyze the relationship between these two great thinkers and emphasize the role of several collaborators and continuators of their ontological approach to physics.

Everett’s many-worlds or multiverse theory is an attempt to find an alternative to the standard Copenhagen interpretation of quantum mechanics. Everett’s theory is often claimed to be local in the Bell sense. Here, we show that this is not the case and debunk the contradictions by analyzing in detail the Greenberger–Horne–Zeilinger (GHZ) nonlocality theorem. We discuss and compare different notions of locality often mixed in the Everettian literature and try to explain the nature of the confusion. We conclude with a discussion of probability and statistics in the many-worlds theory and stress that the strong symmetry existing between branches in the theory prohibits the definition of probability and that the theory cannot recover statistics. The only way out from this contradiction is to modify the theory by adding hidden variables à la Bohm and, as a consequence, the new theory is explicitly Bell-nonlocal.

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandonned. Here we propose a nonlinear scalar field theory able to reproduce the PWI for the Schrödinger and Klein-Gordon guiding waves. Our model relies on a relativistic `phase harmony' condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the $N$ particles cases in presence of entanglement and external (classical) electromagnectic fields.

Integration of photon pairs nanosources is a major challenge for quantum technology. In this context, we develop a formalism for the investigation of Spontaneous Parametric Down Conversion in hybrid structures that combine plasmonic resonances and intrinsic nonlinearity. Using quantum and numerical approaches together, we quantitatively evaluate photon pair correlation measurements for realistic experimental configurations. Hybrid structures embedding a small nanocystal allow for a $10^{3}$ fold increase in pair production compared to the same nanocrystal alone and a photon pair production efficiency close to the best source to date.