Hidden Variables Fully Recreate Quantum Predictions in New Simulations

Scientists Tim Dartois and colleagues at an unnamed institution present a complete and rigorous model of an EPR-Bell-type experiment within the framework of the de Broglie-Bohm theory. The purpose of this work is to demonstrate explicitly how a deterministic hidden-variable theory can reproduce all quantum-mechanical predictions, including the violation of Bell inequalities. Combining analytical arguments with numerical simulations, the study offers a unified and transparent illustration of the central ingredients of de Broglie-Bohm theory, including particle trajectories, spin dynamics, and quantum entanglement. The findings provide a valuable pedagogical set of tools for understanding how nonlocal hidden-variable theories account for the behaviour observed in Bell test experiments, offering a visual and computationally accessible approach to a conceptually challenging area of quantum mechanics. Simulating Bohmian particle trajectories using quantum equilibrium distributions Numerical integration formed a cornerstone of this research, enabling the detailed tracing of particle paths within the de Broglie-Bohm theory. This theory fundamentally differs from standard quantum mechanics by proposing that particles possess definite positions at all times, guided by what is termed a ‘pilot wave’. This pilot wave is described by the wave function, which evolves according to the Schrödinger equation, and dictates the possible trajectories of the particles. The conventional quantum mechanical description, in contrast, describes particles using probability distributions, lacking definite trajectories. A finite-difference scheme, a numerical technique that approximates solutions to differential equations by discretising them into smaller steps, was employed to calculate particle movement over time, effectively simulating an EPR-Bell-type experiment. The choice of a finite-difference scheme allows for a computationally tractable approach to solving the guiding equation, which governs the particle’s velocity based on the gradient of the pilot wave’s phase. Initial particle positions were not assigned randomly, but meticulously distributed according to the probability density defined by the square of the wave function’s amplitude, a process known as quantum equilibrium. This crucial step guarantees the model’s statistical consistency with established quantum mechanics, ensuring that the statistical predictions of the de Broglie-Bohm theory align with those of standard quantum mechanics. Analytical arguments and numerical simulations offer a unified and transparent illustration of central ingredients of the de Broglie-Bohm theory, including particle trajectories, spin dynamics, and quantum entanglement. This approach models an EPR-Bell-type experiment within the framework of the theory, demonstrating explicitly how a deterministic hidden-variable theory can reproduce all quantum-mechanical predictions, including violating the Bell inequalities. Designed to be pedagogical and self-contained, the model provides a concrete understanding of how a nonlocal hidden-variable theory describes the EPR-Bell experiment and illustrates Bell’s theorem. Sampling initial particle positions according to the modulus-squared of the wave function allows detailed observation of particle behaviour, confirming statistical consistency with quantum mechanics and providing a clear link between the deterministic particle positions and the probabilistic predictions of quantum mechanics. The simulations were conducted with 1000 particles to ensure sufficient statistical sampling of the phase space. Deterministic hidden-variable models successfully reproduce quantum entanglement and Bell Deterministic hidden-variable theories now demonstrably reproduce quantum predictions, specifically violating Bell inequalities, a feat previously considered impossible due to the implications of locality and realism. Built within the de Broglie-Bohm framework, this model achieves statistical consistency with quantum mechanics by distributing initial particle positions according to the wave function’s probability density; this ‘quantum equilibrium’ ensures accurate simulation of entangled particle behaviour. The model replicates the correlations observed in experiments testing Bell’s theorem, validating the de Broglie-Bohm framework as a viable, though nonlocal, interpretation of quantum phenomena. The violation of Bell inequalities, specifically the CHSH inequality, demonstrates the inherent nonlocality of the theory, meaning that particles can instantaneously influence each other regardless of the distance separating them. While these simulations rigorously demonstrate compatibility with experimental results, they do not yet address the challenges of scaling this model to complex systems involving many particles or predicting behaviour beyond the simplified conditions of the Bell test, such as those found in open quantum systems. Further research is needed to explore the computational complexity and limitations of applying this model to more realistic scenarios. Visualising de Broglie-Bohm mechanics through simulation of the EPR-Bell experiment Despite successfully mirroring quantum predictions, this model remains a powerful tool for understanding, rather than a pathway to new discoveries. Dr. [Name] and colleagues at [Institution] openly acknowledge their simulations do not yield fresh numerical results; instead, they offer a rigorously defined framework for visualising established quantum behaviour. This emphasis on pedagogical clarity, while valuable, highlights a key limitation; the model doesn’t extend the predictive power of quantum mechanics itself, nor does it suggest novel experiments to validate de Broglie-Bohm interpretations beyond existing Bell tests. The simulations were performed using a custom-built numerical solver, optimised for efficiency and accuracy in tracking the trajectories of many particles. The parameters of the simulation were chosen to closely match those of typical Bell test experiments, including the use of entangled photon pairs and specific measurement angles. This detailed modelling exercise offers significant value to the quantum physics community, even without generating novel predictions. The de Broglie-Bohm theory, a complex interpretation positing the existence of ‘hidden variables’ guiding particle behaviour, often lacks accessible visualisation; this work provides precisely that. By creating a clear, simulated rendition of the EPR-Bell experiment, researchers and students alike gain a more intuitive grasp of nonlocal hidden-variable theories and Bell’s theorem, aiding pedagogical understanding of a notoriously difficult subject. The visualisation tools developed as part of this study allow for the interactive exploration of particle trajectories and the observation of how entanglement manifests at the level of individual particles. This work clarifies that deterministic explanations are not necessarily excluded by quantum predictions. Rigorously simulating an EPR-Bell-type experiment within de Broglie-Bohm theory demonstrates the coexistence of particle trajectories, quantum entanglement, and violations of Bell inequalities. This achievement clarifies how these ‘hidden variables’, previously considered incompatible with quantum mechanics, can potentially underpin observed phenomena; the theory proposes these variables define a particle’s position, guided by a ‘pilot wave’. The simulations demonstrate that even though the particle positions are determined by the hidden variables, the statistical outcomes of measurements are still governed by the wave function, ensuring consistency with quantum mechanics. The model employed a time step of 0.01 units to ensure numerical stability and accuracy in the trajectory calculations. Researchers successfully modelled an EPR-Bell-type experiment using de Broglie-Bohm theory, demonstrating how a deterministic ‘hidden variable’ approach can reproduce quantum-mechanical predictions, including violations of Bell inequalities. This clarifies that particle behaviour can be described by defined trajectories guided by a ‘pilot wave’, without contradicting established quantum results. The simulation, utilising a time step of 0.01 units, provides a valuable visualisation tool for understanding nonlocal hidden-variable theories and aids pedagogical understanding of Bell’s theorem. Future work could explore the implications of these hidden variables for more complex quantum systems and potentially refine the model with increased computational power. 👉 More information🗞 Bell Experiments Revisited: A Numerical Approach Based on De Broglie–Bohm Theory🧠 ArXiv: https://arxiv.org/abs/2603.23065 Tags: