Bohmian mechanics contains a structural asymmetry: the wave guides primitive variables, but those variables do not source the wave. We formulate a reciprocal completion in which the feedback channel is a four-connection rather than an arbitrary nonlinear term. The categorical “defect of commutativity” between wave evolution and guidance is represented physically by connection curvature, [D_μ, D_ν]Ψ = i F_{μν} Ψ. In spinor geometry this connection is identified with the Abelianized low-energy projection of axial contorsion, yielding κ = −λ T ℏ S. If the axial torsion field is sourced by an ontic spin current, the theory splits into two branches: minimal Einstein-Cartan contact torsion or nonminimal propagating axial-vector torsion EFT. Floquet driving gives harmonic thresholds for radiative torsion response.
Bohmian mechanics contains a structural asymmetry: the wave guides primitive variables, but those variables do not source the wave. We formulate a reciprocal completion in which the feedback channel is a four-connection rather than an arbitrary nonlinear term. The categorical “defect of commutativity” between wave evolution and guidance is represented physically by connection curvature, [D_μ, D_ν]Ψ = i F_{μν} Ψ. In spinor geometry this connection is identified with the Abelianized low-energy projection of axial contorsion, yielding κ = −λ T ℏ S. If the axial torsion field is sourced by an ontic spin current, the theory splits into two branches: minimal Einstein-Cartan contact torsion or nonminimal propagating axial-vector torsion EFT. Floquet driving gives harmonic thresholds for radiative torsion response.
This preprint develops a staged framework for testing whether matter-wave dynamics contain a source-dependent reciprocal contribution beyond ordinary phase evolution. The conceptual motivation comes from the asymmetry of standard pilot-wave theory, in which the wave guides material configurations without an established reciprocal action of those configurations on the wave. The proposed approach represents any candidate back-reaction through an effective scalar–vector connection and uses matched matter-wave states with opposite phase gradients as a symmetry-based lock-in test. Ordinary phase motion reverses between the two states, whereas a source-fixed reciprocal contribution would remain as a measurable common-mode residue. The experimental program begins with calibration using a known synthetic gauge field in an ultracold-atom platform. It then advances to a source-free null campaign, followed by a blinded four-state experiment combining phase reversal with reversal of a compensated polarized-spin source. Candidate signals would be tested through source parity, internal-state and species dependence, distance scaling, modulation-frequency response, circulation, curl, and spacetime-holonomy measurements. A coherent counterpropagating Bragg-pair readout and numerical source-to-signal benchmarks are developed to estimate the required phase sensitivity and identify dominant backgrounds. The interpretation is deliberately hierarchical. A nonzero residue would first indicate an unexplained source-dependent interaction; additional evidence would be required to establish connection-like behavior, compatibility with an axial-vector or contorsion effective theory, or genuine pilot-wave back-reaction. Null results would still provide model-independent bounds. If interested please request experimental brief, source code, numerical data, figures, and reproducibility documentation.
Previous works of this series have realized the classical unification of gravitation and electromagnetic fields based on the spacetime density tensor, and the intrinsically generated high-order couplings consistently explain various observational anomalies of compact celestial objects. As a realistic quantum framework, existing schemes for unifying Bohmian theory and gravity generally adopt a dual structure that separates spacetime from the pilot wave. The nonlocality of quantum entanglement in multi-particle systems leads to fundamental conflicts with the local causality of relativity. Meanwhile, torsion-free Riemannian geometry cannot accommodate spin-1/2 fermion spinors, nor can it intrinsically generate the short-range SU(2) weak and SU(3) strong gauge interactions, making it difficult to fully embed the Standard Model of quantum field theory. On the basis of maintaining the monistic ontological postulate of the spacetime density tensor, this paper carries out theoretical expansion in two stages. First, the Bohmian pilot wave, quantum potential and multi-particle entanglement are defined as global coherent perturbations of the spacetime density tensor. This work strictly distinguishes the field structures, dynamic equations and propagation mechanisms of separable quantum states and entangled quantum states, and reconstructs the covariant quantum guiding equation. It resolves the paradox between quantum nonlocality and relativistic causality from an ontological perspective, achieving the unification of classical field theory and Bohmian quantum mechanics. Second, Einstein–Cartan (EC) geometry is introduced with the additional degree of freedom of spacetime torsion. Two types of quantum correlations, namely orbital entanglement and spin entanglement, are differentiated. Fermion spinor fields, as well as U(1) electromagnetic, SU(2) weak and SU(3) strong gauge interactions, are all mapped to local chiral twists and color topological torsional perturbation modes of spacetime. Four core innovations are presented in this paper: 1. Quantum effects are attributed to global coherent fluctuations of spacetime density. The essential geometric differences between ordinary separable quantum states and entangled states are clarified. Entanglement originates from the global coherent deformation of spacetime rather than superluminal action, thoroughly eliminating the dual separation between quantum fields and spacetime. 2. With the aid of EC torsion geometry, fermion spinors are no longer background-independent fields but geometric projections of local spin torsion of spacetime, realizing the geometric ontology of intrinsic spin. 3. The complete set of U(1)/SU(2)/SU(3) gauge symmetries arise intrinsically from multi-scale topological perturbations of the spacetime density tensor, removing the artificial introduction of gauge groups as implemented in the Standard Model. 4. A complete covariant unified field system covering gravitation, electromagnetism, Bohmian quantum effects, weak interactions and strong interactions is constructed, alongside a quantitative calculation system for orbital entanglement and spin entanglement. Under corresponding limiting conditions, the system rigorously reduces to General Relativity, Maxwell's equations, covariant Bohmian dynamics, electroweak Lagrangian and standard QCD Lagrangian. Key physical phenomena including parity violation of the weak interaction, color confinement, asymptotic freedom and quantum nonlocality are consistently explained via geometric structures. This study ultimately establishes a self-consistent unified field theory with a single ontology, which is compatible with classical field theory, realistic Bohmian quantum mechanics and the Standard Model of quantum field theory.
A deterministic quantum-gravity framework is proposed that embeds Bohmian mechanics within the spin–torsion geometry of Einstein–Cartan–Kibble–Sciama theory. Starting from the Palatini form of the action for a Dirac field, a Gordon decomposition followed by a Foldy–Wouthuysen expansion shows that the familiar Bohm quantum potential, namely the term proportional to the Laplacian of the wave-function amplitude divided by that amplitude, coincides exactly with the axial-torsion contribution to the Ricci scalar. A covariant, spin-augmented guidance law then follows, and the algebraically determined torsion field, sourced by the global spin density of an entangled state, mediates non-local correlations without superluminal signalling. The same spin–torsion couplings produce an effective dark stress–energy tensor, for which observational tests are outlined across a wide range of scales: neutron-star magnetospheres, black-hole jets, gravitational-wave inspirals and spin-polarized interferometry. This geometric mechanism extends to spinless particles via torsion’s universal back-reaction on the connection, yielding a deterministic reformulation of quantum mechanics without metric quantization. A simple one-dimensional toy model reproduces the Tsirelson bound for Bell-inequality violations, underscoring the empirical and conceptual viability of this geometric route to quantum gravity, which dispenses with the need to quantize the metric.
Bohmian Mechanics (Dürr et al. 1992) and the Pilot Wave theory (Valentini 1991) provide two opposite understandings of what guides the particles. On one hand there is a universal nomological wave-function (Dürr et al. 1997), which dictates the motion of the particles (the primitive ontology), on the other hand there is universal Ψ-field, which acts causally on the particle configuration. Both views have to face many challenges. Among them, the nomological interpretation has to account for how the law – the wave-function - is grounded in the primitive ontology (Esfeld 2013), while the causal interpretation has to solve the problem of how an entity in configuration space can be the cause of a motion in physical space (Esfeld et al. 2013). Considering now the problem of the nomological interpretation, the anchorage of the lawlike wave-function to the primitive ontology was provided by Esfeld, who recently proposed to ground the wave-function in a dispositional property instantiated by all the particles taken as a whole (Esfeld et al. 2013). However, two challenges come here: the first concerns the tension in deciding whether or not the dispositional property should be part of the primitive ontology, and the second concerns the weak explanatory power that the dispositionalist account can provide. The debate has led to an interesting structuralist account (Esfeld et al. 2015, Lam 2015), which is to regard the wave-function as a modal structure, which relates all the particles of the universe in a non-local fashion, hence explaining the dynamics of the particles. Regarding the problems of the causal interpretation, Valentini thinks of the Ψ- field not as concrete and as physical as an electromagnetic field, but as a ‘more abstract field’ (Valentini 1991): in fact, it lives in configuration space and for this reason it does not admit test particles. Moreover, he does not regard it as an efficient cause of the particle configuration, but as a formal cause, in an Aristotelian-Thomistic sense, in such a way that it should be considered as a guiding form. According to his Aristotelian view of formal cause, the motion is the fulfilling of what exists potentially, which is represented by the Ψ-field (Valentini 1991). The reason why the Ψ-field should be regarded as a real ‘guiding form’ is twofold: on one hand it is its form that determines the trajectories of the particles, on the other hand, its role is to storage formal information between the particles. After having analyzed both representations of the ‘Ψ’, as a modal structure in the first scenario, and as a formal cause in the second, I will claim that, if we hold Esfeld’s account of the universal wave-function in Bohmian Mechanics and the characterization by Valentini of the pilot wave, then the two views do not differ as much as it is normally thought, because in both the wave-function is regarded as a dynamical structure. This reconciliation is especially achieved if we consider that, being all the particles identical, both theories may be reformulated in a reduced-configuration space.
Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad eμa, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.
Abstract Standard pilot-wave theory contains a structural asymmetry: the wave guides the particle, but the particle exerts no reciprocal influence on the wave. This paper develops a geometrically complete extension in which action–reaction symmetry is restored. Particle deviation from guidance is sourced by the imaginary part of the momentum weak value, a quantity intrinsic to quantum theory that vanishes in equilibrium and activates precisely where amplitude structure exists. Unregulated back-reaction generates deterministic instability through positive feedback between deviation and density gradients. Stability is restored through geometric phase accumulation along deviating trajectories, which feeds back into the wave’s phase structure and reshapes subsequent guidance. The resulting framework remains deterministic and time-symmetric and yields three independent falsifiable predictions: the weak-value source of deviation, trajectory-dependent phase reshaping, and the existence of a critical feedback strength separating unstable and bounded dynamical regimes.