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DQ as a geometric hidden-variable extension of the Schrödinger dynamics

JUAN JOSE ESPINOSA

Published Dec 10, 2025• 0 citations
Publisher

Abstract

In the Diffusion Quantum (DQ) framework, the standard wavefunction ψ(x, t) on physical space is extended to a higher-dimensional state Ψ(x, ξ, t), where ξ denotes coordinates in a 12-dimensional informational subspace. These extra coordinates play the role of geometric hidden variables: they are not directly accessible to measurements in ordinary space, but they are fully dynamical and influence the observed statistics through their coupling to x.

DOI
10.5281/zenodo.17882624

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In the Diffusion Quantum (DQ) framework, the standard wavefunction ψ(x, t) on physical space is extended to a higher-dimensional state Ψ(x, ξ, t), where ξ denotes coordinates in a 12-dimensional informational subspace. These extra coordinates play the role of geometric hidden variables: they are not directly accessible to measurements in ordinary space, but they are fully dynamical and influence the observed statistics through their coupling to x.
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The Diffusion Quantum (DQ) framework is proposed explicitly as a speculative but disciplined research programme, rather than as a fully established fundamental theory. Its primary ambition is exploratory: to provide a structured way of thinking about how information, coherence and geometry might be related at sub–Planckian scales, and how such structures could leave faint but observable imprints in systems ranging from entangled pairs to plasmas and astrophysical environments. From the outset, we do not assume that DQ in its present form is the “true ontology” of nature. Instead, we treat it as a working hypothesis about an extended configuration space , in which encodes geometric hidden variables or informational degrees of freedom beyond standard spacetime. In this view, the usual quantum formalism (QM/QFT) is regarded as an effective projection of a richer dynamics, but all existing empirical successes of quantum theory and relativity are taken as non–negotiable constraints that any DQ model must reproduce in the appropriate limits.
This paper proposes a hypothesis in which two entangled particles, while spatially separated in four-dimensional spacetime, can instantaneously share spin information because they occupy the same location—or are the same object—in higher-dimensional space. The model suggests that quantum entanglement arises not from superluminal communication, but from a deeper geometric identity in extra dimensions. The entangled wavefunction is expressed as: Ψ(X) = ψ₄(x₁, x₂) ⊗ δ(y₁ - y₂)with y1,y2y₁, y₂y1​,y2​ representing coordinates in compactified higher dimensions. An effective Lagrangian formulation is introduced: L(Ψ) = ∫ dⁿy₁ dⁿy₂ δ(y₁ - y₂) Ψ* Ĥ ΨThis framework parallels D-brane physics and noncommutative geometry, and aligns with the ER=EPR conjecture. Observable consequences may include deviations in Bell-test correlations under extreme conditions, suggesting a new geometrical lens for quantum entanglement.