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A Higher-Dimensional Interpretation of Quantum Entanglement and Its Extension to a High-Dimensional Schrödinger Equation

Ichiro Tsukamoto

Published May 2, 2025• 1 citation
Publisher

Abstract

Quantum entanglement, wherein a measurement on one particle instantaneously determines the spin state of another, challenges the locality and causality principles in four-dimensional spacetime. I hypothesize that two entangled electrons are unified as a single higher-dimensional object across compactified extra dimensions (5th to 11th dimensions). Embedding the entangled wavefunction ψ(x₁, x₂) = (1/√2) [|↑⟩₁|↓⟩₂ ± |↓⟩₁|↑⟩₂] into an extended configuration space X = (x₁, x₂, y₁, y₂) with a delta-function constraint δ(y₁ - y₂), I interpret entanglement not as nonlocal influence, but as a manifestation of geometric unity in higher dimensions. I further develop a higher-dimensional Schrödinger equation to describe the dynamics: iℏ ∂Ψ(x₁, x₂, y, t)/∂t = ( -ℏ²/2m₁ ∇²_{x₁} - ℏ²/2m₂ ∇²_{x₂} - ℏ²/2m_y ∇²_{y} + V(x₁, x₂, y) ) Ψ(x₁, x₂, y, t) My model offers a geometrical reinterpretation of quantum entanglement as projections of a single coherent higher-dimensional entity and suggests new pathways for understanding quantum foundations and spacetime structure.

DOI
10.20944/preprints202505.0014.v1

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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.
Quantum entanglement is often described as a mysterious nonlocal connection between two particles. While experimentally precise, this interpretation implicitly assumes that the observed multiplicity is fundamental. This paper proposes an alternative, geometrically grounded view: that so-called twin entanglement may arise from a single physical entity embedded in higher-dimensional spacetime, intersecting a 3D+1 observational slice at multiple locations. By separating the roles of space and time—allowing spatial dimensionality to vary while time remains one-dimensional—the work explains instantaneous correlations without invoking signaling, interaction, or duplication. Opposite spin correlations are shown to emerge naturally from geometric orientation of intersection, rather than from coordinated particle behavior. Within a block-universe and retrocausal framework, entanglement is reinterpreted as global consistency rather than dynamical influence. Two experimentally testable directions are outlined, including asymmetric local manipulation tests, while acknowledging the intrinsic limitations imposed by lower-dimensional observation. The paper concludes that many conceptual difficulties surrounding entanglement may stem not from nature itself, but from the language and intuition of observers confined to a limited dimensional slice. The problem was never the elephant — it was the blindness.
This work aims at exploring whether the nonlocal correlations due to quantum entanglement could exist without nonlocal causation. This is done with the aid of a toy model which is based on a simple but decidedly unorthodox physical hypothesis: the nonlocally correlated outcomes of the wavefunction collapse of two entangled particles is driven by an exchange of information between them. Of course exchange of information between spacelike separated entities is forbidden in 3+1 space-time, thus we can wonder whether or not a way out could be found by invoking the existence of some hidden field propagating in an extra time dimension to make the mentioned exchange of information occurring at finite velocity through this extra dimension. Only the description of the wavefunction collapse would be affected by the existence of this extra-time dimension. The model proposed here is defined by borrowing Bohm-Bub’s proposal to describe the wavefunction collapse by means of nonlinear (non-unitary) dynamical equations and then elaborating this approach for an entangled system. The model so obtained is just speculative without any claim of being robust against any criticism, nevertheless, it satisfies the purpose of giving the possibility to the hypotheses formulated above to be verified experimentally; in fact, it makes the proposal of an experiment potentially interesting which would otherwise be immediately dismissed as manifestly trivial. The proposed experiment would consist of checking the possible violation of Bell’s inequality between two identical but independent systems under appropriate conditions. Beyond its theoretical interest, entanglement is a key topic in quantum computing and quantum technologies, so any attempt to gain a deeper understanding of it could be useful.
Quantum entanglement is a fundamental feature of quantum mechanics whose underlying physical interpretation remains an active topic of research. In this work, we develop a geometric framework in which physical states are defined on a higher-dimensional manifold, while observable states arise from a coherent projection onto spacetime. We show that this projection acts as a non-injective mapping on the underlying state space, generically transforming separable higher-dimensional states into non-factorizable states in the observable domain. Within this construction, quantum correlations emerge as a consequence of interference along a compact dimension. Under conditions of phase coherence, the standard quantum predictions are recovered. More generally, incomplete phase cancellation leads to a well-defined deviation from the usual correlation structure, introducing an additional angular dependence beyond the relative measurement settings. The framework is fully compatible with the standard quantum formalism at the effective level, while extending it through experimentally testable predictions. Moreover, the presence of such additional angular contributions provides a potential signature of projection-induced effects. These results suggest that quantum entanglement may be interpreted as an emergent phenomenon associated with geometric projection, in which effective nonlocal behavior arises from dimensional reduction.
Revised Abstract (Version 1.1 – Geometric Clarification) This preprint introduces field-depth (w) as an intrinsic sequential resonance coordinate associated with spatial structure, providing a geometric basis for key quantum phenomena. In this framework, the wavefunction is expressed as Ψ(x, y, z; w), where w does not represent an additional spatial dimension but an sequential coherence parameter governing the stability of standing-wave configurations within a three-dimensional spatial manifold. A localized particle state is interpreted not as a projection from a higher-dimensional space, but as the observable manifestation of a resonance-stabilized nodal structure whose internal coherence configuration is dynamically fixed. This formulation yields direct geometric interpretations of several quantum-mechanical features that are typically treated as abstract or axiomatic: • Wave–particle duality emerges naturally: quantum entities are extended resonance structures, while particle detections correspond to stabilized spatial envelopes of internally coherent states. • Spin arises as a phase-orientation condition within the resonance structure, producing the known 4π periodicity of spin-½ systems without requiring additional spatial geometry. • Quantum entanglement is understood as shared internal resonance configuration, allowing correlated outcomes without invoking superluminal signaling or geometric nonlocality. This model does not modify the Schrödinger or Dirac equations; rather, it clarifies the geometric and coherence-theoretic context in which their solutions are realized. The approach remains consistent with the SU(2) fiber-bundle structure of spinor fields and with experimental tests of quantum correlations. A forthcoming Version 2 will further refine the geometric interpretation by explicitly distinguishing spatial dimensionality from sequential coherence structure and by developing the implications of this clarification for electron stability, charge distribution, and resonance-mediated interactions.