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.
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.
This paper proposes a geometric interpretive framework for a set of foundational phenomena in quantum physics, including the measurement problem, quantum entanglement, and the emergence of classical spacetime structure. Building on the dimensional analogy introduced by Abbott (1884), we develop a model in which observed physical events correspond to lower dimensional intersections of higher-dimensional wave-like structures with an observer's accessible domain. Within this picture, a particle detection event is reinterpreted as the intersection of an extended wave with an observer's plane, and measurement outcomes arise from the geometric relationship between the observer's orientation and the underlying structure, rather than from a physical collapse process. In the context of entanglement, we develop a model in whichcorrelated outcomes observed by spatially separated detectors are understood as local samplings of a single wave generated at a common origin event . The dependence of measurement correlations on detector settings is interpreted in terms of angular separation along the shared wave front, yielding an account consistent with the standard quantum prediction P(same) = cos²(θ/2). The proposal does not modify the mathematical formalism of quantum mechanics and does not introduce novel quantitative predictions at this stage. Its contribution is conceptual: it provides a coherent geometric perspective that unifies several interpretive challenges—wave–particle duality, the measurement problem, and apparent non-locality—within a single structuralpicture. Connections to relational quantum mechanics, holographic duality, and the ER = EPR conjecture are identified as indications of structural compatibility. Open questions and possible directions for formalization are outlined.
ABSTRACT The emergence of quantum entanglement correlations across spatially separated measurement regions renders the interpretation of the relationship between quantum mechanics and relativistic causality a core problem in quantum foundations [Einstein et al., 1935; Bell, 1964]. In this study, two entangled particles are modeled not as two independent physical objects in Minkowski spacetime, but as a joint quantum state in configuration space. The relative space and time coordinates of the joint state are defined via: and the ideal space-time correlation limit assumed in the model is expressed as: This limit is not a general definition of quantum entanglement, but an idealized geometric assumption representing strong correlation in the relative coordinates of the joint state within the proposed model. In this approach, physical spacetime is treated as a geometric structure representing the projection of the joint quantum state onto observable spacetime coordinates. To ensure the projection is Lorentz-covariant, the light-like interval: is employed as the constitutive geometric condition of the model. This condition is accepted not as a mandatory Minkowski interval between physical measurement events, but as the mathematical postulate of the proposed projection geometry. The dynamic scale parameter of the model is grounded in total relativistic quantum energy instead of rest mass, establishing a dimensionless Planck-scaling factor defined as: To encompass both massive and massless systems, quantum energy density is defined via the energy density component of the stress-energy tensor relative to an observer. The required consistency condition for covariant energy-momentum conservation is derived in its general form. Furthermore, modeling the proposed geometric effect as a dimensionless metric perturbation yields a phenomenological first-order geometric phase correction defined as: where is the energy-dependent reduced wavelength. Under fixed and finite , the vanishing of the proposed correction in the low-energy regime relative to the Planck scale () demonstrates that the geometric effect added by the model to standard low-energy quantum mechanics becomes negligible. This study proposes a testable theoretical model aimed at explaining the spatiotemporal correlations of quantum entanglement within a Lorentz-covariant, energy-scaled, and phenomenological geometric framework.
Quantum entanglement is usually formulated as a nonseparable state in Hilbert space whose measurement statistics violate Bell-type inequalities. This paper proposes a speculative geometric framework intended not as a replacement for quantum mechanics, but as a candidate interpretive and model-building language for entanglement correlations. The central idea is that an apparently separated pair of three-dimensional measurement events may be regarded as low-dimensional projections of a single higher-dimensional object. In a lower-dimensional analogy, an observer represented by a point in a one-dimensional observational domain probes a two-dimensional circular object by emitting a ray. Entanglement preparation is modeled as the generation of concentric layers inside the higher-dimensional object. A measurement operation selects a layer, while the time of measurement fixes a common ray direction. The observed result is the intersection point between the time-ray and the selected concentric layer. Correlation arises because distinct layer-intersection points share a common ray and belong to a common higher-dimensional object. The framework is then generalized into a mathematical model in which measurement settings correspond to layer coordinates, time fixes a common phase variable, and correlations are determined by a layer-distance function. Because the model treats measurement settings as constrained by a common higher-dimensional/time-phase structure, it explicitly relaxes measurement independence, placing it near the family of superdeterministic or measurement-dependent hidden-variable approaches. The paper derives the minimal structural requirements for such a framework to reproduce the singlet-state correlation E(a,b)=−cos(a−b) and discusses its relationship to Bell's theorem, contextuality, nonlocality, invariant-set ideas, and deterministic approaches to quantum foundations. The proposal remains a conceptual and mathematical scaffold; its physical value depends on whether it can yield testable deviations, a principled dynamics for the time-ray, and a non-ad-hoc account of layer selection.
The work presents a structural and geometric framework for understanding interference and quantum entanglement without modifying the formalism of quantum mechanics. Apparent nonlocality is interpreted as a consequence of finite measurement resolution rather than a fundamental physical property. The approach introduces a mirror-symmetric interval structure (I11) and shows how interference, entanglement, and related phenomena emerge as resolution-dependent projections of an underlying continuous geometry. The focus is conceptual and interpretative, aiming to provide a coherent geometric reading that remains fully compatible with established quantum theory and experimental results.
We propose a unified geometric framework in which space and time emerge as observer-dependent projections of quantum correlations embedded in the universal wavefunction. In this approach, we formulate six axioms (including a duality between entanglement and time) that establish a correspondence between correlation structures and effective spacetime geometry. We introduce the "correlationhedron", a convex geometric object representing the set of all permissible correlation vectors of a given state, and show how different observer "slicings" (modeled by projection maps) yield distinct emergent spacetimes from this object. An emergent metric is defined on each observer's spacetime via the second derivative of a correlation density (analogous to a Fisher information metric), linking gradients in quantum entanglement to curvature. This paper establishes the conceptual foundations of this approach as the first in a planned series of investigations. We illustrate the framework with conceptual and quantitative examples, including an explicit calculation of the emergent geometry for a two- qubit system in both separable and entangled states. Connections to holography (AdS/CFT) (Maldacena1998, Ryu2006), tensor networks (Swingle2012), and relational quantum approaches (Rovelli1996) are discussed, along with experimental signatures (such as curvature variations with entanglement) that could support the theory. Finally, we outline the limitations of the framework, particularly regarding dynamics and observer-dependent causality, to guide future investigations. This kinematic framework establishes the conceptual skeleton of emergent spacetime; detailed constructions, proofs of smoothness, and dynamical laws will appear in forthcoming work.
I propose that quantum entanglement may reflect relational connectivity at a level where ordinary spatial distance is not fundamental. In the geometric framework considered here, particle pairs arise from an underlying field, retain a shared quantum structure, and participate in a network from which three-dimensional space emerges. Spatial separation in the emergent description need not imply complete independence at the underlying level. I formulate this idea as a conceptual hypothesis and distinguish it from established quantum mechanics, from classical common-cause explanations, and from specific proposals relating entanglement to spacetime geometry. Standard entanglement, Bell correlations, and the no-signalling condition provide consistency requirements; they are not derived from the proposed framework. No graviton-mediated mechanism, dynamical law, or experimentally distinguishable prediction is established in this paper. The hypothesis motivates a research programme requiring a defined state space, a rule for emergent geometry, a treatment of measurement and decoherence, and a quantitative comparison with quantum theory.