ABSTRACT The representation of two spatially separated particles by a single entangled quantum state raises the question of whether their laboratory coordinate separation and their relational distance in the configuration space of the joint state are the same quantity. In this study, the relative sector of a two-particle system is described by the coordinates and . While the laboratory coordinate separation is held fixed, a phenomenological model is proposed in which the effective proper distance assigned to the joint state depends on the correlation energy and the relativistic phase velocity. The constitutive geometric postulate of the model is a reciprocal choice of the temporal and spatial metric coefficients in the reduced -dimensional relative configuration-space sector: . This condition preserves the metric determinant and the two-dimensional volume element of the relative sector. The induced metric on a constant-relative-time slice yields (1) Consequently, although remains unchanged, in the limit . Under the null constraint, the coordinate characteristic speed becomes , whereas the speed measured with local physical time and length intervals remains exactly . The response amplitude is related to a correlation-energy scale , the phase velocity , and a correlation-localization factor . It is also shown explicitly that a finite-energy, Planck-suppressed ansatz does not produce in the laboratory regime. Vanishing proper distance is therefore not presented as a necessary consequence of standard quantum mechanics or finite entanglement, but as a boundary behavior of the geometry in the strong-response limit. The model quantifies relational proximity for an entangled joint state without claiming that the physical coordinate distance disappears
ABSTRACT The representation of two spatially separated particles by a single entangled quantum state raises the question of whether their laboratory coordinate separation and their relational distance in the configuration space of the joint state are the same quantity. In this study, the relative sector of a two-particle system is described by the coordinates and . While the laboratory coordinate separation is held fixed, a phenomenological model is proposed in which the effective proper distance assigned to the joint state depends on the correlation energy and the relativistic phase velocity. The constitutive geometric postulate of the model is a reciprocal choice of the temporal and spatial metric coefficients in the reduced -dimensional relative configuration-space sector: . This condition preserves the metric determinant and the two-dimensional volume element of the relative sector. The induced metric on a constant-relative-time slice yields (1) Consequently, although remains unchanged, in the limit . Under the null constraint, the coordinate characteristic speed becomes , whereas the speed measured with local physical time and length intervals remains exactly . The response amplitude is related to a correlation-energy scale , the phase velocity , and a correlation-localization factor . It is also shown explicitly that a finite-energy, Planck-suppressed ansatz does not produce in the laboratory regime. Vanishing proper distance is therefore not presented as a necessary consequence of standard quantum mechanics or finite entanglement, but as a boundary behavior of the geometry in the strong-response limit. The model quantifies relational proximity for an entangled joint state without claiming that the physical coordinate distance disappears
ABSTRACT The representation of two spatially separated particles by a single entangled quantum state raises the question of whether their laboratory coordinate separation and their relational distance in the configuration space of the joint state are the same quantity. In this study, the relative sector of a two-particle system is described by the coordinates and . While the laboratory coordinate separation is held fixed, a phenomenological model is proposed in which the effective proper distance assigned to the joint state depends on the correlation energy and the relativistic phase velocity. The constitutive geometric postulate of the model is a reciprocal choice of the temporal and spatial metric coefficients in the reduced -dimensional relative configuration-space sector: . This condition preserves the metric determinant and the two-dimensional volume element of the relative sector. The induced metric on a constant-relative-time slice yields (1) Consequently, although remains unchanged, in the limit . Under the null constraint, the coordinate characteristic speed becomes , whereas the speed measured with local physical time and length intervals remains exactly . The response amplitude is related to a correlation-energy scale , the phase velocity , and a correlation-localization factor . It is also shown explicitly that a finite-energy, Planck-suppressed ansatz does not produce in the laboratory regime. Vanishing proper distance is therefore not presented as a necessary consequence of standard quantum mechanics or finite entanglement, but as a boundary behavior of the geometry in the strong-response limit. The model quantifies relational proximity for an entangled joint state without claiming that the physical coordinate distance disappears
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 a central resource of quantum information science, yet its correlations are ordinarily treated as properties of the quantum state rather than as the outcome of an underlying physical process. Here we explore the hypothesis that these correlations are mediated dynamically by a field propagating locally at finite velocity through an extension of ordinary spacetime. The model embeds physical (3,1)-dimensional spacetime in a warped five-dimensional geometry containing an additional timelike coordinate. Within the adopted geometric ansatz, the form of the extended spacetime metric is determined by the five-dimensional vacuum Einstein equations. A massless field propagating through the resulting five-dimensional bulk can mediate correlations whose projection onto observable four-dimensional spacetime connects arbitrarily distant locations at equal laboratory time, while preserving operational no-signaling. Coupling this field to a Bohm--Bub-inspired collapse scheme provides a possible dynamical realization of entanglement correlations and, under a stated statistical consistency condition, reproduces Born statistics. The framework leads to a concrete experimental test. Two nominally independent Bell pairs are predicted to develop a weak, distance-dependent contextual correlation between particles belonging to different pairs, as a consequence of bulk-field mediation. This cross-pair correlation is absent in standard quantum mechanics for independently prepared systems and is predicted to decrease as the inverse square of their separation. It could therefore be tested by varying the distance between two simultaneous Bell experiments using existing photonic technology. Observation of such a signal would support a dynamical spacetime account of quantum entanglement and could have implications for quantum networks employing multiple independent entangled resources.
We develop a complete geometric framework in which each quantum particle possesses its own private spacetime—a world-block—constructed from Fermi–Walker coordinates. The intrinsic spatial metric on each proper-time slice is a dynamical field governed by an action with a universal stiffness constant A0. A single world-block exhibits kinematic non-locality: the metric perturbation at a point depends on the entire wavefunction through an integral relation, while maintaining dynamic locality via causal wave equations. This duality captures the essential non-locality of quantum mechanics without violating relativistic causality. When two particles interact, their world-blocks are stitched along a common boundary, forming a single compound world-block in ordinary four-dimensional spacetime. The stitching imposes local matching conditions that yield a non-separable strain field, providing a geometric account of quantum entanglement. Measurements correspond to fixing boundary conditions on one part of the compound block; the correlated outcome on the distant part is automatically determined by the shared global geometry, not by any superluminal signal. Thus, the apparent non-locality of EPR correlations is explained as a manifestation of geometric connectivity within a single 4D manifold, consistent with Bell’s theorem because the geometry itself is non-local. In the continuum limit of many overlapping blocks, coarse-graining restores an effective local description, and Newton’s law of universal gravitation emerges exactly, with Newton’s constant given by G = 3c4/(8πA0). The model offers a unified, deterministic, and fully relativistic foundation for quantum mechanics and gravity, without invoking extra dimensions or stochastic elements. Experimental signatures in ultrafast interferometry and possible connections to dark energy are discussed. The framework aligns with recent developments in emergent gravity and provides a concrete geometric realization of spacetime from quantum entanglement.
Can spatial distance and proper time be defined operationally — by how a system leaks information to its environment — rather than postulated as primitive geometric quantities? This paper answers affirmatively for both, within Markovian open quantum dynamics, building on the survival-expansion framework of the companion paper "Local Curvature of Quantum Information" (doi:10.5281/zenodo.18792424). Spatial distance is defined as the excess irreversibility generated by superposing two states: when a system is superposed over two locations, the environment learns which at a rate growing with their separation. This distance is proven to be a genuine metric — it satisfies the triangle inequality via an isometric embedding into environmental "shadow space", recovers the Euclidean metric of R³ for independent position channels, and becomes undefined before decoherence even for orthogonal states, so that geometry and classicality emerge together. Proper time is defined as elapsed background time minus the minimal dissipation needed to traverse a worldline. The reversed triangle inequality of relativity (the twin paradox) then follows automatically from the subadditivity of optimal costs, and the exact Minkowski interval corresponds to a dissipation rate that saturates at high transport velocity: the light cone as a bound on irreversibility production. Both Lorentzian signatures are traced to a single convex-analytic root: spatial distance is directly a subadditive object (a norm), while proper time is an additive duration minus a subadditive optimal cost, hence superadditive. In an exactly solvable driven damped-oscillator model, the information deficit coincides identically with Clausius entropy production, the minimal transport deficit obeys Λ∗=2kBTbγmTΔx2, and the emergent light speed is c2=γmκkBTb=κD, with D the Einstein diffusion coefficient. The universality of the emergent light cone is shown to be equivalent to a Compton-clock scaling of the dissipation–time conversion rate (κ=ℏ2mc2), with the quantum–classical crossover condition kBTb=2ℏγ arising as an internal consistency requirement rather than a postulate. A junction-cost theorem establishes that velocity discontinuities incur strictly positive excess dissipation, so the turning twin ages strictly less even at equal speeds. All results are verified numerically on lattice decoherence models, exact linear–quadratic optimal control, and Fock-space computations; the verification scripts accompany the manuscript. Locality of the environmental couplings is assumed, not derived, and the construction has analog-gravity status: a Lorentzian interval in a preferred frame defined by the bath.
When two particles are created together in a single quantum event, they can become entangled: their properties remain correlated no matter how far apart they travel. Measure one, and the outcome of measuring the other is no longer independent. This correlation is the central puzzle of quantum mechanics. Classical physics sets a hard limit on how strong such correlations can be. The CHSH inequality (Clauser, Horne, Shimony, and Holt, 1969) formalises that limit: for any theory in which each particle carries its own independent set of predetermined answers, the correlation measure S cannot exceed 2. Bell-type experiments consistently violate this bound, with the maximum ideal value predicted by quantum mechanics being S = 2√2. Something does not fit. Several explanations have been proposed. Some invoke extra dimensions. Others appeal to wormhole geometries connecting the particles. The mainstream position is that the outcomes "collapse and become correlated," which states the observation without explaining the mechanism. All of these either add dramatic ontological furniture or repackage the mystery as an answer. This paper proposes a simpler reading. The value 2√2 is not a mystery to be explained by exotic physics. It is the geometric signature of a jointly structured bipartite state whose correlation was fixed at the source, at the moment of entanglement, not at measurement time. The two particles are not two independent objects that later communicate. They are two readout surfaces of a single joint preparation. The cosine correlation law, the Tsirelson bound, and the full Bell violation follow directly from the geometry of the two-qubit state space and the relative orientation of the measurement settings. No signal, no extra dimension, no new physics is required. Three companion papers in this series explored the opposite hypothesis: The Speed of Light and Its Limits [1] examined whether entanglement could circumvent relativistic constraints; Quantum Entanglement as a Communication Channel [2] proposed a synchronized-clock experiment to detect timing signatures; and Parametrizing Correlation Timing [3] developed a Lorentz-structured ansatz for concurrence-dependent delays. If those experimental proposals return null, the present reading is reinforced: not by proof, but by elimination of the alternatives that require more. A final section develops geometric and regime-based frameworks consistent with the source-structural reading, including the measurement torus as the natural geometry of Bell experiments, a jointness index based on Concurrence, and connections to emergent spacetime programmes. These are offered as directions for future development.