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Toward Constitutive Quantum Phenomenology: A Unified Statistical Description of Double-Slit Interference and Nonlocal Correlations in Quantum Gravity Theory Based on Inverted Relativity

Martín Fuertes Oliva

Published Jul 29, 2026• 0 citations
Publisher

Abstract

The previous statistical formulation of Quantum Gravity Theory based on Inverted Rel-ativity (QGT:IR) established a constitutive description of the vacuum through a hierarchyof correlation functions, effective Green functions, and constitutive electromagnetic kernels.Those results demonstrated that the constitutive vacuum possesses the mathematical struc-tures required for correlated propagation and interference-like dynamics, while explicitlyavoiding any claim of deriving Quantum Mechanics.The present work investigates whether this constitutive statistical framework can beextended to reproduce the mathematical structure of two fundamental quantum phenomena:double-slit interference and nonlocal correlations. Starting exclusively from the constitutivescalar action and its statistical extension, we derive the effective electromagnetic responsegenerated by multiple constitutive sources, construct the corresponding intensity functionalmeasured by an ideal detector, and establish the conditions under which interference patternsemerge from constitutive vacuum correlations.The same formalism is then generalized to spatially separated constitutive regions, al-lowing the construction of normalized constitutive correlation functions analogous to thoseemployed in quantum correlation experiments. Their mathematical properties are analyzedtogether with the conditions required for long-range constitutive coherence.Throughout the article a strict distinction is maintained between exact mathematicalderivations, effective constitutive models, and working hypotheses. No claim is made thatthe Born rule, Hilbert-space structure, wavefunctions, quantum entanglement, or violationsof Bell inequalities are derived. Instead, the present work establishes a unified constitutiveframework from which experimentally testable interference and nonlocal correlation phenom-ena may emerge as effective macroscopic consequences of statistical vacuum dynamics.

DOI
10.5281/zenodo.21684918

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The previous statistical formulation of Quantum Gravity Theory based on Inverted Rel-ativity (QGT:IR) established a constitutive description of the vacuum through a hierarchyof correlation functions, effective Green functions, and constitutive electromagnetic kernels.Those results demonstrated that the constitutive vacuum possesses the mathematical struc-tures required for correlated propagation and interference-like dynamics, while explicitlyavoiding any claim of deriving Quantum Mechanics.The present work investigates whether this constitutive statistical framework can beextended to reproduce the mathematical structure of two fundamental quantum phenomena:double-slit interference and nonlocal correlations. Starting exclusively from the constitutivescalar action and its statistical extension, we derive the effective electromagnetic responsegenerated by multiple constitutive sources, construct the corresponding intensity functionalmeasured by an ideal detector, and establish the conditions under which interference patternsemerge from constitutive vacuum correlations.The same formalism is then generalized to spatially separated constitutive regions, al-lowing the construction of normalized constitutive correlation functions analogous to thoseemployed in quantum correlation experiments. Their mathematical properties are analyzedtogether with the conditions required for long-range constitutive coherence.Throughout the article a strict distinction is maintained between exact mathematicalderivations, effective constitutive models, and working hypotheses. No claim is made thatthe Born rule, Hilbert-space structure, wavefunctions, quantum entanglement, or violationsof Bell inequalities are derived. Instead, the present work establishes a unified constitutiveframework from which experimentally testable interference and nonlocal correlation phenom-ena may emerge as effective macroscopic consequences of statistical vacuum dynamics.
Previous developments of Quantum Gravity Theory based on Inverted Relativity (QGT:IR)established a deterministic constitutive description of the physical vacuum and subsequentlyextended it to a statistical framework through constitutive correlation hierarchies, Greenfunctions, and effective electromagnetic kernels. A further study demonstrated that thesestructures naturally generate interference-like terms and long-range constitutive correlationsresembling important mathematical features of double-slit interference and Bell-type experi-ments. Nevertheless, one essential element remained absent: a constitutive theory connectingvacuum correlations with observable detector events.The present work introduces a Constitutive Detection Theory (CDT) intended to providethis missing link. Starting exclusively from the constitutive scalar action and its statisticalextension, a local detector-response functional is constructed and coupled to the constitutivecorrelation hierarchy. Without introducing wavefunctions, Hilbert spaces, quantum opera-tors, or the Born postulate, the formalism derives an effective detection functional whosestatistical properties are determined by the vacuum correlation functions.The analysis investigates whether experimentally observed interference patterns and non-local detector correlations may emerge as macroscopic consequences of constitutive vacuumdynamics. Exact mathematical derivations are distinguished rigorously from constitutive hy-potheses and phenomenological assumptions. Particular attention is devoted to identifyingwhich elements follow uniquely from the constitutive action and which require independentexperimental determination.If successful, Constitutive Detection Theory provides the final mathematical componentrequired to transform the previous constitutive framework into a predictive phenomenologicaltheory capable of generating measurable detector statistics while remaining fundamentallydeterministic. No claim is made that Quantum Mechanics is derived. Rather, the presentwork investigates whether quantum-like statistical observations can emerge as effective man-ifestations of constitutive vacuum dynamics.
This preprint presents a physical reinterpretation of quantum phenomena within the framework of Relativistic Coherent Vacuum Gravity Theory (rCVGT). The theory models the vacuum as a structured medium described by four dynamical fields governing coherence, flow, and time rate. Quantum entanglement, interference, and measurement are interpreted as manifestations of vacuum-coherence dynamics rather than abstract postulates. Nonlocal correlations arise from extended vacuum coherence without superluminal signaling or superdeterminism. Measurement-induced collapse corresponds to localized vacuum decoherence driven by macroscopic interactions. The double-slit experiment is explained through vacuum-mediated coherent propagation. The framework preserves the empirical predictions of quantum mechanics while providing a physical mechanism consistent with relativistic causality. rCVGT unifies quantum and gravitational behavior by assigning physical structure to the vacuum. The work offers testable predictions and experimental pathways. It aims to contribute to quantum foundations and the reconciliation of quantum mechanics with relativity.
Quantum mechanics is assumed throughout as a fundamental and experimentallyvalidated formalism. This work does not seek to replace or modify its mathematicalstructure. Instead, we investigate whether several well-known quantum phenomenacan be understood as universal consequences of treating quantum systems as opensystems embedded in a structured physical vacuum.Within the Quantum Gravity Theory based on Inverted Relativity (QGT:IR), thevacuum is modeled as a scalar medium with spectral response properties, and all physicalsystems are assumed to exchange energy weakly but persistently with this vacuum.Under these assumptions, we show that quantum decoherence, vacuum-induced noise,hierarchies of state lifetimes, and an effective arrow of time emerge naturally withoutaltering the Hilbert-space formalism, operator algebra, or measurement postulates ofquantum mechanics.A strict methodological distinction is maintained between results that are deriveddirectly from the framework and physical interpretations that provide ontological orconceptual insight without introducing new predictions. The domain of validity of theapproach is carefully delineated, and its continuity with standard quantum mechanicsand quantum field theory is emphasized.
Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.
We present a mathematically rigorous five-dimensional extension of spacetime inwhich the extra dimension is a physical angular coordinate Θ ∈ [0, 2π). This “realmspace” geometry explains quantum interference, nonlocal correlations, and measurement collapse as deterministic geometric effects. Wavefunctions occupy multiple Θmodes in free evolution, while measurement corresponds to sharp localization in Θ. Weprovide a complete Fourier decomposition of the 5D wavefunction, show how the 4Dinterference pattern emerges via integration over Θ, and rigorously demonstrate how localization removes interference. The double-slit experiment is derived fully within thisframework, providing a definitive geometric interpretation that reproduces all standardquantum predictions while offering a clear explanation for the apparent paradoxes ofquantum mechanics