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The Quantum Boundary of Spacetime. Four Paths, One Transition.

Barry Kieran Radcliffe

Published May 14, 2026• 0 citations
Publisher

Abstract

Quantum behavior is the boundary of spacetime. Spacetime provides four distinct paths to this boundary: extreme spatial localization, extreme spatial non-localization, extreme temporal localization, and extreme temporal non-localization. Each path approaches the same transition boundary, where distinguishable structure dissolves and classical continuity fails. Quantum mechanics is not mysterious. It is the transition between distinguishability and undivided continuity, between the measurable and the immeasurable, between separable structure and the dissolution of separation itself. From within spacetime there are four paths to this singular boundary, but only one transition.

DOI
10.5281/zenodo.20172827

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Quantum behavior is the boundary of spacetime. Spacetime provides four distinct paths to this boundary: extreme spatial localization, extreme spatial non-localization, extreme temporal localization, and extreme temporal non-localization. Each path approaches the same transition boundary, where distinguishable structure dissolves and classical continuity fails. Quantum mechanics is not mysterious. It is the transition between distinguishability and undivided continuity, between the measurable and the immeasurable, between separable structure and the dissolution of separation itself. From within spacetime there are four paths to this singular boundary, but only one transition.
The spacetime boundary is the transition between spacetime and non-spacetime. As such, the boundary acquires attributes of both. We call those attributes quantum mechanics.Entanglement and superposition are the natural attributes of a boundary defining spatial and temporal localization from indistinguishable unity. Uncertainty, nonlocality, entanglement, and incompleteness emerge naturally because the boundary is neither fully spacetime nor fully non-spacetime. The four observational interfaces from within spacetime only differ in the specific nature of the interface itself: extreme spatial localization, extreme spatial delocalization, extreme temporal localization, and extreme temporal delocalization. At the boundary itself these distinctions acquire less and less meaning, eventually becoming completely meaningless as one crosses the boundary. The common pattern is uncertainty because uncertainty is the only possible condition of a boundary existing between spacetime and non-spacetime. Four separate and distinct observations from within spacetime, one unified pattern of interaction at the boundary.
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.
This paper develops a dual-domain framework for quantum foundations grounded in a structural distinction between a nonlocal, atemporal coherence domain (denoted −0) and a local, temporal decoherence domain (denoted +1). Quantum states are interpreted as existing within −0, while classical outcomes emerge when these states transition irreversibly into +1 through decoherence and measurement. The framework is not a modification of quantum mechanics but a reinterpretation of its ontological domain. The framework provides a unified ontological account of: quantum entanglement and nonlocal correlations; the absence of superluminal signalling; the emergence of classicality through decoherence; the mass dependence of decoherence rates; and the persistent incompatibility between quantum field theory and general relativity. Within this model, entanglement corresponds to the persistence of a single −0 state across multiple +1 localisations. Measurement is interpreted not as a collapse occurring within spacetime, but as a boundary transition from coherence to localisation. The paper further argues that gravity should not be interpreted as a quantum field propagating within spacetime, but rather as the geometric structure of the coherence–decoherence boundary itself. This perspective offers a principled explanation for the persistent incompatibility between quantum field theory and general relativity — a tension that may arise not from technical deficiency but from a category error: attempting to describe boundary geometry as though it were content within one of the domains it separates.
This paper began with a thought experiment exploring whether sufficiently accelerated temporal localization produces behavior structurally analogous to the quantum-regime phenomena observed under extreme spatial localization. Modern microscopy already demonstrates that progressively compressed spatial distinguishability destabilizes classical localization and produces wave-like, probabilistic, and nonlocal behavior associated with quantum mechanics. This paper asks whether equivalent destabilization would emerge if distinguishability were compressed temporally rather than spatially. The paper proposes that under sufficiently compressed temporal localization, stable classical persistence would progressively fail in ways structurally analogous to quantum-regime spatial localization. Galaxies, stars, and large-scale cosmic structures would no longer appear as persistent classical objects, but as evolving relational density patterns whose distinguishability becomes increasingly unstable across compressed observational intervals. The central argument is that quantum behavior does not arise from microscopic scale alone, but from sufficient localization of distinguishable structure within spacetime. At extreme localization, both spatial and temporal distinguishability progressively fail and converge toward the same quantum boundary condition. The only difference is whether distinguishability is compressed spatially or temporally from within spacetime. Accordingly, spatial localization and temporal localization become structurally equivalent under sufficient compression. At the boundary, the distinction between space and time ceases to retain independent physical meaning.
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.
Abstract The relationship between quantum mechanics and classical spacetime remains one of the central conceptual problems in modern physics. Quantum theory describes physical systems through superpositions of states, while general relativity treats spacetime as a classical geometric structure. The mechanism by which classical spacetime emerges from an underlying quantum description remains unresolved. This work proposes a conceptual framework in which the transition between quantum coherence and classical spacetime is associated with a scalar parameter describing temporal coherence, denoted as the Q field. In this approach, time is not assumed to be a globally fixed background parameter but emerges from the consistency of interacting physical subsystems. The Q field is introduced as an effective scalar field defined over spacetime, providing a structural criterion for temporal compatibility among configurations. The framework suggests that classical spacetime may emerge when interacting subsystems share a consistent temporal ordering, potentially defining a mesoscopic boundary between quantum and classical behavior. Esto suena mucho más académico.