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From Phase to Spacetime

Rob ten Napel

Published Feb 15, 2026• 0 citations
Publisher

Abstract

From Phase to Spacetime (Phase Ontology — Part II) develops the central consequence of Part I (Phase Without Ontology): if phase coherence is treated as an ontologically primary layer, then spacetime cannot be fundamental. This paper proposes a conceptual pathway by which temporal order, spatial geometry, and gravitational effects can be understood as emergent structures arising from stable phase relations—without introducing new dynamics or speculative entities. The core move is operational: clocks are oscillators, and what we call “time” is the comparison and synchronization of counted cycles across systems. Temporal order appears where phase relations are stable; divergence in clock rates appears where coherence conditions vary. In this framework, proper time corresponds to a system’s internal phase evolution, and relativistic phenomena (time dilation, gravitational redshift) are reinterpreted as changes in phase evolution induced by coherence gradients. Spatial distance and geometry are treated as doubly derivative: they are inferred through timing relations, synchronization procedures, and stable relational structure across extended systems. Uniform coherence yields an effectively “flat” geometry; varying coherence yields curvature-like behavior. The paper also sketches how inertia and acceleration can be viewed as resistance to reconfiguring phase-locked relations, aligning naturally with the equivalence principle. This work is Part II of a seven-part series that reframes foundational problems—unification, measurement, nonlocality, and the status of time—through the lens of phase coherence. Part III addresses measurement and classical definiteness; Part VII discusses experimental implications and falsifiability.

DOI
10.5281/zenodo.18648322

Related papers

Phase Without Ontology

Rob ten Napel

Phase Without Ontology is Part I of the Phase Ontology series (Parts I–VII). It argues that modern physics relies on phase everywhere—interference, the quantum wave function, gauge theory, the Aharonov–Bohm effect, superconductivity, and macroscopic coherence—yet typically treats phase as merely mathematical rather than ontologically primary. This “ontological restraint,” the paper claims, is not a neutral habit: it helps sustain persistent conceptual fragmentation around measurement, time, and the status of spacetime. Rather than proposing new equations or dynamics, the paper proposes an ontological re-ordering of already-successful formalism: phase coherence is treated as the fundamental organizing layer, with matter as stable phase-locked configurations, time as countable phase evolution, and spacetime as an emergent relational projection of stable phase relations. The framework is explicitly not an ether theory: it introduces no spatial medium, no preferred rest frame, and no “wind” effects—only relational coherence. The conclusion motivates the remainder of the series, which develops implications for emergent spacetime (Part II), measurement (Part III), entanglement (Part IV), time and entropy (Part V), mass and gravity (Part VI), and experimental falsifiability (Part VII).

•Feb 15, 2026•0 citations

Coherence, Entropy, and the Arrow of Time: Why Time Has a Direction in a Phase Ontology

Rob ten Napel

Coherence, Entropy, and the Arrow of Time: Why Time Has a Direction in a Phase Ontology (Phase Ontology — Part V) proposes a phase-centered explanation for one of physics’ strangest asymmetries: microscopic laws are largely time-symmetric, yet macroscopic reality is not. Cups shatter but do not reassemble; heat flows from hot to cold; correlations decay; memories accumulate. This paper argues that the arrow of time becomes conceptually clear once phase coherence is treated as ontologically primary. In this framework, time is not fundamental. It emerges operationally from countable phase evolution in physical clocks (all clocks are oscillators) and from synchronization between systems. A shared “global time” is therefore a relational structure sustained by coherence, not a background substance that governs dynamics. The paper then reframes entropy growth as the loss of accessible phase information in open systems. As systems interact with environments that contain many degrees of freedom, phase correlations disperse outward and become physically inaccessible, even if not destroyed in principle. Decoherence is elevated from a technical detail to the central engine of macroscopic irreversibility: reversing decoherence would require re-phasing an astronomically large environment, which is practically impossible. Building on Part III, the paper also interprets measurement as phase locking: once a macroscopic coupling stabilizes one local configuration, alternative phase possibilities are effectively dispersed into the environment. Classical definiteness and temporal irreversibility are thus treated as two faces of the same process—coherence flow. This manuscript is Part V of a seven-part series (Parts I–VII). It connects Parts I–IV to time asymmetry and points forward to Part VI (mass, inertia, gravitation) and Part VII (experimental implications and falsifiability).

•Feb 15, 2026•0 citations

Entanglement and Nonlocal Coherence: Why Nonlocality Is Natural in a Phase Ontology

Rob ten Napel

Entanglement and Nonlocal Coherence: Why Nonlocality Is Natural in a Phase Ontology (Phase Ontology — Part IV) reframes quantum entanglement by changing the usual starting assumption. The paper argues that entanglement only looks paradoxical if spacetime separation is assumed to imply ontological separation. If phase coherence is treated as a primary layer of reality (as developed in Parts I–III), then nonlocal correlations become expected rather than mysterious. In this view, entangled systems share a single coherent phase structure prior to measurement. Measurement is described as local phase locking: an interaction with a detector stabilizes a definite outcome locally, while the joint correlations arise because both outcomes are constrained by the same underlying phase structure. No superluminal signal is required; correlations are revealed rather than transmitted. The paper also addresses compatibility with relativity: since no information is communicated faster than light, relativistic causality remains intact. Locality is treated as an emergent property of spacetime, while coherence relations can be nonlocal because they are not fundamentally “in spacetime” to begin with. This manuscript is Part IV of a seven-part series (Parts I–VII). It connects the measurement framework of Part III to entanglement and points ahead to Part V (time, irreversibility) and Part VII (experimental implications and falsifiability).

•Feb 15, 2026•0 citations

Emergent Time from Quantum Phase, A Relational Interpretation Based on Phase Accumulation and Synchronization

Roberto Carlos Moleirinho Batista

Abstract The physical status of time remains one of the most persistent open questions in fundamental physics. In quantum mechanics, time appears as an external parameter governing evolution but not as an observable, while in general relativity it is embedded in the geometric structure of spacetime and becomes observer-dependent. Despite their empirical success, neither framework explains the physical origin of time or its singular role among fundamental quantities. In this work, we propose an emergent interpretation of physical time grounded in quantum phase. Phase is treated as a pre-temporal structural feature of quantum systems, rather than as a quantity defined with respect to an underlying temporal parameter. Energy is interpreted as a relational characterisation of regularities in phase structure, and proper time emerges only in contexts where phase accumulation can be compared and synchronised between interacting systems. An isolated quantum system may possess phase, but it does not possess physical time in the operational sense; time arises only through relational compatibility. This approach does not introduce new fundamental dynamics nor posit a physical mechanism responsible for the generation of time. Instead, it establishes an ontological hierarchy in which phase is fundamental, energy is relational, and time is a phenomenological quantity that emerges from stable conditions of synchronisation. Within this framework, classical reality corresponds to domains of temporal compatibility, while loss of compatibility underlies the emergence of horizons and geometric structure. By reframing time as an emergent relational phenomenon rooted in quantum phase, this work provides a coherent interpretative framework in which the absence of a time operator in quantum mechanics and the difficulty of quantising time and gravity are understood as consequences of their non-fundamental status, rather than as shortcomings of existing formalisms.

•Dec 29, 2025•0 citations

Experimental Signatures and Falsifiability of Phase Ontology: How a Phase-Primary Framework Can Be Tested

Rob ten Napel

Experimental Signatures and Falsifiability of Phase Ontology: How a Phase-Primary Framework Can Be Tested (Phase Ontology — Part VII) completes the Phase Ontology series by translating its core claims into concrete, falsifiable expectations. While Parts I–VI argue that phase coherence is physically real and that spacetime is an emergent projection of stable phase relations, this paper makes the scientific demand explicit: the framework must constrain what should be observed in the laboratory—not merely reinterpret existing results. The paper outlines a set of testable signatures that should appear if measurement is genuinely a phase-locking process, if coherence is a physical resource that can be preserved or dispersed, and if detectors and environments are active material participants rather than generic sources of noise. Key experimental arenas include: (1) detector-dependent phase-locking thresholds (e.g., interferometry where small, controlled detector-material changes produce disproportionate shifts in localization/fringe behavior), (2) coherence capacity and delayed classicality (engineered environments that produce non-linear regime changes rather than only smooth decoherence), (3) entanglement under structured phase environments (sensitivity to structured phase modulation beyond standard loss/noise parameters), (4) precision clocks as phase probes (searching for residual coherence-environment dependencies beyond known systematics), and (5) macroscopic coherence bridge regimes in superconducting and mesoscopic networks where topology and coupling geometry should matter in structured ways. Crucially, the paper states what falsification would look like in practice: if across multiple platforms detector variations yield no structured threshold effects, coherence isolation produces only fully predictable smooth behavior, entanglement responds solely to standard channel parameters, and precision clocks show no reproducible residual coherence-structure dependence, then Phase Ontology remains an interpretation but loses its claim to be an empirically distinct physical framework. A staged experimental program is proposed, moving from tabletop interferometry to progressively more demanding coherence and clock tests.

•Feb 15, 2026•0 citations

Material Extension and Relational Separation Without Fundamental Spacetime

Peter Erik Ronald van Heijst

Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.

•Jan 29, 2026•0 citations
From Phase to Spacetime (Phase Ontology — Part II) develops the central consequence of Part I (Phase Without Ontology): if phase coherence is treated as an ontologically primary layer, then spacetime cannot be fundamental. This paper proposes a conceptual pathway by which temporal order, spatial geometry, and gravitational effects can be understood as emergent structures arising from stable phase relations—without introducing new dynamics or speculative entities. The core move is operational: clocks are oscillators, and what we call “time” is the comparison and synchronization of counted cycles across systems. Temporal order appears where phase relations are stable; divergence in clock rates appears where coherence conditions vary. In this framework, proper time corresponds to a system’s internal phase evolution, and relativistic phenomena (time dilation, gravitational redshift) are reinterpreted as changes in phase evolution induced by coherence gradients. Spatial distance and geometry are treated as doubly derivative: they are inferred through timing relations, synchronization procedures, and stable relational structure across extended systems. Uniform coherence yields an effectively “flat” geometry; varying coherence yields curvature-like behavior. The paper also sketches how inertia and acceleration can be viewed as resistance to reconfiguring phase-locked relations, aligning naturally with the equivalence principle. This work is Part II of a seven-part series that reframes foundational problems—unification, measurement, nonlocality, and the status of time—through the lens of phase coherence. Part III addresses measurement and classical definiteness; Part VII discusses experimental implications and falsifiability.
Phase Without Ontology is Part I of the Phase Ontology series (Parts I–VII). It argues that modern physics relies on phase everywhere—interference, the quantum wave function, gauge theory, the Aharonov–Bohm effect, superconductivity, and macroscopic coherence—yet typically treats phase as merely mathematical rather than ontologically primary. This “ontological restraint,” the paper claims, is not a neutral habit: it helps sustain persistent conceptual fragmentation around measurement, time, and the status of spacetime. Rather than proposing new equations or dynamics, the paper proposes an ontological re-ordering of already-successful formalism: phase coherence is treated as the fundamental organizing layer, with matter as stable phase-locked configurations, time as countable phase evolution, and spacetime as an emergent relational projection of stable phase relations. The framework is explicitly not an ether theory: it introduces no spatial medium, no preferred rest frame, and no “wind” effects—only relational coherence. The conclusion motivates the remainder of the series, which develops implications for emergent spacetime (Part II), measurement (Part III), entanglement (Part IV), time and entropy (Part V), mass and gravity (Part VI), and experimental falsifiability (Part VII).
Coherence, Entropy, and the Arrow of Time: Why Time Has a Direction in a Phase Ontology (Phase Ontology — Part V) proposes a phase-centered explanation for one of physics’ strangest asymmetries: microscopic laws are largely time-symmetric, yet macroscopic reality is not. Cups shatter but do not reassemble; heat flows from hot to cold; correlations decay; memories accumulate. This paper argues that the arrow of time becomes conceptually clear once phase coherence is treated as ontologically primary. In this framework, time is not fundamental. It emerges operationally from countable phase evolution in physical clocks (all clocks are oscillators) and from synchronization between systems. A shared “global time” is therefore a relational structure sustained by coherence, not a background substance that governs dynamics. The paper then reframes entropy growth as the loss of accessible phase information in open systems. As systems interact with environments that contain many degrees of freedom, phase correlations disperse outward and become physically inaccessible, even if not destroyed in principle. Decoherence is elevated from a technical detail to the central engine of macroscopic irreversibility: reversing decoherence would require re-phasing an astronomically large environment, which is practically impossible. Building on Part III, the paper also interprets measurement as phase locking: once a macroscopic coupling stabilizes one local configuration, alternative phase possibilities are effectively dispersed into the environment. Classical definiteness and temporal irreversibility are thus treated as two faces of the same process—coherence flow. This manuscript is Part V of a seven-part series (Parts I–VII). It connects Parts I–IV to time asymmetry and points forward to Part VI (mass, inertia, gravitation) and Part VII (experimental implications and falsifiability).
Entanglement and Nonlocal Coherence: Why Nonlocality Is Natural in a Phase Ontology (Phase Ontology — Part IV) reframes quantum entanglement by changing the usual starting assumption. The paper argues that entanglement only looks paradoxical if spacetime separation is assumed to imply ontological separation. If phase coherence is treated as a primary layer of reality (as developed in Parts I–III), then nonlocal correlations become expected rather than mysterious. In this view, entangled systems share a single coherent phase structure prior to measurement. Measurement is described as local phase locking: an interaction with a detector stabilizes a definite outcome locally, while the joint correlations arise because both outcomes are constrained by the same underlying phase structure. No superluminal signal is required; correlations are revealed rather than transmitted. The paper also addresses compatibility with relativity: since no information is communicated faster than light, relativistic causality remains intact. Locality is treated as an emergent property of spacetime, while coherence relations can be nonlocal because they are not fundamentally “in spacetime” to begin with. This manuscript is Part IV of a seven-part series (Parts I–VII). It connects the measurement framework of Part III to entanglement and points ahead to Part V (time, irreversibility) and Part VII (experimental implications and falsifiability).
Abstract The physical status of time remains one of the most persistent open questions in fundamental physics. In quantum mechanics, time appears as an external parameter governing evolution but not as an observable, while in general relativity it is embedded in the geometric structure of spacetime and becomes observer-dependent. Despite their empirical success, neither framework explains the physical origin of time or its singular role among fundamental quantities. In this work, we propose an emergent interpretation of physical time grounded in quantum phase. Phase is treated as a pre-temporal structural feature of quantum systems, rather than as a quantity defined with respect to an underlying temporal parameter. Energy is interpreted as a relational characterisation of regularities in phase structure, and proper time emerges only in contexts where phase accumulation can be compared and synchronised between interacting systems. An isolated quantum system may possess phase, but it does not possess physical time in the operational sense; time arises only through relational compatibility. This approach does not introduce new fundamental dynamics nor posit a physical mechanism responsible for the generation of time. Instead, it establishes an ontological hierarchy in which phase is fundamental, energy is relational, and time is a phenomenological quantity that emerges from stable conditions of synchronisation. Within this framework, classical reality corresponds to domains of temporal compatibility, while loss of compatibility underlies the emergence of horizons and geometric structure. By reframing time as an emergent relational phenomenon rooted in quantum phase, this work provides a coherent interpretative framework in which the absence of a time operator in quantum mechanics and the difficulty of quantising time and gravity are understood as consequences of their non-fundamental status, rather than as shortcomings of existing formalisms.
Experimental Signatures and Falsifiability of Phase Ontology: How a Phase-Primary Framework Can Be Tested (Phase Ontology — Part VII) completes the Phase Ontology series by translating its core claims into concrete, falsifiable expectations. While Parts I–VI argue that phase coherence is physically real and that spacetime is an emergent projection of stable phase relations, this paper makes the scientific demand explicit: the framework must constrain what should be observed in the laboratory—not merely reinterpret existing results. The paper outlines a set of testable signatures that should appear if measurement is genuinely a phase-locking process, if coherence is a physical resource that can be preserved or dispersed, and if detectors and environments are active material participants rather than generic sources of noise. Key experimental arenas include: (1) detector-dependent phase-locking thresholds (e.g., interferometry where small, controlled detector-material changes produce disproportionate shifts in localization/fringe behavior), (2) coherence capacity and delayed classicality (engineered environments that produce non-linear regime changes rather than only smooth decoherence), (3) entanglement under structured phase environments (sensitivity to structured phase modulation beyond standard loss/noise parameters), (4) precision clocks as phase probes (searching for residual coherence-environment dependencies beyond known systematics), and (5) macroscopic coherence bridge regimes in superconducting and mesoscopic networks where topology and coupling geometry should matter in structured ways. Crucially, the paper states what falsification would look like in practice: if across multiple platforms detector variations yield no structured threshold effects, coherence isolation produces only fully predictable smooth behavior, entanglement responds solely to standard channel parameters, and precision clocks show no reproducible residual coherence-structure dependence, then Phase Ontology remains an interpretation but loses its claim to be an empirically distinct physical framework. A staged experimental program is proposed, moving from tabletop interferometry to progressively more demanding coherence and clock tests.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.