This paper investigates the emergence of the flow of time, spatial reality, and the dynamics of quantum measurement experienced by a local observer within the framework of a 'Static Relational Structure under Global Zero Constraint ($\sum U_i = 0$)', as established in the preceding studies of this series (Paper I and II). We define an observer not merely as a subsystem, but as a subgraph with memory capable of recording states and maintaining them irreversibly. This definition allows for the construction of a partial ordering of accessible relations. Consequently, time is not treated as a fundamental physical flow but emerges as the cumulative order of information (correlation entropy) acquired by the observer. Furthermore, 3-dimensional space is shown to be the result of information compression necessary for the efficient processing of complex relational networks. Key contributions of this study include: Reinterpretation of Quantum Measurement: Measurement is defined as a graph merger process via Topological Surgery between the observer and the target graph. Mechanism of Wavefunction Collapse: Collapse is mathematically proven to be a phenomenon of discontinuous Spectral Rearrangement of the Laplacian spectrum, governed by the Cauchy Interlacing Theorem. Derivation of Universal Constraints: We derive five universal constraint conditions that the universe's spectral structure must satisfy for such an observer to exist, including a non-zero spectral gap, quasi-continuity, and a spectral dimension fixed point of $d_s \approx 4$. This work proposes that the observed physical conditions of our universe are not arbitrary but are necessary structural consequences for the existence of an observer within a static global constraint.
This paper investigates the emergence of the flow of time, spatial reality, and the dynamics of quantum measurement experienced by a local observer within the framework of a 'Static Relational Structure under Global Zero Constraint (∑Ui=0)', as established in the preceding studies of this series (Paper I and II). We define an observer not merely as a subsystem, but as a subgraph with memory capable of recording states and maintaining them irreversibly. This definition allows for the construction of a partial ordering of accessible relations. Consequently, time is not treated as a fundamental physical flow but emerges as the cumulative order of information (correlation entropy) acquired by the observer. Furthermore, 3-dimensional space is shown to be the result of information compression necessary for the efficient processing of complex relational networks. Key contributions of this study include: Reinterpretation of Quantum Measurement: Measurement is defined as a graph merger process via Topological Surgery between the observer and the target graph. Mechanism of Wavefunction Collapse: Collapse is mathematically proven to be a phenomenon of discontinuous Spectral Rearrangement of the Laplacian spectrum, governed by the Cauchy Interlacing Theorem. Derivation of Universal Constraints: We derive five universal constraint conditions that the universe's spectral structure must satisfy for such an observer to exist, including a non-zero spectral gap, quasi-continuity, and a spectral dimension fixed point of ds≈4. This work proposes that the observed physical conditions of our universe are not arbitrary but are necessary structural consequences for the existence of an observer within a static global constraint.
This project investigates the emergence of time from a fundamentally timeless description of the universe. Rather than assuming time as a primitive background parameter, we study the physical and informational conditions under which temporal ordering, dynamics, and irreversibility appear for an observer embedded in the system. The core of the framework is a unified relational formula—extending the Page–Wootters mechanism—that shows how three traditionally distinct aspects of the “problem of time” arise from the same operational structure: (i) quantum dynamics from conditioning on physical clock states, (ii) the thermodynamic arrow from partial access to environmental degrees of freedom, and (iii) observer-dependent time from the locality of the clock subsystem. Crucially, the framework does not modify unitary quantum mechanics, introduce collapse postulates, or assume a fundamental flow of time. All temporal features emerge from projection, partial trace, and normalization applied to a single global atemporal state satisfying a Hamiltonian constraint. The project includes analytical results, numerical simulations (implemented in QuTiP), pedagogical companion notes, and philosophical analysis. Together, these components support a central claim: time is not a property of the universe itself, but a property of restricted descriptions generated by physical observers with limited informational access. This OSF repository serves as a living container for the formal development, conceptual interpretation, and future extensions of this observer-dependent approach to temporal emergence.
The nature of time remains a central problem in fundamental physics, spanning quantum mechanics, thermodynamics, and relativity. In this work, we develop an observer-dependent framework in which time is not assumed as a fundamental background parameter, but emerges operationally from restricted access to a globally timeless quantum state. Building on and extending the Page–Wootters mechanism, we introduce a unified relational formula that shows how three traditionally distinct aspects of temporality arise from the same structure: quantum dynamics from conditioning on physical clock states, thermodynamic irreversibility from partial tracing over inaccessible degrees of freedom, and observer-relative time from the locality of the clock subsystem. No modification of unitary quantum mechanics, collapse postulates, or fundamental time flow is required. Analytical arguments and numerical simulations demonstrate that, in the limit of complete information access, all temporal ordering disappears, while effective Schrödinger dynamics and an arrow of time emerge naturally under informational and observational constraints. These results support a central claim: time is not a property of the universe itself, but a property of descriptions generated by physical observers embedded within it.
The measurement problem in quantum mechanics and the embedding of observers in general relativity jointly point to the awkward position of the observer in physical theory: traditional theories place the observer outside the system, but in a self-contained universe, the observer must be internal to the physical world. This paper models the observer as a local subnet inside an emergent spacetime constraint network, whose internal constraint structure forms a compressed generative model of the external network state. The measurement event is reinterpreted as a non-equilibrium phase transition of the internal constraint conffguration when the constraint propagation between the observer subnet and the target subnet reaches a critical threshold, and wavefunction collapse is reduced to a sudden transition of a local subnet from a symmetric multi-basin state to a single-basin broken-symmetry state. Based on a formalisation of the microscopic dynamics of constraint networks, symmetry and conservation laws, and the emergence of an arrow of time, this framework uniffes the historical interpretation of decoherence with active inference in the free energy principle, and argues that a self-referential universe can contain a self-referential subnet, thereby making physical laws cognisable. Physics and cognitive science achieve a deep unity at the ontological level of constraint networks.
The concepts of “observation” and “collapse” in quantum mechanics have long been treated as either mysterious or merely phenomenological. Within the information‐dynamics framework of the Logical Universe (LU_v3.1), we propose a complete ontological model in which observation is identified as chiral–topological coupling between information solitons; collapse is the topological compression of a superposed field state into a single material path; and decoherence is the release of the material state back into the field, but this return is not reversible—it irreversibly inscribes the entire topological history of the collapse into the global light‐field structure. Matter is thus interpreted as a temporary collapsed snapshot of the field, and the “past” is defined as the irreversible information texture engraved into the topological structure of the field. This model provides a unified ontological foundation for the quantum–classical transition, the measurement problem, and the origin of temporal irreversibility, and yields experimentally testable consequences.
This paper presents an observer-inclusive, semiclassical framework in which quantum measurement, the emergence of time, and spacetime curvature are unified through the dynamics of record formation. Measurement is modeled as a local, causal stabilization process driven by irreversible record creation within closed quantum systems, eliminating the need for external wavefunction collapse. Time is shown to emerge as a derived quantity proportional to record flux rather than as a fundamental background parameter. Regions of suppressed entropy production correspond to effective “timeless” steady states, while ordinary relativistic proper time is recovered in semiclassical regimes. The framework introduces a covariant, Planck-suppressed coupling between spacetime curvature and local record flow. Record density is defined on invariant causal diamonds using sandwiched Rényi mutual information to preserve Lorentz covariance and ultraviolet regularity. The energetic cost of record formation is compensated via Landauer’s principle, ensuring consistency with the Bianchi identities, null energy conditions, and the no-signaling theorem. The resulting theory is explicitly effective and semiclassical. It makes no claim to a fundamental quantum gravity completion, but provides a consistent, observer-inclusive description of measurement, time, and geometric response compatible with known physical constraints and open to experimental falsification.
Quantum mechanics lacks a physical definition of measurement, observer, probability, and experienced time. These notions are instead treated as primitive or interpretation-dependent, leading to persistent foundational problems including the measurement problem, the origin of the Born rule, observer disagreement in Wigner’s Friend scenarios, the arrow of time, and apparent information loss in black hole evaporation. In this work, we show that these problems share a single missing ingredient: the absence of an operational definition of observers as bounded physical systems. We define observers as physically realizable systems capable of forming irreversible internal records under unitary dynamics. Measurement is identified with record formation, probability with record redundancy, experienced time with record accumulation, and irreversibility with computational inaccessibility rather than non-unitarity. Using decoherence and quantum Darwinism, we show that the number of accessible, decoherence-stable records associated with an outcome scales with the squared amplitude, yielding the Born rule from record counting without invoking collapse, subjective probability, or additional axioms. Observer-relative paradoxes dissolve once outcome definiteness is indexed to record formation rather than to the global quantum state. Reconstruction of global quantum information is shown to require exponential resources, rendering measurement and black hole evaporation operationally irreversible despite global unitarity. The resulting framework closes quantum mechanics conceptually by eliminating undefined primitives, without modifying its mathematical structure or introducing new dynamical postulates.