Revision Note: While attempting to more properly define a few fuzzy concepts here,such as incompatibility and the joint frame, we realized the concept of uncountablegeneration used to narrow down to coarse grain is vacuous, a countable union or product of standard Borel is again standard Borel.And using a uncountable join parameter could solve that, but is hard to justify.So we all claims here mathematically invalid. The main concept, we believe, might still work with the proper definition of whatis incompatible. But it will require further work and possibly adjusting the definitionof admissible maps. We have one more attempt coming on this purely measure theoreticalapproach, using the concept of \emph{contextuality}. Abstract:We formulate a minimal, fully measure-theoretic solution to the quantum measurement problem based on a new principle, the Relativity of Information Frames (RIF). An \emph{information frame} is a probability space $(X,\Sigma,P)$ describing the distinguishable events available to a physical subsystem. When two systems interact, their frames combine through \emph{admissible maps}: measurable, probability-preserving, and information-non\-increasing transformations satisfying a finite-join condition that enforces countable generation of the joint $\sigma$-algebra. Measurement appears when the joint $\sigma$-algebra generated by system and apparatus ceases to refine indefinitely; the limiting $\sigma$-algebra is the pointer basis. Collapse arises from martingale convergence of conditional expectations, and the Born rule follows from the structure of admissible refinements. No Hilbert space, no decoherence postulates, and no collapse postulate are required. Standard quantum mechanics appears as one representation of an admissible frame.
Revision Note: While attempting to more properly define a few fuzzy concepts here,such as incompatibility and the joint frame, we realized the concept of uncountablegeneration used to narrow down to coarse grain is vacuous, a countable union or product of standard Borel is again standard Borel.And using a uncountable join parameter could solve that, but is hard to justify.So we all claims here mathematically invalid. The main concept, we believe, might still work with the proper definition of whatis incompatible. But it will require further work and possibly adjusting the definitionof admissible maps. We have one more attempt coming on this purely measure theoreticalapproach, using the concept of \emph{contextuality}. Abstract:We formulate a minimal, fully measure-theoretic solution to the quantum measurement problem based on a new principle, the Relativity of Information Frames (RIF). An \emph{information frame} is a probability space (X,Σ,P) describing the distinguishable events available to a physical subsystem. When two systems interact, their frames combine through \emph{admissible maps}: measurable, probability-preserving, and information-non-increasing transformations satisfying a finite-join condition that enforces countable generation of the joint σ-algebra. Measurement appears when the joint σ-algebra generated by system and apparatus ceases to refine indefinitely; the limiting σ-algebra is the pointer basis. Collapse arises from martingale convergence of conditional expectations, and the Born rule follows from the structure of admissible refinements. No Hilbert space, no decoherence postulates, and no collapse postulate are required. Standard quantum mechanics appears as one representation of an admissible frame.
This paper introduces the Relativity of Information Frames (RIF), a foundational framework that precedes and constrains dynamical theories. RIF treats information frames—σ-algebras of distinguishable events—as the fundamental objects of physical description, and formulates interaction as the joint realization of such frames subject to a symmetry principle: no information frame may be privileged over another. From this principle alone, the framework derives a canonical restriction on joint event structures. We prove the existence of a distinguished σ-algebra—the pointer algebra—which is the unique maximal event algebra compatible with perspectival symmetry and the existence of consistent probability assignments. Any empirical model admits a global probability measure on this algebra, while any strict extension generically fails to do so, reintroducing contextuality. These results impose non-trivial structural constraints that any admissible dynamics must respect. The framework is applied to quantum theory, not by postulating dynamics, but by showing how its core structures arise necessarily from informational consistency. Observables appear as perspectival maps, state update corresponds to interaction-induced coarse-graining, the Born rule follows from a martingale structure on the induced σ-algebra filtrations, Wigner-type scenarios are consistent, and unitary evolution is reinterpreted as gauge freedom in joint descriptions rather than ontic time evolution. RIF does not replace dynamical theories; it delimits them. It identifies which event structures, probability assignments, and symmetries are admissible prior to dynamics, and therefore clarifies what features of quantum theory are structural necessities rather than contingent dynamical postulates. The framework further implies intrinsic irreversibility, a relational notion of locality, and constraints on emergent geometric structure, which any subsequent dynamical formulation must accommodate.
The quantum measurement problem arises from the apparent incompatibility between unitary evolution, definite outcomes, and the Born rule. Standard formulations treat measurement as a special physical process, introducing either collapse, branching, or hidden variables. In this paper we adopt a different approach. We do not modify quantum dynamics. Instead, we redefine the structure to which measurement applies. We introduce a minimal continuation-based framework in which physical systems are described by admissible succession structures and observable outcomes arise through coarse-graining projections. Measurement is defined as a non-injective projection from the space of admissible continuations to a finite outcome space. We show that non-injectivity generically induces apparent indeterminacy, while conditioning on the projection fiber replaces collapse. Within the weak-correlation regime, the Born rule emerges as the unique aggregation-stable weighting under additive continuation composition. Decoherence is modelled as constraint-induced suppression of continuation multiplicity, recovering the phenomenology of environmental decoherence without collapse. Under these conditions, three components of the measurement problem (definite outcomes, probabilistic weights, and classical stability) admit structural reformulations as consequences of projection and aggregation rather than postulates. A fourth component, the projection selection problem: which coarse-graining is realised in a given physical context: is identified as a residual open question of comparable difficulty to the preferred basis problem; the dissolution claim is conditional on its eventual resolution.
The quantum measurement problem arises from a structural asymmetry in standard formulations of quantum mechanics: while unitary evolution is treated as fundamental, irreversible events are introduced only through ad hoc postulates. As a result, measurement, decoherence, and probability appear conceptually disconnected. In this work, we propose a minimal reformulation in which irreversible interaction events are taken as ontological primitives. An event is defined as a completely positive, trace-preserving map that is not equivalent to any unitary transformation. Unitary evolution emerges as an effective description valid between events. Within this framework, quantum measurement is not a special process but a particular class of irreversible events with outcome-resolving structure. The Born rule arises naturally from the statistical structure of event realizations, and environmental decoherence is reinterpreted as a high density of irreversible events. No collapse postulate, observer-dependent rule, or modification of quantum dynamics is required. This formulation provides a unified and physically grounded resolution of the measurement problem and establishes a conceptual foundation for event-based extensions connecting quantum theory with spacetime and gravity.
We propose that the quantum measurement problem is a frame problem, resolved by recognizing that coherence is relative to a choice of coherence frame—analogous to the relativity of simultaneity in special relativity. We introduce coherence relativity, a geometric framework in which physical reality is described on a joint manifold M×Σ, where M is emergent spacetime and Σ is a coherence manifold whose points represent distinct observational perspectives. In this framework, wave function collapse is not a dynamical process but a transformation between coherence frames induced by measurement interactions. We present a derivation of the Born rule—that measurement probabilities equal squared amplitudes—as the unique probability measure invariant under coherence-frame relabelings and splittings, given additivity and continuity. This derivation unifies insights from Gleason's theorem, Zurek's envariance, and operational reconstruction programs within a single geometric structure. We demonstrate the framework with the double-slit experiment in two coherence frames and identify six experimentally testable signatures distinguishing Coherence Relativity from standard quantum mechanics: non-linear visibility scaling, frame-transformation hysteresis, coherence-space curvature effects, modified gravitational decoherence, measurable transformation timescales, and coherence revival. The most accessible predictions—erasure hysteresis and transformation timescales—are testable with current superconducting qubit and trapped ion platforms. v4 (April 2026): Adds three new paradox resolutions (Quantum Zeno with D_f completion interpretation, Sleeping Beauty via CR-internal derivation from axioms A1+A3, and a unifying meta-theorem characterizing all quantum paradoxes as non-Born-compliant frame transport). Introduces Prediction 7 (Zeno/anti-Zeno crossover at τ_meas ≈ τ_transform with pointer-basis dependence). Total experimentally testable signatures increased from six to seven. 21 pages.
Abstract: The quantum measurement problem has been the deepest conceptual difficulty since the birth of quantum mechanics. Standard quantum mechanics accepts wavefunction collapse as an independent postulate but never provides a physical explanation. The decoherence approach attributes collapse to the interaction between the system and its environment, but faces two fundamental limitations: the “infinite regress” problem and the “insufficiency of decoherence” problem. Within the framework of the Self-Construction Theory (SCT), this paper provides a complete resolution of the measurement problem. The core thesis is that quantum measurement is not a fundamental process independent of the laws of physical evolution, but rather a local manifestation of constructive renormalization—the scale evolution of the spacetime complex field K from microscopic degrees of freedom to macroscopic effective descriptions. The origins of wavefunction collapse, decoherence, and the Born rule receive a unified first‑principles interpretation in this framework. SCT’s spontaneous decoherence mechanism is the key to the resolution. Constructive renormalization inherently involves information loss—the integrated‑out microscopic degrees of freedom no longer exist in the macroscopic effective description. During a measurement, the measuring apparatus possesses a huge number (∼1023) of microscopic degrees of freedom. When the apparatus interacts with the measured system, constructive renormalization triggers information compression of these degrees of freedom—the apparatus can no longer distinguish which branch of the superposition it is in, and quantum coherence is thus spontaneously lost. No “external environment” is needed—the constructive renormalization dynamics of spacetime itself is the ultimate source of decoherence, thereby completely solving the “infinite regress” problem. Among the probability distribution given by the Born rule, the weights of non‑maximal probability branches are further suppressed by information compression under the huge number of microscopic degrees of freedom, so that macroscopic observers can perceive only a definite outcome in the effective description. The information loss caused by constructive renormalization is ontological—it does not rely on any approximation or truncation, thus fundamentally solving the “insufficiency of decoherence” problem. The Born rule—that measurement outcomes occur with probabilities given by the squared amplitudes—is directly derived from the constructive integral structure in SCT. In the constructive renormalization limit, interference terms between different configurations are naturally suppressed by off‑diagonal phase randomization, and the system automatically switches to a classical probabilistic description. In the diagonal density matrix representation, the squared amplitude is the only natural weight that is simultaneously real and non‑negative. Hence the Born rule is not an additional postulate of quantum mechanics but a necessary and unique manifestation of the relative frequencies of the constructive integral in the constructive renormalization limit. This derivation is rigorous within the mathematical framework of constructive renormalization—it does not rely on any approximations or truncations. SCT’s quantum measurement theory is deeply unified with the black hole information paradox. The “collapse” in quantum measurement and the “information loss” in black hole evaporation are different manifestations of the same core mechanism—the redistribution of information due to constructive renormalization—in two extreme physical situations. In quantum measurement, information is redistributed into the degrees of freedom of the macroscopic apparatus; in black hole evaporation, information is redistributed into the time‑point configurations on the horizon. This unification is the strongest proof of the universality of constructive renormalization as an information‑processing mechanism. Keywords: quantum measurement; spontaneous decoherence; constructive renormalization; Born rule; wavefunction collapse; information redistribution; Self-Construction Theory
Admissibility Physics — Quantum Structure from Finite Enforceability (Paper 5) This Zenodo community collects research outputs associated with Admissibility Physics, with primary focus on Paper 5 — Quantum Structure from Finite Enforceability and the derivation of quantum mechanics as an admissible representational regime. Paper 5 shows that the mathematical structure of quantum mechanics—Hilbert space, linearity, inner products, tensor products, unitary evolution, CPTP maps, and the Born rule—is not postulated, but forced by admissibility once coherent, jointly enforceable distinctions exist under finite correlation capacity. Quantum structure emerges as the unique bookkeeping required to represent interference, refinement, and recombination while preserving admissibility. The derivation does not assume probability, measurement postulates, dynamics, or spacetime geometry. Probability enters only as a secondary representation, with the Born rule arising uniquely from admissibility invariance and refinement consistency. Measurement is treated as a regime transition associated with saturation and record formation, not as a fundamental collapse mechanism. Quantum mechanics is shown to be conditionally valid: exact in regimes where coherence and non-saturation permit admissible composition, and structurally inapplicable where capacity is exhausted. Monogamy, entanglement limits, and decoherence follow from non-closure under composition and finite interface capacity, rather than from quantum axioms. All subsequent works in this community rely on the quantum-admissible representation established in Paper 5. Later papers show how variational dynamics and spacetime geometry arise as further conditional representations layered on top of quantum structure, and how quantum description itself fails at saturation boundaries, horizons, and measurement-like events. This community serves as a curated, citable archive centered on the derivation and limits of quantum structure within Admissibility Physics. Paper 5 functions as the representational keystone of the program: the point at which finite enforceability yields the quantum formalism without postulation. Core papers are frozen where noted; companion papers, mathematical appendices, figures, and computational artifacts document derivations, regime conditions, and testable consequences.