## Abstract Textbook quantum mechanics defines measurement using ideas that are not themselves basic physics: "observer," "macroscopic apparatus," "irreversible record." We take this definition apart and find that it bundles two different things: the physical event of an interaction, and the statistical fact that the event's result becomes hard to erase. We separate them. A measurement, in its minimal form, is a causal link: when event A and event B interact, a fact is established between them — B's state relative to A. This happens at every interaction, at every scale, with no apparatus required. What laboratories call "a measurement" is the same kind of event, after its result has spread — fanned out — into so many further causal links that undoing it is no longer practical. This reading gives the quantum eraser a clean explanation: an outcome is erasable exactly as long as its causal fan-out stays narrow. It also clarifies what decoherence theory does and does not do: decoherence is the physics of fan-out, and it does that job well; the question it was criticized for not answering (why one outcome, with Born-rule probability) belongs to a different layer. Nothing in the existing formalism changes. What changes is the definition — and with it, the need for a separate "collapse mechanism" disappears. Because the basic unit here is a causal link, the whole picture can be built directly on discrete causal structures, which we identify as the natural next step. Keywords: measurement problem, decoherence, causal link, quantum eraser, relational quantum mechanics
Abstract Textbook quantum mechanics defines measurement using ideas that are not themselves basic physics: "observer," "macroscopic apparatus," "irreversible record." We take this definition apart and find that it bundles two different things: the physical event of an interaction, and the statistical fact that the event's result becomes hard to erase. We separate them. A measurement, in its minimal form, is a causal link: when event A and event B interact, a fact is established between them — B's state relative to A. This happens at every interaction, at every scale, with no apparatus required. What laboratories call "a measurement" is the same kind of event, after its result has spread — fanned out — into so many further causal links that undoing it is no longer practical. This reading gives the quantum eraser a clean explanation: an outcome is erasable exactly as long as its causal fan-out stays narrow. It also clarifies what decoherence theory does and does not do: decoherence is the physics of fan-out, and it does that job well; the question it was criticized for not answering (why one outcome, with Born-rule probability) belongs to a different layer. Nothing in the existing formalism changes. What changes is the definition — and with it, the need for a separate "collapse mechanism" disappears. Because the basic unit here is a causal link, the whole picture can be built directly on discrete causal structures, which we identify as the natural next step. Keywords: measurement problem, decoherence, causal link, quantum eraser, relational quantum mechanics
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.
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.
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
Abstract The measurement problem in quantum mechanics is commonly framed as a conflict between unitary dynamics and the appearance of definite outcomes. This paper argues that the conflict arises from a misplaced assumption about what outcomes must be. In experimental practice, outcomes are not arbitrarily precise microscopic states or instantaneous events, but stable physical records produced in measurement interactions. Treating outcomes as such records allows them to be formalized as coarse-grained equivalence classes of physical states that persist in time and support consistent interaction across systems. On this basis, decoherence explains the stability of outcomes without selecting a unique global result or modifying quantum dynamics. Objectivity is recovered through the robustness of records rather than through absolute, observer-independent outcome facts. The measurement problem is thereby dissolved without invoking collapse mechanisms, branching universes, or observer-dependent postulates, while preserving all standard empirical predictions of quantum mechanics.
The quantum measurement problem persists because physics has never provided an operational definition of "observer" specifying which physical interactions constitute observations. We apply a thermodynamic operational definition developed from a prior observer framework: an observer is any self-maintaining bounded system that reduces entropy through differential environmental processing, where the system's persistence depends on the character of that processing. We distinguish between measurement (any interaction satisfying the definition's first two conditions, producing decoherence that suppresses quantum interference) and observation (an interaction involving a system satisfying all three conditions, producing autonomous, feedback-sustained decoherence). This distinction resolves the observer ambiguity in the canonical measurement-problem thought experiments: it specifies which systems observe, where in any causal chain observation occurs, and why the intuitive placement of the Heisenberg cut at the apparatus is practically correct. The Frauchiger-Renner inconsistency becomes identifiable and addressable once observer status is operationally assigned, because the definition identifies where the domain of unrestricted unitary description must be constrained. The nature of that constraint (collapse, irreversible branching, transaction completion) is interpretation-dependent; the criterion for where it applies is not, though the strength of the resulting resolution varies across interpretations. The definition does not resolve the problem of definite outcomes, derive the Born rule, or select the preferred basis. It resolves the component of the measurement problem that has blocked progress on those questions: the absence of any criterion for which systems perform observations.
This work proposes a threshold-based picture of decoherence in quantum measurement. Microscopic quantum dynamics remain fully continuous and unitary, but real detectors implement thresholded amplification and nonlinear gain boundaries that partition continuous microscopic inputs into discrete macroscopic outcomes. Within this framework, discreteness and irreversibility arise from scale asymmetry between a continuous microscopic energy distribution and a finite macroscopic threshold ΔE_threshold, without invoking fundamental collapse, branching, or uncontrolled environmental decoherence. The measurement apparatus effectively performs an analog-to-digital conversion: it maps a continuous input distribution ρ(E) to a binary output variable X_eff ∈ {0,1} according toP(event) = ∫_{ΔE_threshold}^{∞} ρ(E) dE,while the recording layer irreversibly erases phase information by structural codomain restriction. This threshold-based decoherence model preserves standard quantum mechanics, provides an operational bridge across major interpretations of quantum theory, and locates the origin of discrete outcomes in the architecture of measurement rather than in quantum ontology itself. In short, this paper views discrete measurement outcomes as emerging from threshold detector architecture rather than from any fundamental discreteness of the quantum substrate.