An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added environment) in a quantum measurement process. We show that this open system can be well described by an "almost" quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a density matrix can be constructed to give the Born's probability rule, realizing a (non-dynamical) decoherence. The concept of the ("almost") quotient space can also be used to explain the classical properties of a macroscopic system. We show further that the definite outcomes in a quantum measurement are mainly caused by the "almost" quotient space of the macroscopic apparatus.
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added environment) in a quantum measurement process. We show that this open system can be well described by an "almost" quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a density matrix can be constructed to give the Born's probability rule, realizing a (non-dynamical) decoherence. The concept of the ("almost") quotient space can also be used to explain the classical properties of a macroscopic system. We show further that the definite outcomes in a quantum measurement are mainly caused by the "almost" quotient space of the macroscopic apparatus.
The problem of measurement taken at face value shows clearly that there is an inconsistency inside the quantum formalism.The phenomenon of decoherence is often presented as a solution to it.A widely debated question is to decide between two different interpretations.The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate.For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed and so, to explain the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears.In this case, explaining why only one single definite outcome is observed remains to do.In this paper, we examine arguments for and against both interpretations and defend a position according to which the outcome that is observed is relative to the observer in close parallel to the Everett interpretation.
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
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.
Measurement as Phase Locking: A Physical Interpretation of Quantum Measurement (Phase Ontology — Part III) addresses one of the most stubborn puzzles in modern physics: what “measurement” physically is, and why a quantum superposition yields a single definite outcome. The paper argues that the measurement problem persists largely because phase is treated as merely descriptive, rather than as a physically real organizing layer. Within a phase-ontological framework, measurement is reinterpreted as a coupling-driven coherence transition. A quantum system begins as a distributed phase configuration. When it interacts with a macroscopic detector (and its environment), the interaction imposes many competing constraints on phase relations. Once coupling crosses a practical threshold, only those configurations that can remain coherently stable with the detector–environment system survive: the system phase-locks into a local, dynamically stable configuration. What standard interpretations call “collapse” is therefore not a mysterious, observer-triggered discontinuity, but an emergent stabilization process governed by coupling strength, environmental structure, and phase stability. The paper also situates this account relative to decoherence: decoherence explains the suppression of interference, while phase locking is proposed as the missing stabilizing mechanism that explains why one localized outcome is realized. Probabilities are interpreted not as hidden variables, but as the relative stability of available phase-locking channels, offering a physical reading of the Born rule. This work is Part III of a seven-part series (Parts I–VII). It builds on the foundations of Parts I and II, prepares the ground for Part IV (entanglement and nonlocal correlations), and points ahead to Part VII for experimental implications and falsifiability.
One of the main goals of no-collapse interpretations of quantum mechanics is to show how results of measurements are objectified, or, in a more poignant terminology, how in a measurement situation facts arise. One needs to show how in their dynamical evolution the measured system and, perhaps more importantly, the measuring apparatus acquire, or at least appear to acquire, the definite properties that are otherwise explained by the collapse of the state. This can be seen as a special case of the problem whether quantum mechanics alone can account for the classical behaviour of macroscopic systems; in particular, the permanent definiteness of at least those properties of macroscopic systems that are directly observable, such as the position of the pointer of a measuring apparatus. In other words, whether quantum mechanics can account for macrofacts of the familiar kind.
Environmental decoherence is central to contemporary accounts of quantum measurement, yet its relation to definite outcomes remains disputed. This review distinguishes four explanatory demands: interference suppression, preferred-basis selection, operational objectivity, and outcome actualization. It compares open-system formalism and experimental evidence with the principal philosophical accounts of definiteness. In nonrelativistic models, environmental entanglement disperses phase coherence into inaccessible correlations, rendering the reduced system–apparatus state approximately diagonal in an interaction-selected pointer basis. Experiments support this loss of locally observable interference, while einselection and redundant environmental records explain the stability and intersubjective accessibility of macroscopic properties. These achievements neither convert an improper mixture into ignorance about an actual result nor select one component of the global state. Everettian interpretations reject global uniqueness, Bohmian mechanics adds an actual configuration, objective-collapse theories modify the dynamics, and QBist or pragmatist approaches revise quantum-state semantics. Decoherence is therefore indispensable to the formation of classical records but insufficient, by itself, for an interpretation-neutral derivation of unique actualization. Its foundational significance lies in identifying where unitary dynamical explanation ends and an ontological, dynamical, or semantic account of definiteness must begin.