Counting outcomes is the obvious algorithm for generating probabilities in quantum mechanics without state-vector reduction (i.e. many-worlds). This procedure has usually been rejected because for purely linear dynamics it gives results in disagreement with experiment. Here it is shown that if non-linear decoherence effects (previously proposed by other authors) are combined with an exponential time dependence of the scale for the non-linear effects, the correct measure-dependent probabilities can emerge via outcome counting, without the addition of any stochastic fields or metaphysical hypotheses.
Counting outcomes is the obvious algorithm for generating probabilities in quantum mechanics without state-vector reduction (i.e. many-worlds). This procedure has usually been rejected because for purely linear dynamics it gives results in disagreement with experiment. Here it is shown that if non-linear decoherence effects (previously proposed by other authors) are combined with an exponential time dependence of the scale for the non-linear effects, the correct measure-dependent probabilities can emerge via outcome counting, without the addition of any stochastic fields or metaphysical hypotheses.
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.
Decoherence theory has played a central role in explaining the suppression of interference and the emergence of classicality in quantum systems. However, it remains unclear whether decoherence alone can universally account for the origin of quantum probabilities themselves. In the present work, we examine the consequences of interpreting decoherence not merely as an interference-suppression mechanism, but as the fundamental generator of probabilistic measurement outcomes. If quantum probabilities are produced through system–apparatus–environment interactions, the resulting probabilities would generally be expected to depend on the detailed structure of those interactions. Such dependence would imply the possibility of interaction-dependent corrections to the Born-rule probabilities. However, the experimentally observed universality and robustness of the Born rule strongly constrain such a possibility. We therefore argue that decoherence successfully explains the effective suppression of interference terms, but does not by itself universally determine quantum probabilities without additional principles ensuring probability invariance. Based on this distinction, we propose that the origin of quantum probabilities should be conceptually separated from decoherence-induced classicality. Within the Intrinsic Observability Framework (IOF), this separation arises naturally through structural limitations on observability rather than through environment-generated probability formation. The present analysis suggests a conceptual reorganization of the role of decoherence in the quantum measurement problem.
“… persuaded of these principles, what havoc must we make ?” — Hume ABSTRACT Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of the state vector at measurements. Probabilities are computed by summing the squares of amplitudes over alternatives which could have been measured but weren't. Measurements are limited by uncertainty principles and by other restrictions arising from the principles of quantum mechanics. This essay examines the extent to which those features of the quantum mechanics of measured subsystems that are explicitly tied to measurement situations are incorporated or modified in the more general quantum mechanics of closed systems in which measurement is not a fundamental notion. There, probabilities are predicted for decohering sets of alternative time histories of the closed system, whether or not they represent a measurement situation. Reduction of the state vector is a necessary part of the description of such histories. Uncertainty principles limit the possible alternatives at one time from which histories may be constructed. Models of measurement situations are exhibited within the quantum mechanics of the closed system containing both measured subsystem and measuring apparatus.
It is shown that the quantum-mechanical state vector correctly describes not only the probabilities for the outcomes of measurements, but also the correlations between the outcomes of successive measurements. In particular, von Neumann's axiom M is shown to be redundant. Consequently, no extra---quantum-mechanical "reduction" of the joint object-apparatus state vector is required for a full statistical description of a sequence of measurements. It is also shown that any attempt to determine experimentally whether or not a reduction of the joint state vector has taken place during a measurement is incompatible with the preservation of the outcome of that measurement.
A marquee feature of quantum behavior is that, upon probing, the microscopic system emerges in one of multiple possible states. While quantum mechanics postulates the respective probabilities, the effective abundance of these simultaneous ``identities'', if a meaningful concept at all, has to be inferred. To address such problems, we construct and analyze the theory of functions assigning the quantity (effective number) of objects endowed with probability weights. In a surprising outcome, the consistency of such probability-dependent measure assignments entails the existence of a minimal amount, realized by a unique effective number function. This result provides a well-founded solution to identity-counting problems in quantum mechanics. Such problems range from counting the basis states contained in an output of a quantum computation, and relevant in the analysis of quantum algorithms, to a novel way to characterize complex states such as QCD vacuum or eigenstates of quantum spin systems. In accompanying works, we analyze notable consequences of these findings, namely expressing quantum uncertainty as a measure, the ensuing universal treatment of localization phenomena, and effective description of quantum states. At the basic level, our results point to useful extensions for concepts of measure and support, and to a new probability notion of effective choices.
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring system and a measured one. These properties result directly from the Schrödinger equation. They cannot be formulated in terms of observables, do not affect the wave functions themselves but express their history in an irreversible way. They carry a specific new kind of local probabilities, which evolve with a finite velocity under nonlinear wave equations. The second category of results extends these local properties to the case of a macroscopic system and its environment. Fluctuations in their interaction are predicted then and generate a specific incoherence in the quantum state of the system. These two kinds of effects act together when a macroscopic measuring system interacts with a measured system and with an environment. Their combination yields then an explicit and effective mechanism of collapse, with a random behavior resulting from random incoherence. Born's basic probability rule for the results of measurements turns out then simply a consequence of quantum dynamics. Some conjectures still enter into the derivation of these effects, which one may recognize to look hardly credible at first sight. They fit however so well together that one proposes a more thorough investigation of their approach as a promising strategy for a self-contained explanation of collapse.