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arXiv:2412.13214

Resolving the Quantum Measurement Problem through Leveraging the Uncertainty Principle

Kyoung Yeon Kim

Published Dec 13, 2024• 0 citations
arXivHTMLPDF

Abstract

The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the uncertainty principle and, therefore, cannot interpret definite observations without uncertainty. Here, we resolve this enigma by demonstrating that in phase space quantum mechanics, particularly through the Wigner Moyal equation, uncertainty can be arbitrarily adjusted by tuning the observation window. An observation window much smaller than the uncertainty limit causes substantial nonlocality, rendering the problem ill posed. This suggests that only with sufficient uncertainty does nonlocality become bounded, resulting in a well posed universe. Conversely, in the absence of uncertainty, spacetime is warped beyond recognition, and the system exists as a superposition of numerous possible states. Measurement collapses this superposition into a unique solution, exhibiting timeless nonlocal interactions. Our framework bridges seemingly disparate concepts such as classical mechanics, quantum mechanics, decoherence, and measurement within intrinsic quantum mechanics even without invoking new theory.

DOI
10.48550/arxiv.2412.13214

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•Jan 29, 2021•1 citation
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the uncertainty principle and, therefore, cannot interpret definite observations without uncertainty. Here, we resolve this enigma by demonstrating that in phase space quantum mechanics, particularly through the Wigner Moyal equation, uncertainty can be arbitrarily adjusted by tuning the observation window. An observation window much smaller than the uncertainty limit causes substantial nonlocality, rendering the problem ill posed. This suggests that only with sufficient uncertainty does nonlocality become bounded, resulting in a well posed universe. Conversely, in the absence of uncertainty, spacetime is warped beyond recognition, and the system exists as a superposition of numerous possible states. Measurement collapses this superposition into a unique solution, exhibiting timeless nonlocal interactions. Our framework bridges seemingly disparate concepts such as classical mechanics, quantum mechanics, decoherence, and measurement within intrinsic quantum mechanics even without invoking new theory.
In this study, we show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates.We do not delve into a deep discussion regarding what the measurement problem actually is, and only examine the problems that seem to exist between classical and quantum physics.Relations between quantum and classical equations of motion are briefly reviewed to show that the transition from a superposition of quantum states to an eigenstate, namely, decoherence, is necessary to ensure that the expectation values in quantum mechanics obey the classical equations of motion.Several Bell-type inequalities and the Kochen-Specker theorem are also reviewed to clarify the concepts of nonseparability and counterfactual definiteness in quantum mechanics.The main objective of this study is to show that decoherence is an inherent characteristic of quantum states caused by the quantum uncertainty relation.We conclude that the quantum measurement process can indeed be explained within the framework of pure quantum mechanics.We also show that our conclusion is consistent with the counterfactual indefiniteness of quantum mechanics.
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 KKK 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\sim10^{23}∼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
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.
We propose an interpretation of quantum mechanics in which the wavefunction represents unresolved potential relative to an observer, measurement is deterministic resonance stabilisation, and Born-rule probability quantifies the observer’s incomplete access to the full entropic and phase-geometric state of the observer–system interaction. An observer is defined operationally as any bounded system capable of converting external entropy into internal coherence. On this view,superposition is not a set of co-existing realities but an unresolved field of possible coherence resolutions; collapse is not a stochastic discontinuity but a deterministic phase-lock between observer and system; and the classical world is the high-coherence limit in which environmental observation is dense enough to continuously stabilise macroscopic facts.The interpretation preserves the full predictive machinery of quantum mechanics while providing a unified account of the measurement problem, the Born rule, decoherence, entanglement, delayed choice, Wigner’s friend, and the quantum-to-classical transition. We formalise the framework through a resonance-selection rule, an observer equation of collapse, and a prime-modal state-space structure, and identify five classes of empirically accessible predictions.
The measurement problem in quantum mechanics can be characterized as explaining the question of definite outcomes, where a measurement of a superposed quantum state only gives a single definite outcome. According to quantum mechanics, the wave function, ψ, defines the state of the system, while the Schrödinger equation is a linear superposition of states that evolves deterministically. When a measurement is made, the outcome always uncovers the physical system as being in a definite state, and the future evolution of the wave function is amended based on the state that was measured. This change is often referred to as the “collapse” of the wave function. The problem concerns the question of what and how the measurement affected the system and why this changed the wave function. This paper addresses the measurement problem by separating it into five separate questions that are resolved through linking measurements to an entropy transfer from the superposed state to the environment. The underlying premise is the wave function is descriptive and not prescriptive, and entropy—the metric of quantum uncertainty and uncertainty in general—is the fundamental property rather than the wave function.
Abstract In the context of the century-long debate on quantum measurement problem, the current work proposes a model that describes the process of collapse of state by quantum interaction, which resolves the controversies of the framework of quantum mechanics and describes the entire domain of quantum-to-classical world including the weak measurement and partial collapse. ‘Measurement’, being the process of physically interacting with a system in order to extracting information from it, is theorized in the current model by synthesizing the quantum interaction between system and measuring apparatus with the information entropy of such process. The model assumes Schrödinger equation to be the only guiding equation for all physical systems including the measuring apparatus, and does not presuppose ‘superposition principle’, rather derives it theoretically from the formulation. The superposed state is shown to be independent of the choice of measurement operator (observable) or basis states (pointers) of the measuring apparatus. Most interestingly, the current model explains the non-observance of ‘superposition principle’ by classical systems as the classical limit of such quantum description of measurement. Along with solving the quantum measurement problem, the work also explains weak measurement and partial collapse, which can be further extended to investigate such several emerging critical phenomena.