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arXiv:1601.05222

Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective

Diederik Aerts, Massimiliano Sassoli de Bianchi

Published Jan 20, 2016• 10 citations
arXivHTMLPDF

Abstract

The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient transactions, no specific mechanism was actually provided to explain why the weights of such symmetry breaking are precisely those given by the Born rule. In other terms, PTI, similarly to decoherence theory, doesn't explain a quantum measurement in a complete way, but just the transition from a pure state to a fully reduced density matrix state. On the other hand, the recently derived extended Bloch representation (EBR) - a specific implementation the HMI - precisely provides such missing piece of explanation, i.e., a qualitative description of the WSB as a process of actualization of hidden measurement-interactions and, more importantly, a quantitative prediction of the values of the associated weights that is compatible with the Born rule of probabilistic assignment. Therefore, from the PTI viewpoint, the EBR provide the missing link for a complete description of a quantum measurement. However, EBR is in a sense more general than PTI, as it does not rely on the specific notion of transaction, and therefore remains compatible with other physical mechanisms that could be at the origin of the measurement-interactions.

DOI
10.48550/arxiv.1601.05222

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The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient transactions, no specific mechanism was actually provided to explain why the weights of such symmetry breaking are precisely those given by the Born rule. In other terms, PTI, similarly to decoherence theory, doesn't explain a quantum measurement in a complete way, but just the transition from a pure state to a fully reduced density matrix state. On the other hand, the recently derived extended Bloch representation (EBR) - a specific implementation the HMI - precisely provides such missing piece of explanation, i.e., a qualitative description of the WSB as a process of actualization of hidden measurement-interactions and, more importantly, a quantitative prediction of the values of the associated weights that is compatible with the Born rule of probabilistic assignment. Therefore, from the PTI viewpoint, the EBR provide the missing link for a complete description of a quantum measurement. However, EBR is in a sense more general than PTI, as it does not rely on the specific notion of transaction, and therefore remains compatible with other physical mechanisms that could be at the origin of the measurement-interactions.
A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.
The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like "beginner's mind" in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant ("PTI"), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don't), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don't bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010).
Providing a comprehensive exposition of the transactional interpretation (TI) of quantum mechanics, this book sheds new light on long-standing problems in quantum theory such as the physical meaning of the 'Born Rule' for the probabilities of measurement results, and demonstrates the ability of TI to solve the measurement problem of quantum mechanics. It provides robust refutations of various objections and challenges to TI, such as Maudlin's inconsistency challenge, and explicitly extends TI into the relativistic domain, providing new insight into the basic compatibility of TI with relativity and the meaning of 'virtual particles.' It breaks new ground in approaches to interpreting quantum theory and presents a compelling new ontological picture of quantum reality. This substantially revised and updated second edition is ideal for researchers and graduate students interested in the philosophy of physics and the interpretation of quantum mechanics.
A comprehensive exposition of the transactional interpretation of quantum mechanics (TI), this book sheds new light on longstanding problems in quantum theory and provides insight into the compatibility of TI with relativity. It breaks new ground in interpreting quantum theory, presenting a compelling new picture of quantum reality. The book shows how TI can be used to solve the measurement problem of quantum mechanics and explain other puzzles, such as the origin of the 'Born Rule' for the probabilities of measurement results. It addresses and resolves various objections and challenges to TI, such as Maudlin's inconsistency challenge. It explicitly extends TI into the relativistic domain, providing new insight into the basic compatibility of TI with relativity and the physical meaning of 'virtual particles'. This book is ideal for researchers and graduate students interested in the philosophy of physics and the interpretation of quantum mechanics.
An extended Bloch representation of quantum mechanics was recently derived to offer a possible (hidden-measurements) solution to the measurement problem. In this article we use this representation to investigate the geometry of superposition and entangled states, explaining interference effects and entanglement correlations in terms of the different orientations a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), which we show to be particularly suitable for the description of multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description where sub-entities can remain in well-defined states, even when entangled. This means that the completed version of quantum mechanics provided by the extended Bloch representation, where density operators are also considered to be representative of genuine states (providing a complete description), not only offers a plausible solution to the measurement problem but also to the lesser-known entanglement problem. This is because we no longer need to give up the general physical principle saying that a composite entity exists and therefore is in a well-defined state, if and only if its components also exist and therefore are also in well-defined states.
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.