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The Quantum Mechanical Frame of Reference Part 1: QBism and Psi-Ontology

Soltau, Andrew

Published Dec 31, 2015• 0 citations
OpenAlex

Abstract

QBism explicitly takes the subjective view: probabilities of events are defined solely by past experiences, i.e. the record of observations. As shown by the authors (Fuchs et al, 2013), this: “... removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades”. It is criticised for its lack of ontology and anthropocentric nature. However, if Everett's (1957) formulation is taken at face value, exactly the features of QBism are the result, and the ontology is inherent. The anthropocentric nature of the solution is simply an indication that the quantum state is relative, as is central to Everett. Problems of measurement and locality do not arise. As described by Tegmark (1997), Everett defines the relationship between two fundamentally different views of the world, different types of frame of reference. The outside view is defined by the unitary wave function, the inside view by the record of observations. As Lockwood (1989) states, the preferred basis problem is fully resolved if the latter is taken as the basis. Taken literally, only that defined by the record of observations is determinate in the physical world of this inside view. The reality of QBism is the result. The same can be derived from first principles in the no-collapse universe. Taking the outside view to define all possible decoherent quasi-classical worlds, the physical world of the inside view is the superposition of all such worlds in which it is instantiated. In this quantum mechanical frame of reference only that observed is determinate. The quantum state as ontology is questioned because it defines only the linear dynamics and cannot account for collapse. No deeper reality is required, however: the inside view, and the collapse dynamics that operates in this type of frame of reference, are emergent properties of the system, and operate at a different level of logical type. The world operates as described by QBism, but is nonetheless defined by the quantum state.

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QBism explicitly takes the subjective view: probabilities of events are defined solely by past experiences, i.e. the record of observations. As shown by the authors (Fuchs et al, 2013), this: “... removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades”. It is criticised for its lack of ontology and anthropocentric nature. However, if Everett's (1957) formulation is taken at face value, exactly the features of QBism are the result, and the ontology is inherent. The anthropocentric nature of the solution is simply an indication that the quantum state is relative, as is central to Everett. Problems of measurement and locality do not arise. As described by Tegmark (1997), Everett defines the relationship between two fundamentally different views of the world, different types of frame of reference. The outside view is defined by the unitary wave function, the inside view by the record of observations. As Lockwood (1989) states, the preferred basis problem is fully resolved if the latter is taken as the basis. Taken literally, only that defined by the record of observations is determinate in the physical world of this inside view. The reality of QBism is the result. The same can be derived from first principles in the no-collapse universe. Taking the outside view to define all possible decoherent quasi-classical worlds, the physical world of the inside view is the superposition of all such worlds in which it is instantiated. In this quantum mechanical frame of reference only that observed is determinate. The quantum state as ontology is questioned because it defines only the linear dynamics and cannot account for collapse. No deeper reality is required, however: the inside view, and the collapse dynamics that operates in this type of frame of reference, are emergent properties of the system, and operate at a different level of logical type. The world operates as described by QBism, but is nonetheless defined by the quantum state.
QBism has long recognized quantum states, positive-operator-valued measure elements, Kraus operators, and even unitary operations to be of the same type: they express aspects of an agent's belief system concerning the consequences (for her) of actions she might take upon her external world. Such action-consequence pairs have conventionally been called ``quantum measurements.'' The calculus of quantum theory is then viewed as an empirically motivated addition to Bayesian decision theory when brought to this notion of measurement. This radical approach has allowed QBism to eliminate conceptual problems that plague other interpretations of quantum mechanics. However, one issue has remained elusive: If a QBist does not believe in the existence of an ontic (agent-independent) dynamical variable evolving over time, why would there be any constraints on her quantum-state assignment in the absence of performing a measurement? Why would she introduce unitary or open-system quantum dynamics at all? Here, we present a representation theorem based on van Fraassen's reflection principle to answer these questions. Simply put, an agent's assignment of quantum dynamics represents her belief that a measurement action she is contemplating would not change her current odds for future gambles. A corollary to this approach is that one can make sense of ``open-system dynamics'' without the need to introduce an ``environment with a measurement record,'' as is common in decoherence accounts of quantum measurement. QBism's understanding instead rests more fundamentally on an agent's beliefs about the system of interest (not system plus environment) and her judgments about measurements she might perform on that system. More broadly, this result establishes QBism's contention that measurement itself is the central concept of quantum theory and thus the framework upon which any future QBist ontology must hang.
We present a historical-epistemological analysis of the foundations of quantum mechanics, highlighting the relationships between quantum mechanics and scientific realism, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of the measurement process in the context of quantum mechanics is underlined as an essential element in providing a coherent description of reality, moving from micro to macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the related ontological problems, the question of the objectification of the wave function, and that of the definition of discernibility. We consider also an overview of the most important alternative proposals to the standard interpretation of quantum mechanics (Copenhagen interpretation), with particular reference to hidden variable theories and other alternatives to standard quantum mechanics philosophical approach, that are modifying the vision of reality, such as the Everett’s many-worlds theory, the QBism and unified holistic approaches, such as the Primordial Dynamic Space.
The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. No new physics is required. The complex formalism that seems deeply counterintuitive is class arithmetic. Superposition and interference: properties of classes of worlds. Measurement: set-selection of a subclass compatible with the observed outcome. The uncertainty principle: incompatible set-selections. Fourier transforms: switching set-selection. Operators: enactment of set-selection. Decoherence: loss of coherence between worlds. Normalisation is required because all worlds are equally real, thus the probability of an outcome is essentially the proportion of worlds that instantiate it. True probability arises through phase, which is the degree to which the rest of each world aligns internally with this outcome. This is the second-logical-type phenomenon of interference: the degree to which worlds cohere in the classical actions that give rise to the outcome.This transforms the familiar structures of the formalism from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world: this is the quantum realm. The classical world, quantum mechanics and relativistic physics are unified in logical types.
This work presents a historical-epistemological analysis of the foundations of quantum mechanics. From a philosophical point of view, the relationships between quantum mechanics and scientific realism are highlighted, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of measurement in the context of quantum mechanics is underlined, as an essential element in providing a coherent description of reality moving from the microcosm to the macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the ontological problem, the problem of the objectification of the wave function and the problem of the definition of discernibility. This is followed by an overview of the most important alternative proposals to the standard interpretation (Copenhagen interpretation), with particular reference to hidden variable theories, and other alternatives to standard quantum mechanics that profoundly modify the vision of reality, such as the Everett’s many-worlds theory, the QBism, the unified holistic approach.
QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth: They express aspects of an agent's belief system concerning the consequences (for her) of actions she might take upon her external world. Such action-consequence pairs have conventionally been called "quantum measurements." The calculus of quantum theory is then viewed as an empirically motivated addition to Bayesian decision theory when brought to this notion of measurement. This radical approach has allowed QBism to eliminate conceptual problems that plague other interpretations of quantum mechanics. However, one issue has remained elusive: If a QBist does not believe in the existence of an ontic (agent-independent) dynamical variable evolving over time, why would there be any constraints on her quantum-state assignment in the absence of performing a measurement? Why would she introduce unitary or open-system quantum dynamics at all? Here, we present a representation theorem based on van Fraassen's reflection principle to answer these questions. Simply put, an agent's assignment of quantum dynamics represents her belief that a measurement action she is contemplating would not change her current odds for future gambles. A corollary to this approach is that one can make sense of "open-system dynamics" without the need to introduce an "environment with a measurement record," as is common in decoherence accounts of quantum measurement. QBism's understanding instead rests more fundamentally on an agent's beliefs about the system of interest (not system plus environment) and her judgments about measurements she might perform on that system. More broadly, this result establishes QBism's contention that measurement itself is the central concept of quantum theory and thus the framework upon which any future QBist ontology must hang.