8 found
  1.  48
    A priori probability and localized observers.Matthew J. Donald - 1992 - Foundations of Physics 22 (9):1111-1172.
    A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous “wave-packet collapse” across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with (...)
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  2.  40
    A mathematical characterization of the physical structure of observers.Matthew J. Donald - 1995 - Foundations of Physics 25 (4):529-571.
    It is proposed that the physical structure of an observer in quantum mechanics is constituted by a pattern of elementary localized switching events. A key preliminary step in giving mathematical expression to this proposal is the introduction of an equivalence relation on sequences of spacetime sets which relates a sequence to any other sequence to which it can be deformed without change of causal arrangement. This allows an individual observer to be associated with a finite structure. The identification of suitable (...)
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  3.  51
    On many-minds interpretations of quantum theory.Matthew J. Donald - unknown
    This paper is a response to some recent discussions of many-minds interpretations in the philosophical literature. After an introduction to the many-minds idea, the complexity of quantum states for macroscopic objects is stressed. Then it is proposed that a characterization of the physical structure of observers is a proper goal for physical theory. It is argued that an observer cannot be defined merely by the instantaneous structure of a brain, but that the history of the brain's functioning must also be (...)
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  4. Neural unpredictability, the interpretation of quantum theory, and the mind-body problem.Matthew J. Donald - 2002 - Quant-Ph/0208033.
    It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of psycho-physical parallelism and about how we could define probabilities for our individual future observations given our individual present and previous observations. The complexity of the problems is underlined by arguments that unpredictability in ordinary everyday neural functioning, ultimately stemming from small-scale uncertainties (...)
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  5. A Proof of Everett's Correlation Conjecture.Matthew J. Donald - unknown
    In his long 1957 paper, “The Theory of the Universal Wave Function”, Hugh Everett III made some significant preliminary steps towards the application and generalization of Shannon’s information theory to quantum mechanics. In the course of doing so, he conjectured that, for a given wavefunction on a compound space, the Schmidt decomposition maximises the correlation between subsystem bases. This is proved here.
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    Constitutions of Matter.Matthew J. Donald - 1998 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 29 (2):277-280.
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  7. Probabilities for Observing Mixed Quantum States given Limited Prior Information.Matthew J. Donald - unknown
    The original development of the formalism of quantum mechanics involved the study of isolated quantum systems in pure states. Such systems fail to capture important aspects of the warm, wet, and noisy physical world which can better be modelled by quantum statistical mechanics and local quantum field theory using mixed states of continuous systems. In this context, we need to be able to compute quantum probabilities given only partial information. Specifically, suppose that B is a set of operators. This set (...)
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  8. Review Articles-Decoherence and the Appearance of a Classical World in Quantum Theory.Matthew J. Donald - 1999 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 30 (3):437-442.