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Matthew Donald [18]Matthew J. Donald [6]
  1. Matthew Donald, A Brief Summary.
    Quantum theory is highly successful in explaining properties of classes of systems: e.g. chemistry --- molecular binding energies optics --- frequency-dependent susceptibilities superconductivity --- energy gaps nuclear magnetic resonance --- chemical shifts particle physics --- scattering cross-sections cosmology --- helium abundance but many questions arise: What does quantum theory tell us about the nature of reality? Is quantum theory universally valid? Can quantum theory describe individual events? Can quantum theory be applied consistently at the macroscopic level? Is an algorithmic treatment (...)
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  2. Matthew Donald, A Debate with Henry Stapp.
    After my review of his work appeared on quant-ph, Henry Stapp posted a reply on his web site . I reproduced that reply, quoting the points to which he had replied and giving my subsequent responses to him. Following correspondence, and with some editing from us both, this has now developed into the multi-stage debate which is presented here. Some discussion of my 1999 paper is included.
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  3. Matthew Donald, A Review of The Physics of Consciousness by Evan Harris Walker. [REVIEW]
    At least three books struggle to emerge from this volume. One book, at the level of popular science, leads us through the development of physics, from Newton's laws to Bell's inequalities, in order to argue for the relevance of consciousness to the understanding of quantum theory. This is followed by a sketch of an interpretation of quantum mechanics. Interwoven with both is a memoir of Walker's teenage girlfriend, who died of Hodgkin's disease nearly fifty years ago. The theme which holds (...)
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  4. Matthew Donald, Book Notes. [REVIEW]
    A clear, careful, thoughtful, critical survey introducing a wide range of ideas about many worlds and related interpretations. The book is particularly suited to those with some knowledge of quantum mechanics who prefer words to equations. At first sight, much of Barrett's concern is with theories which are clearly implausible, such as the “bare theory” or “Bell's Everett (?) theory”, but Barrett uses these theories skilfully as simple examples elucidating issues of wider significance. The book includes a detailed reading of (...)
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  5. Matthew Donald, Book Review. [REVIEW]
    In “Quantum Evolution”, Johnjoe McFadden makes far-reaching claims for the importance of quantum physics in the solution of problems in biological science. In this review, I shall discuss the relevance of unitary wavefunction dynamics to biological systems, analyse the inverse quantum Zeno effect, and argue that McFadden’s use of quantum theory is deeply flawed.
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  6. Matthew Donald, Continuity and Discontinuity of Definite Properties in the Modal Interpretation.
    Technical results about the time dependence of eigenvectors of reduced density operators are considered, and the relevance of these results is discussed for modal interpretations of quantum mechanics which take the corresponding eigenprojections to represent definite properties. Continuous eigenvectors can be found if degeneracies are avoided. We show that, in finite dimensions, the space of degenerate operators has co-dimension 3 in the space of all reduced operators, suggesting that continuous eigenvectors almost surely exist. In any dimension, even when degeneracies are (...)
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  7. Matthew Donald, E-Mail: Mjd1014@Cam.Ac.Uk.
    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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  8. Matthew Donald, Frequently Asked Questions.
    How come quantum theory has anything to do with mind? Is your theory refutable? What is the point of all the technical detail? Do you suggest that the operation of the brain involves large scale quantum coherence? Isn't large scale quantum coherence necessary to solve the problem of the unity of consciousness? How does a many-minds interpretation survive Occam's razor? What, briefly, is your current philosophical position? What is your understanding of the relationship between mind and brain for split-brain patients? (...)
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  9. Matthew Donald, On the Work of Henry P. Stapp.
    For many years, Henry Stapp and I have been working separately and independently on mind-centered interpretations of quantum theory. In this review, I discuss his work and contrast it with my own. There is much that we agree on, both in the broad problems we have addressed and in some of the specific details of our analyses of neural physics, but ultimately we disagree fundamentally in our views on mind, matter, and quantum mechanics. In particular, I discuss our contrasting opinions (...)
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  10. Matthew Donald, Progress in a Many-Minds Interpretation of Quantum Theory.
    In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field theory. In this paper, which could also serve as an introduction to the earlier papers, three issues are discussed. First, a significant, but fairly straightforward, revision in some of the technical details is proposed. This is used as an opportunity to introduce the formalism. Then (...)
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  11. Matthew Donald, Quantum Theory and the Brain.
    A human brain operates as a pattern of switching. An abstract definition of a quantum mechanical switch is given which allows for the continual random fluctuations in the warm wet environment of the brain. Among several switch-like entities in the brain, we choose to focus on the sodium channel proteins. After explaining what these are, we analyse the ways in which our definition of a quantum switch can be satisfied by portions of such proteins. We calculate the perturbing effects of (...)
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  12. Matthew Donald, Readings From Quant-Ph.
    Notes on some papers available from the physics e-print archive which are relevant, or significant, or recommended in the broad context of the many-minds interpretation of quantum theory presented on my home page: http://www.bss.phy.cam.ac.uk/~mjd1014..
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  13. Matthew Donald, Realism, the Interpretation of Quantum Theory, and Idealism.
    Confused ideas about the weirdness of quantum mechanics have sometimes been blamed for the spread of anti-realist positions in philosophy. In this seminar, I shall re-examine the relation between realism and quantum theory. My goal is to argue that one can remain a realist in a reasonably familiar sense, while adopting a theory which amounts to a form of idealism. After sketching the abstract mathematical structure of quantum theory, I will introduce realism and consider some of its problems and some (...)
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  14. Matthew J. Donald, A Proof of Everett's Correlation Conjecture.
    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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  15. Matthew J. Donald, Probabilities for Observing Mixed Quantum States Given Limited Prior Information.
    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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  16. Matthew Donald (2002). Neural Unpredictability, the Interpretation of Quantum Theory, and the Mind-Body Problem. 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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  17. Matthew J. Donald (1999). Review Articles-Decoherence and the Appearance of a Classical World in Quantum Theory. Studies in History and Philosophy of Science-Part B 30 (3):437-442.
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  18. Matthew J. Donald (1998). Constitutions of Matter. Studies in History and Philosophy of Science-Part B 29 (2):277-280.
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  19. Matthew J. Donald, On Many-Minds Interpretations of Quantum Theory.
    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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  20. Matthew Donald (1995). A Mathematical Characterization of the Physical Structure of Observers. 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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  21. Matthew Donald (1995). The Neurobiology of Human Consciousness: An Evolutionary Approach. Neuropsychologia 33:1087-1102.
  22. Matthew Donald (1992). A Priori Probability and Localized Observers. 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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  23. Matthew Donald, Instability, Isolation, and the Tridecompositional Uniqueness Theorem.
    The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a wavefunction in a triple tensor product Hilbert space has at most one decomposition into a sum of product wavefunctions with each set of component wavefunctions linearly independent. I demonstrate that, in many circumstances, the unique component wavefunctions and the coefficients in the expansion are both hopelessly unstable, both under small changes in global wavefunction and under small changes in global tensor product structure. In my opinion, this means that (...)
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