We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of nonlocality. (...) 1 Introduction 2 Albert and Loewer's interpretation 3 Probabilities in Lockwood's interpretation 4 Sets of minds and their correlations 5 Many minds and GHZ. (shrink)

As shown in The Quantum Mechanical Frame of Reference, Everett's formulation inherently defines idiosyncratic effective physical environments for each version of the functional identity of the observer, defined solely by observations, in the manner of Rovelli's Relational Quantum Mechanics. This accounts for determinate measurement records, and completes his resolution of the measurement problem. The remaining task is to make everyday sense of Everett's concept. He defines the functional identity as the record of sensory observations and machine configuration, which seems merely (...) an epiphenomenon of the body-mind of the observer. This functional identity is intensely familiar to each observer. It is simply the subjective reality, the known world, here the 'world hologram'. In Everett's formulation, the cut in the von Neumann chain is implicitly made at the level of conscious sensory awareness. Thus, not only is the effective physical environment defined solely by the record of observations, the self-identity synthesised from observations defines the sole determinacy of the body-mind of the observer. Everett's formulation is not addressing obscure issues of brain state, but the determinant of the effective physical reality of the observer, including the body-mind. Although highly counter-intuitive, it is nonetheless empirically coherent. On the 'inside view', as defined by Tegmark, Everett's relative state corresponds, directly and precisely, to human experience. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

Some relations between physics and finitary and infinitary mathematics are explored in the context of a many-minds interpretation of quantum theory. The analogy between mathematical ``existence'' and physical ``existence'' is considered from the point of view of philosophical idealism. Some of the ways in which infinitary mathematics arises in modern mathematical physics are discussed. Empirical science has led to the mathematics of quantum theory. This in turn can be taken to suggest a picture of reality involving possible minds and the (...) physical laws which determine their probabilities. In this picture, finitary and infinitary mathematics play separate roles. It is argued that mind, language, and finitary mathematics have similar prerequisites, in that each depends on the possibility of possibilities. The infinite, on the other hand, can be described but never experienced, and yet it seems that sets of possibilities and the physical laws which define their probabilities can be described most simply in terms of infinitary mathematics. (shrink)

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 (...) the volume together is Walker's insistence on the importance of looking beyond materialism. (shrink)

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 (...) in molecular motions, may overwhelm, by many orders of magnitude, many conventionally recognized sources of observed ``quantum'' uncertainty. Some possible ways of avoiding the problems are considered but found wanting. It is proposed that a complete understanding of the relationship between subjective experience and its physical correlates requires the introduction of mathematical definitions and indeed of new physical laws. (shrink)