On the Present State of the Philosophy of Quantum Mathematics

Abstract
It is suggested that the true physical significance of the Hilbert space structure in quantum mechanics remains (despite the undoubted significance of the elucidation given early by von Neumann, and further clarified by later discussions) less well understood than is usually supposed. Reasons are given for this view from considerations internal to the theory; a (remote) analogy is considered to the role, and presumed physical significance, of the notion of "ether" in nineteenth-century physics; the issues of measurement (or, more generally, application of the theory) are touched on, as well as the significance of Bell's results concerning locality, and the difficulties confronting the application of quantum mechanics to the whole cosmos.
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