Afriat, Alexander
(1999)
Quantum waves in configuration space.
PhD thesis, London School of Economics and Political Science.
Abstract
The thesis deals with issues in the foundations of quantum mechanics, having to do with configuration space, the physical reality of quantum waves, additive conservation and EPR experiments. After a historical sketch of optical theories, concentrating on the dual nature of light, the passage from Hamilton's optico-mechanical analogy to wave mechanics is looked at. The wave-particle duality of de Broglie's theorie de la double solution is favoured after comparison with some of Schrodinger's views. Three experiments are considered which support that realist duality by indicating corpuscular and undulatory properties. If wave and particle coexist and the wave guides the particle along its trajectory, the wave must have a physical reality. The issue is whether such a wave can propagate in a fictitious configuration space. Features of quantum-mechanical interference are represented on the Riemann sphere. The treatment is generalized to infinite dimensions and then to tensor product spaces. 'Entanglement' is defined; certain states of composite systems cannot be broken up in such a way that every subsystem has a (pure) state. Entanglement is shown to be always empirically visible in principle; for every entangled state there exists a 'sensitive' observable which can tell apart from any mixture of factorizable states. Observables represented by functions of tensor products of operators cannot, however, tell the difference. Additive conservation is considered separately from interference, and is related to Schmidt's theorem and Bertlmann's socks in cases involving two subsystems. The treatment is then generalized to N subsystems. Interference and additive conservation are combined in two examples; the violation of Bell's inequality, and the theorem of Wigner, Araki and Yanase. Schrodinger's cat is made to 'oscillate.' Interpretations of quantum waves in configuration space are assessed and Furry's hypothesis discarded. The distinction is drawn between weak Bell inequalities deduced from local realism alone, and strong inequalities which involve physically unreasonable additional assumptions. It is shown that, as long as inefficient detectors are employed, photons can only be used to violate strong inequalities. Kaons are almost always detected and can be used to discriminate between quantum mechanics and local realism, and determine whether quantum waves really propagate in configuration space.
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