By Pieter E. Vermaas
Modal interpretations supply a normal framework during which quantum mechanics could be regarded as a thought that describes truth by way of actual structures owning yes homes. Modal interpretations are really new makes an attempt to provide quantum mechanics as a idea which, like different actual theories, describes an observer-independent fact. during this booklet, Pieter Vermaas information the result of this paintings. He presents either an available survey and a scientific reference paintings approximately the right way to comprehend quantum mechanics utilizing a modal interpretation. The ebook may be of significant worth to undergraduates, graduate scholars and researchers in philosophy of technology and physics departments with an curiosity in studying approximately modal interpretations of quantum mechanics.
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Additional info for A Philosopher's Understanding of Quantum Mechanics: Possibilities and Impossibilities of a Modal Interpretation
I do not discuss the modal interpretation by Healey (1989). This interpretation is in many respects similar to the bi modal interpretation of Kochen and Dieks. 27) The reason why I limit myself to the bi, spectral and atomic modal interpretations, is that they can be seen as being part of one and the same programme towards an interpretation of quantum mechanics. Historically this programme started with the bi modal interpretation. The spectral modal interpretation followed in order to answer questions left open by the bi modal interpretation.
The mixed state W^ix denned in the main text is an example of a proper mixture. And the device state W^ is, according to the proof given in this footnote, an example of an improper mixture. 26 Modal interpretations resent ignorance about the actual properties and about the actual state of systems. Modal interpretations can thus be defined by means of this characteristic of rejecting ignorance with regard to states. Consider any theory and let TS denote the Theoretical State which this theory assigns to a system (for quantum mechanics TS is thus a density operator) and let SoA denote a description of a State of Affairs for that system (in quantum mechanics SoA is a set of definite properties of the system or a set of values assigned to magnitudes of that system).
However, if one tries to do so, one can be confronted with the measurement problem for interpretations. In order^to formulate this measurement problem more generally, consider the state W^ of a measurement device after a measurement of A*. Let M^ = ]£ • mj ^ be the pointer reading magnitude. Then the standard formulation predicts that the measurement yields with probability Tr^iW^Rj) the outcome corresponding to the eigenvalue aj of A*. This prediction implies that the measurement device possesses the property JR?