Graduate studies at Western
Studies in History and Philosophy of Science Part B 34 (3):381-393 (2003)
|Abstract||We consider probability theories in general. In the first part of the paper, various constraints are imposed and classical probability and quantum theory are recovered as special cases. Quantum theory follows from a set of five reasonable axioms. The key axiom which gives us quantum theory rather than classical probability theory is the continuity axiom, which demands that there exists a continuous reversible transformation between any pair of pure states. In the second part of this paper, we consider in detail how the measurement process works in both the classical and the quantum case. The key differences and similarities are elucidated. It is shown how measurement in the classical case can be given a simple ontological interpretation which is not open to us in the quantum case. On the other hand, it is shown that the measurement process can be treated mathematically in the same way in both theories even to the extent that the equations governing the state update after measurement are identical. The difference between the two cases is seen to be due not to something intrinsic to the measurement process itself but, rather, to the nature of the set of allowed states and, therefore, ultimately to the continuity axiom.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Arthur I. Fine (1968). Logic, Probability, and Quantum Theory. Philosophy of Science 35 (2):101-111.
I. I. I. Durand (1960). On the Theory of Measurement in Quantum Mechanical Systems. Philosophy of Science 27 (2):115-133.
James L. Park (1968). Quantum Theoretical Concepts of Measurement: Part I. Philosophy of Science 35 (3):205-231.
Peter J. Lewis (2010). Probability in Everettian Quantum Mechanics. Manuscrito 33:285--306.
David Atkinson & Jeanne Peijnenburg (1999). Probability as a Theory Dependent Concept. Synthese 118 (3):307-328.
Added to index2009-01-28
Total downloads4 ( #189,469 of 740,467 )
Recent downloads (6 months)0
How can I increase my downloads?