Taylor, Peter
The Relation Between Classical and Quantum Mechanics.
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Abstract
This thesis examines the relation between classical and quantum mechanics from philosophical, mathematical and physical standpoints.
It first presents arguments in support of “conjectural realism” in scientific theories distinguished by explicit contextual structure and empirical testability; and it analyses intertheoretic reduction in terms of weakly equivalent theories over a domain of applicability.
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic prob ability structure. This theory is developed to the stage where theorems from quantum logic enable expression of the state geometry in Hilbert space. Quan tum and classical mechanics are then elaborated and applied to subsystems and the measurement process. Consideration is also given to spacetime geometry and the constraints this places on the dynamics.
Physics and Mathematics, it is argued, are growing apart; the inadequate treatment of approximations in general and localisation in quantum mechanics in particular are seen as contributing factors. In the description of systems, the link between localisation and lack of knowledge shows that quantum mechanics should reflect the domain of applicability. Restricting the class of states provides a means of achieving this goal. Localisation is then shown to have a mathematical expression in terms of compactness, which in turn is applied to yield a topological theory of bound and scattering states.
Finally, the thesis questions the validity of “classical limits” and “quantisations” in intertheoretic reduction, and demonstrates that a widely accepted classical limit does not constitute a proof of reduction. It proposes a procedure for determining whether classical and quantum mechanics are weakly equivalent over a domain of applicability, and concludes that, in this restricted sense, classical mechanics reduces to quantum mechanics.
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Additional Information: 
This monograph is a dissertation for the degree of Doctor of Philosophy, University of Oxford, 1984. 
Keywords: 
Quantum mechanics, classical mechanics, theory reduction, classical limit, quantum logic, lattice theory, quantum axioms, approximation methods, mathematical physics 
Subjects: 
Specific Sciences > Physics > Classical Physics General Issues > Determinism/Indeterminism General Issues > Models and Idealization Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics General Issues > Realism/Antirealism General Issues > Reductionism/Holism General Issues > Structure of Theories 
Depositing User: 
simon saunders

Date Deposited: 
19 May 2018 19:15 
Last Modified: 
19 May 2018 19:15 
Item ID: 
14693 
Subjects: 
Specific Sciences > Physics > Classical Physics General Issues > Determinism/Indeterminism General Issues > Models and Idealization Specific Sciences > Probability/Statistics Specific Sciences > Physics > Quantum Mechanics General Issues > Realism/Antirealism General Issues > Reductionism/Holism General Issues > Structure of Theories 
URI: 
https://philsciarchivedev.library.pitt.edu/id/eprint/14693 
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