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https://hdl.handle.net/2142/71249
Description
Title
Measurement and Quasi-States in Quantum-Mechanics
Author(s)
Harper, C. Douglas
Issue Date
1987
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Physics, General
Abstract
Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems: interacting quantum mechanical systems do not possess states, so their states cannot collapse. Only the externally non-interacting composite system formed from all the interacting systems possesses a state, yet quantum theory is based on assigning state to interacting systems. Before any progress can be made in the quantum logical problem of measurement, this seeming paradox must be resolved, for a measurement is (at least) an interaction of physical systems.
In this dissertation, it is shown that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it.
A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system gives rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state.
The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value.
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