The pursuit of locality in quantum mechanics
Abstract
The rampant success of quantum theory is the result of applications of the 'new' quantum
mechanics of Schrödinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum
Electrodynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9),
and Quantum Chromodynamics (1973-); in fact, this success of `the' quantum theory has depended
on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully
concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously
accurate calculational tools there has been no sensible explanation of all that is going on. It is even
argued that such an understanding is nothing to do with physics. A long-standing and famous
illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935).
Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic
objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency.
This project encompasses a detailed, critical survey of the tangled history of Position
within quantum theories. The first step is to show that, contrary to appearances, canonical quantum
mechanics has only a vague notion of locality. After analysing a number of previous attempts at a
`relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work
of Wan and students, which is shown to be no real improvement on the usual `nonrelativistic' theory.
The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface
in space-time. There remain considerable difficulties in the way of producing a consistent scheme here.
To keep things nicely stirred up, the author then proposes his own approach - an adaptation
of Feynman's QED propagators.
This new approach is distinguished from Feynman's since the propagator or Green's function
is not obtained by Feynman's rule. The type of equation solved is also different: instead of an
initial-value problem, a solution that obeys a time-symmetric causality criterion is found for an
inhomogeneous partial differential equation with homogeneous boundary conditions.
To make the consideration of locality more precise, some results of Fourier transform theory are
presented in a form that is directly applicable.
Somewhat away from the main thrust of the thesis, there is also an attempt to explain the
manner in which quantum effects disappear as the number of particles increases in such things as
experimental realisations of the EPR and de Broglie thought experiments.
Type
Thesis, PhD Doctor of Philosophy
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