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A Gravitational Theory of Quantum Mechanics

Thesis submitted by Mark J Hadley in December 1996.

Passed 17 February 1997.

University of Warwick

Thesis Abstract

An explanation for quantum mechanics is given in terms of a classical theory (general relativity) for the first time. Specifically, it is shown that certain structures in classical general relativity can give rise to the non-classical logic normally associated with quantum mechanics.

An artificial classical model of quantum logic is constructed to show how the Hilbert space structure of quantum mechanics is a natural way to describe a measurement-dependent stochastic process.

A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution; the measurement apparatus itself can impose further non-redundant boundary conditions. When measurements of an object provide additional non-redundant boundary conditions, the associated propositions would fail to satisfy the distributive law of classical physics.

Using the 4-geon model, an orthomodular lattice of propositions, characteristic of quantum mechanics, is formally constructed within the framework of classical general relativity.

The model described provides a classical gravitational basis for quantum mechanics, obviating the need for quantum gravity. The equations of quantum mechanics are unmodified, but quantum behaviour is not universal; classical particles and waves could exist and there is no graviton.

 

The text of my thesis is available free of charge as postcript or pdf.