It is shown that certain structures in classical General Relativity can give
rise to non-classical logic, normally associated with Quantum Mechanics. 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 non-redundant boundary conditions. Measurements of
such an object would fail to satisfy the distributive law of classical physics.
This model reconciles General Relativity and Quantum Mechanics without the need
for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it
is not universal; classical particles and waves could exist and there is no
graviton.Comment: 10 pages Latex2e, talk given at the 5th UK Conference on Conceptual
and Philosophical Problems in Physics held in Oxford, 10th-14th September
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