A Gravitational Explanation for Quantum Mechanics

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 199

The orientability of spacetime

Contrary to established beliefs, spacetime may not be time-orientable. By considering an experimental test of time-orientability it is shown that a failure of time-orientability of a spacetime region would be indistinguishable from a particle-antiparticle annihilation event

The Logic of Quantum Mechanics Derived from Classical General Relativity

For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves - a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparation and measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.Comment: 16 pages Late

Charge and the topology of spacetime

A new class of electrically charged wormholes is described in which the outer 2-sphere is not spanned by a compact, co-orientable hypersurface, These wormholes can therefore display net electric charge from the source-free Maxwell equations. This extends the work of Sorkin on non-space-orientable manifolds, to spacetimes which do not admit a time orientation. The work is motivated by the suggestion that quantum theory can be explained by modelling elementary particles as regions of spacetime with non-trivial causal structure. The simplest example of an electrically charged spacetime carries a spherical symmetry

Electrodynamics and time orientability

On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell's equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path. The boundary of a time reversing region can therefore have a net electric flux and appear exactly as a region containing an electric charge. The treatment is purely classical, but motivated by links between acausal structures and quantum theory