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Degenerate space-time paths and the non-locality of quantum mechanics in a Clifford substructure of space-time. (English) Zbl 1065.81557
Summary: The quantized canonical space-time coordinates of a relativistic point particle are expressed in terms of the elements of a complex Clifford algebra which combines the complex properties of $$SL(2.C)$$ and quantum mechanics. When the quantum measurement principle is adapted to the generating space of the Clifford algebra we find that the transition probabilities for twofold degenerate paths in space-time equal the transition amplitudes for the underlying paths in Clifford space. This property is used to show that the apparent non-locality of quantum mechanics in a double slit experiment and in an EPR type of measurement is resolved when analyzed in terms of the full paths in the underlying Clifford space. We comment on the relationship of this model to the time symmetric formulation of quantum mechanics and to the Wheeler-Feynman model.

##### MSC:
 81R25 Spinor and twistor methods applied to problems in quantum theory 15A66 Clifford algebras, spinors 83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
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