MPEJ Volume 6, No.4, 14 pp.
Received June 17 2000, Revised Jul 17 2000, Accepted Aug 14 2000
K. Borchsenius
Degenerate space-time paths and the non-locality of
quantum mechanics in a Clifford substructure of space-time
ABSTRACT:
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.