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A possible correspondence between Ricci identities and Dirac equations in the Newman-Penrose formalism: towards an understanding of gravity induced collapse of the wave-function?
It is well-known that in the Newman-Penrose formalism the Riemann tensor can
be expressed as a set of eighteen complex first-order equations, in terms of
the twelve spin coefficients, known as Ricci identities. The Ricci tensor
herein is determined via the Einstein equations. It is also known that the
Dirac equation in a curved spacetime can be written in the Newman-Penrose
formalism as a set of four first-order coupled equations for the spinor
components of the wave-function. In the present article we suggest that it
might be possible to think of the Dirac equations in the N-P formalism as a
special case of the Ricci identities, after an appropriate identification of
the four Dirac spinor components with four of the spin coefficients, provided
torsion is included in the connection, and after a suitable generalization of
the energy-momentum tensor. We briefly comment on similarities with the
Einstein-Cartan-Sciama-Kibble theory. The motivation for this study is to take
some very preliminary steps towards developing a rigorous description of the
hypothesis that dynamical collapse of the wave-function during a quantum
measurement is caused by gravity.Comment: v2. 30 pages. Additional discussion in Sections IV and V. References
added. To appear in Gen. Rel. Gra
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