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It is well-known that in the Newman-Penrose formalism the Riemann tensor canbe expressed as a set of eighteen complex first-order equations, in terms ofthe twelve spin coefficients, known as Ricci identities. The Ricci tensorherein is determined via the Einstein equations. It is also known that theDirac equation in a curved spacetime can be written in the Newman-Penroseformalism as a set of four first-order coupled equations for the spinorcomponents of the wave-function. In the present article we suggest that itmight be possible to think of the Dirac equations in the N-P formalism as aspecial case of the Ricci identities, after an appropriate identification ofthe four Dirac spinor components with four of the spin coefficients, providedtorsion is included in the connection, and after a suitable generalization ofthe energy-momentum tensor. We briefly comment on similarities with theEinstein-Cartan-Sciama-Kibble theory. The motivation for this study is to takesome very preliminary steps towards developing a rigorous description of thehypothesis that dynamical collapse of the wave-function during a quantummeasurement is caused by gravity.

general relativity and gravitation

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?