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With appropriate modifications, the multi-spin Klein-Gordon (KG) equation ofquantum field theory can be adapted to curved spacetime for spins 0,1,1/2. Theassociated particles in the microworld then move as a wave at all spacetimecoordinates. From the existence in a Lorentzian spacetime of a line elementfield $(X^{\beta},-X^{\beta}) $, the spin-1 KG equation$\nabla_{\mu}\nabla^{\mu}X^{\beta}=k^{2}X^{\beta} $ is derived from an actionfunctional involving $X^{\beta} $ and its covariant derivative. The spin-0 KGequation and the KG equation of the outer product of a spin-1/2 Dirac spinorand its Hermitian conjugate are then constructed. Thus, $ X^{\beta} $ acts as afundamental quantum vector field. The symmetric part of the spin-1 KG equation,$ \tilde{\varPsi}_{\alpha\beta}$, is the Lie derivative of the metric. Thatlinks the multi-spin Klein-Gordon equation to Modified General Relativity (MGR)through its energy-momentum tensor of the gravitational field. From theinvariance of the action functionals under the diffeomorphism group Diff(M),which is not restricted to the Lorentz group, $ \tilde{\varPsi}_{\alpha\beta}$can instantaneously transmit information along $ X^{\beta} $. That establishesthe concept of entanglement within a Lorentzian formalism. The respectivelocal/nonlocal characteristics of MGR and quantum theory no longer present aninsurmountable problem to unify the theories.

Modified General Relativity and quantum theory in curved spacetime