Modified general relativity and quantum theory in curved spacetime

With appropriate modifications, the multi-spin Klein-Gordon (KG) equation of quantum field theory can be adapted to curved space-time for spins 0, 1, 1/2. The associated particles in the microworld then move as a wave at all space-time coordinates. From the existence in a Lorentzian space-time of a line element field (X-beta, -X-beta), the spin-1 KG equation del mu del X-mu(beta) = k(2)X(beta) is derived from an action functional involving X-beta and its covariant derivative. The spin-0 KG equation and the KG equation of the outer product of a spin-1/2 Dirac spinor and its Hermitian conjugate are then constructed. Thus, X-beta acts as a fundamental quantum vector field. The symmetric part of the spin-1 KG equation, (Psi) over bar (alpha beta), is the Lie derivative of the metric. That links the multi-spin KG equation to Modified General Relativity (MGR) through its energy-momentum tensor of the gravitational field. From the invariance of the action functionals under the diffeomorphism group Diff(M), which is not restricted to the Lorentz group, (Psi) over bar (alpha beta) can instantaneously transmit information along X-beta. That establishes the concept of entanglement within a Lorentzian formalism. The respective local/nonlocal characteristics of MGR and quantum theory no longer present an insurmountable problem to unify the theories.

Automated summary

This article discusses how the multi-spin Klein-Gordon equation of quantum field theory can be adapted to curved space-time, focusing on spins 0, 1, and 1/2 particles. By establishing connections between spin-1 KG equation, spin-0 KG equation, Dirac spinor KG equation, and the energy-momentum tensor in Modified General Relativity, the article explores the unification of various theories. Additionally, the importance of instantaneous information transmission, entanglement concept in a Lorentzian formalism is highlighted.