Locally Causal Quantum Mechanics in Space-Time

I introduce a reformulation of quantum mechanics as a theory of physical fields in space-time which obey the constraints of special relativity. Instead of being described by a single de-localized wavefunction in configuration space, the fundamental subsystems within a composite system are each described by a continuum of local relative wavefunctions in space. Each relative wavefunction is defined on a particular world-line through space-time, using only the past states and coupling unitaries of the systems within the past-interaction-cone, and thus obeying explicit local causality. As a result, the narrative and causal structures of this reformulation are Lorentz covariant - unlike single-wavefunction descriptions. This model explains violations of Bell inequalities while obeying local causality, but entanglement correlations are not physically obeyed until Alice's and Bob's measurement results are compared locally in space-time. Explaining their experiences in this experiment then necessitates the existence of multiple Alices and multiple Bobs who got different measurement outcomes, and thus we arrive at a locally-branching many-worlds interpretation of quantum mechanics in space-time which obeys local causality - unlike global-branching many-worlds models.