Past, Present and Future regions of space-time
GR postulates a "fabric" of space-time, comprising 3+1 dimensions. Particles occupy "world-lines" threading through the fabric, in time-like directions. No distinction is made, between past, present, and future. Indeed, Einstein labeled such distinction illusory. A time-like coordinate can parameterize a world-line, but its entire length is fixed. World-lines possess no Quantum pluripotentiality. Classical particles pass through time on a single railroad track, of deterministic fate.
QM demands particles be imbued with pluripotentiality, prior to wave-function "collapse" into a Classically-defined state. Thus, distinction is made, between previously determined past, "collapsing" present, and undetermined future.
Thus, GR is compatible with QM for past regions of the space-time fabric, wherein "events" (xyzt) label wave-function collapses, into Classically-defined states. How to accommodate Quantum pluripotentiality, for future regions the space-time fabric?
Mass-energy warps space-time. If particles can exist, in an undetermined superposition of "here" and "there", then space-time may exist in an undetermined superposition of corresponding curvature. When particles' wave-functions collapse to either "here" or "there", then the fabric of space-time may co-collapse into the curvature caused by the definite presence of mass-energy in a specific state.
Both tensors in the Einstein equation could be extended into QM sums of probability amplitudes multiplying matrices representing the potential curvatures and mass-energies, of particles in their suitably defined basis states.
At any space-like location (xyz), "now" would be that time-like parameter (t) when the entangled wave-functions of particles and the fabric of space-time co-collapse, represented by the probabilistic selection of a single tensor term, on each side of the Einstein equation.
Past portions of the fabric of space-time could continue to be described by single curvature and mass-energy tensors. Future regions of space-time would require sums of amplitude-weighted terms, resembling the Multiverse view of QM. Present comprises presumably space-like slices of space-time, harboring all co-occurring collapse events.
The fully Relativistic Klein-Gordon equation generalizes to include the Minkowski metric for flat space-time, (d/dx) M (d/dx) ¥ = m ¥. Thus, the KGE can be generalized for curved space-time by substituting the GR metric, (d/dx) G (d/dx) ¥ = m ¥. Quantum evolution of mass-energy particles into superposition states would cause both tensors of the Einstein equation to bifurcate into corresponding superposition states. And collapse of particle wave-functions into basis states would cause both tensors of the Einstein equation to telescope correspondingly.
