" We present a minimal geometric extension of General Relativity (GR) that captures the branch structure of Everettian quantum mechanics while preserving local Lorentzian physics. A single time coordinate t is replaced by a direction–dependent clock t(θ, ϕ) defined on the celestial two–sphere attached to each event. The global time coordinate t selects the energy eigenstate, while the angular coordinates (θ, ϕ) select the lobe of that eigenstate (i.e., the corresponding Everettian relative state). At every (θ, ϕ) the induced metric retains the usual +−−− signature, so the construction does not create a six–dimensional (+ + + − −−) spacetime. Instead, spacetime becomes an S¹ bundle over S²—topologically an S³—making it functionally the Hopf fibration. Classical GR is recovered by freezing t(θ, ϕ) →′ t. "This version represents an early draft made available to establish the record ahead of later revisions and co-authorship.
Daniel Davis (Wed,) studied this question.