Tags:ciclicity, Einstein field equation, quantum, Schrödinger equation and universe
Abstract:
The essence of two fundamental physical theories, quantum mechanics and general relativity is concentrated in their basic equations: The Schrödinger equation (SE) and the Einstein field equation (EFE). The mutual consistency of both theories is one of the biggest open problems in physics and its philosophy. The mathematical equivalence of SE and EFE is provable under the axiom of choice. SE and EFE can be considered correspondingly as the nonstandard and standard interpretations (in the sense of Robinson’s nonstandard analysis) of one and the same mathematical structure. The physical sense of their equivalence consists in the equivalent transformation between a smooth continuum of inertial reference frames (as what space-time is considered in general relativity by pseudo-Riemannian space) and complementary pairs of qubits, the one member of which corresponds to the velocity (or dynamically, to the momentum) of a single reference frame, and the other to its position. The quantity of time is reduced to the well-ordering of those pairs for the axiom of choice. Thus, the axiom of choice is what reconciles the space-like time in general relativity to the arrow-like time in quantum mechanics and allows of their equating.
The thesis is: the standard (EFE) and nonstandard (SE) interpretations can be embodied in an ontology equating the whole of the universe to the whole of a quantum. Then, EFE represents reality inside that whole, and SE outside it. The universe is situated within in a quantum.
The Universe in a Quantum: a Possible Interpretation of the Equivalence of the Schrödinger Equation and the Einstein Field Equation