Analogs of wave function reduction, quantum entanglement and EPR experiment in classical physics of spacetimes with time machines

Abstract: It is theoretically revealed that, in classical physics of spacetimes with wormholes, there are analogs of wave function reduction events, quantum entanglement and Einstein-Podolsky-Rosen (EPR) experiment. Within the suggested approach, wormholes are specified by a typical microscopic radius of their mouths, and this causes the size effect in operation of wormhole-based time machines (closed timelike curves; CTCs). For geometric reasons, classical solid balls in a spacetime with a wormhole are divided into the two categories: small and large balls whose traverse through wormholes is permitted and forbidden, respectively. Evolutions of small balls on CTCs can be self-inconsistent (or, in other terms, inconsistent with conventional causality), in which case there is an uncertainty in their behaviors. In contrast, evolutions of large solid balls are always unambiguous. In the situation where small balls can be absorbed by large balls, uncertain behaviors of small balls transform into unambiguous evolutions of large balls in the logical way analogous to that of a quantum measurement - wave function reduction - event. Also, within the suggested approach operating with classical balls in spacetimes with wormholes, analogs of quantum entanglement and EPR experiment are defined and theoretically described.