Space-Time Mixing of Quantum Computing in an Entangled Atomic Chain and Time Crystals

Experimentally observed space-time crystals are modeled here as a 1-D 4-State Cellular Automata (CA) under a specific set of “cyclic” state-transition rules, three of which are analyzed here. The generations of these specific CA rule sets have been previously shown to model the properties of the recently described space-time crystals due to the underlying mathematical model present in these rules. The rules are shown here to display three space-time symmetry rotations in the time crystals generated. Hence, the rotational symmetry property of the computational states of these CA generations is of physical significance to the rules governing space and time in a space-time crystal. The time-crystal generations are mapped onto the surface of a space-time sphere, where the non-Euclidean geometry allows for the interchangeability between space and time in producing space-time crystals.