A unique but flexible space–time could challenge multiverse theories
Highlights: The growing law of a billiard multiverse is independent of the discretization scale E. The time for any final state to be accessible from any initial one is around 3E shocks. The paths of billiard balls can change without changing initial or final states. Space-time flexibility can be achieved through paths commutations and entanglement. -- Abstract: In a previous paper (Guillemant et al., 2018), we have shown using a 2D billiard toy model that the propagation of uncertainties resulting from space–time discretization leads to a classical multiverse. In this one we estimate the growing law of the number of its branches, thanks to an original shock indexation method that permits a very fast comparison of trajectories. For different involved parameters we use random sets of infinitesimally perturbed initial conditions. From each set, we compute a collection up to hundred millions of different billiard histories. Our main result is the calculation of a Brownian saturation time when the number of branches begins to exceed the total number of billiard states. We discuss the possibility suggested by this result to change locally the paths of objects without changing their past and future histories and then subverting their global system. We conclude that a unique but flexible space–time could compete with the current many-worlds interpretation claiming that each branch is a different universe.