Constraints on the universe as a numerical simulation

Abstract

Observable consequences of the hypothesis that the observed universe is a numerical simulation performed on a cubic space-time lattice or grid are explored. The simulation scenario is first motivated by extrapolating current trends in computational resource requirements for lattice QCD into the future. Using the historical development of lattice gauge theory technology as a guide, we assume that our universe is an early numerical simulation with unimproved Wilson fermion discretization and investigate potentially-observable consequences. Among the observables that are considered are the muon g − 2 and the current differences between determinations of α, but the most stringent bound on the inverse lattice spacing of the universe, b −1 > ∼ 10 11 GeV, is derived from the high-energy cut off of the cosmic ray spectrum. The numerical simulation scenario could reveal itself in the distributions of the highest energy cosmic rays exhibiting a degree of rotational symmetry breaking that reflects the structure of the underlying lattice. * beane@hiskp.uni-bonn.de. On leave from the University of New Hampshire. †

Multichannel0→2and1→2transition amplitudes for arbitrary spin particles in a finite volume

“…These are determined by first expressing the operators in terms of the elementary fields appearing in Eq. (38). For scalar particles, for example, the decompositions generically take the form…”

Proton–proton fusion in lattice effective field theory

“…The energy shifts in a periodic box in the presence of a short-ranged interaction is used to calculate the elastic phase shifts. Perturbative Coulomb contributions to two-particle scattering in a finite volume have been considered recently [39] but a general method for calculating Coulomb interactions non-perturbatively at low energy using Lüscher's method doesn't exist. Here we calculate the non-relativistic phase shift in the presence of the long range Coulomb force using a hard spherical wall boundary condition.…”

The Fine-Tuning Argument and the Simulation Hypothesis

“…In fact, there may be such a cut off in the energy of cosmic ray particles, which is known as the Greisen-Zatsepin-Kuzmin or GZK cut off. 20 For these reasons, the simulation hypothesis not only undercuts the alleged evidential connection between 'fine-tuner' (or 'designer') and 'supernatural designer of immense power and knowledge' but it also outperforms the design hypothesis when the two are evaluated in terms of theoretical virtues, such as unification, coherence, simplicity, and testability. For present purposes, I will not argue any further for the superiority of the simulation hypothesis over the design hypothesis but rather rest content with showing (as I think I have) that the simulation hypothesis, which provides an alternative explanation for fine-tuning, undercuts the alleged evidential connection between 'designer' and 'supernatural designer of immense power and knowledge' in much the same way that the multiverse hypothesis undercuts the alleged evidential connection between 'fine-tuning' and 'fine-tuner' (or 'designer').…”