Maximum force and minimum distance: physics in limit statements

Abstract

The newly discovered principle of maximum force makes it possible to summarize special relativity, quantum theory\se, and general relativity in one fundamental limit principle each. The three principles fully contain the three theories and are fully equivalent to their standard formulations. In particular, using a result by Jacobson based on the Raychaudhuri equation, it is shown that a maximum force implies the field equations of general relativity. The maximum force in nature is thus equivalent to the full theory of general relativity. Taken together, the three fundamental principles imply a bound for every physical observable, from acceleration to size. The new, precise limit values differ from the usual Planck values by numerical prefactors of order unity. They are given here for the first time. Among others, a maximum force and thus a minimum length imply that the non-continuity of space-time is an inevitable result of the unification of quantum theory and relativity.