A discrete and finite approach to past physical reality

This paper is a synthesis of previously published material on the topic. We show that an adequate mathematical model for the physical (i.e., perceptible and therefore past) reality must be finite. A finite approach to past proper time is given. Proper time turns out to be proportional to the sum of the return probabilities of a Bernoulli random walk. 1. Introduction. Every physical measurement needs a finite, different-from-zero measurement time and provides information in the form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results would be possible, the choice of a measurement result could deliver an infinite quantity of information. But the results of physical measurements (of finite duration) never deliver an infinite quantity of information; they describe past, finite reality. Therefore, the set of all possible measurement results is a priori finite. In the physical reality, only a finite information quantity can be processed within a finite time interval. For mathematical models whose representation requires a processing of an infinite quantity of information, for example, irrational numbers, no (exact) equivalent exists in the physical reality. So, mathematical calculations, which have an equivalent in physical reality, can include only rational (finitely many elementary) combinations of rational numbers. Conclusions arise from this for the foundations of mathematical physics.