A Non-Linear Model for Time

Abstract

Some recent astronomical observations [4], and a number of experiments in particle physics, seem to cast doubt on the validity of the standard linear model for time. These results raise two (at least) questions:

• (1) If time is not a linear continuum (i.e., if the standard model is incorrect), then why does this model work so well in so many areas of science?

• (2) Whatever the “true nature” of time is, are there any advantages, to science, in replacing the standard model with a more complicated one? The purpose of this paper is to present a non-linear, mathematical model for time that enables us to answer question (1), and to partially answer question (2). Our discussion of question (2) is incomplete, but our results are intriguing. They also show promise of helping us understand some of the observations mentioned above. A rather natural extension of our model brings it into close contact with one that has been used in quantum theory (“Stochastically branching spacetime topology” by Roy Douglas [2]). These points of contact will also be discussed.