Linear Time: The System K _l and Its Variants

Abstract

The standard picture of time is that of a linear series. This appears not only in ordinary conceptions but is assumed in a great portion of physics. The absolute time of Newtonian physics is a one-dimensional linear continuum; even in relativistic physics the ordering of “local” time series is linear. In terms of the relation U of temporal precedence, this means that the temporal order in such conceptions satisfies the requirement both of transitivity:

$$(Utt\prime \& Ut\prime t\prime \prime ) \supset Utt\prime \prime$$

and connectedness:

$$Utt\prime v t = t\prime v Ut\prime t$$

To conform to standard usage, we shall use < throughout this chapter instead of U, to indicate that the specifically linear case is involved, so that we can rewrite the above as:

$$t < t\prime v t = t\prime v t\prime < t$$