The Arrow of Time: The Full Derivation
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This chapter gives a step-by-step derivation of the local arrow of time from timeless notions and based on simple axioms. Using the notion of substance and the set of its states, a definition of “before” is developed. From there, we proceed to define change, and then time as a local quantification of change. Based on this groundwork, and together with an epistemological assumption, it is shown that local time has a linear structure and that the local past is fixed, whereas the local future is open and can be influenced. The asymmetric structure of time is thus real, but entirely local rather than global. Finally, it is explored whether local time is discrete or continuous.