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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 17: Quantum and Gravity

AGPhil 17.2: Talk

Friday, March 22, 2024, 10:00–10:30, PTB SR AvHB

Deriving the local arrow of time — •Daniel Saudek — Neuer Weg 28, Kitzingen

This contribution provides a derivation of time*s ordering properties, its metric properties, and its irreversibility on the basis of simple axioms. It does so in three steps: 1. It starts with the notion of the set of states of an object. There is a characteristic asymmetry on this set which can be defined independently of time, but which can be exploited to define temporal order (*before*) in a way which corresponds, as will be shown, with the order known from everyday experience. 2. The object is equipped with a counting mechanism based on successive inclusion, providing a natural parameter (as in Kuratowski*s construction of the naturals), which can then be fine-grained further to yield a rational and a real parameter. The local parameter so established is shown to increase monotonically with the before-ordering developed in (1). 3. It is shown that, given an object with a particular local index t (as developed under 2), the notion of changing the event content associated with indices less than t leads to a contradiction, whereas there is no event content for indices greater than t. Thus, the local past is fixed, and the future open. In sum, time*s passage is real, but local rather than global.

Keywords: arrow of time; local time; relativity theory; irreversibility; records