Berlin 2015 – scientific programme

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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 2: Philosophy of Science

AGPhil 2.4: Talk

Tuesday, March 17, 2015, 17:30–18:00, A 060

from kant's theory of time to relativistic spacetime and causal sets — •riccardo pinosio — institute for logic, language and computation, university of amsterdam

In the context of his work on the foundations of relativity, A. G. Walker developed an axiomatization of Milne's kinematical relativity whose primitive entities are extended durations. These can be thought of as extended timelike subpaths of the world-line of a particle; point-like instants are then defined in terms of durations, and signal axioms on these are imposed so as to recover Milne's kinematical relativity and a large class of models of general relativity.

Walker's analysis of temporal order, particularly in the category-theoretical formulation given to it by Thomason, bears strong similarities to Immanuel Kant's; thus, we used it to develop a mathematical formalization of Kant's theory of time. To achieve this, the axiomatic approach had to be supplemented by a topological treatment, to formalize various notions crucial to Kant's theory, such as continuity and connectedness of time.

As it turns out, using this formalization one can specify precisely those assumptions which make Kant's theory of space and time Newtonian. Furthermore, lifting these assumptions yeilds a generalization of Walker's construction applicable to arbitrary spacetime manifolds, which can provide an approach to discretizing spacetime related to that developed within the causal set framework.