I introduce a sequence which I call indefinite: a sequence every element of which has a successor but whose number of elements is bounded; this is no contradiction. I then consider the possibility of space and time being indefinitely divisible. This is theoretically possible and agrees with experience. If this is space and time’s structure, then even if the laws of nature are deterministic, the behaviour of physical systems will be probabilistic. This approach might also shed light on directionality in time and other physical phenomena.
There will be dinner after the talk. If you are interested, please send an email with “Dinner” in the heading to firstname.lastname@example.org (please note that all are welcome, but only the speaker’s dinner will be covered). If you have any other questions, please email email@example.com.
Mario Hubert (Columbia)
4:30-6:30pm Wednesday Nov 28; location TBD.
Title: When Fields Are Not Degrees of Freedom (joint work with Vera Hartenstein).
Abstract: We show that in the Maxwell–Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology.