Some relativistic and higher order supertasks

Philosophy of Science 65 (3):502-517 (1998)
The first aim of this paper is to introduce a new way of looking at supertasks in the light of special relativity which makes use of the elementary dynamics of relativistic point particles subjected to elastic binary collisions and constrained to move unidimensionally. In addition, this will enable us to draw new physical consequences from the possibility of supertasks whose ordinal type is higher than the usual ω or ω * considered so far in the literature. Thus, the paper shows how an entire collection of infinitely many particles may place itself spontaneously in motion (mechanical self-acceleration) or even reach the speed of light in a way compatible with special relativity. Interesting implications for classical mechanics are also derived, particularly the possibility of a system of particles disappearing spontaneously in spatial infinity even under the condition of the non-existence of non-collision singularities
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