300 research outputs found
Zeno meets modern science
``No one has ever touched Zeno without refuting him''. We will not refute
Zeno in this paper. Instead we review some unexpected encounters of Zeno with
modern science. The paper begins with a brief biography of Zeno of Elea
followed by his famous paradoxes of motion. Reflections on continuity of space
and time lead us to Banach and Tarski and to their celebrated paradox, which is
in fact not a paradox at all but a strict mathematical theorem, although very
counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes.
Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental
facts. Then we discuss supertasks and bifurcated supertasks. The concept of
localization leads us to Newton and Wigner and to interesting phenomenon of
quantum revivals. At last we note that the paradoxical idea of timeless
universe, defended by Zeno and Parmenides at ancient times, is still alive in
quantum gravity. The list of references that follows is necessarily incomplete
but we hope it will assist interested reader to fill in details.Comment: 40 pages, LaTeX, 10 figure
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