Zurab Silagadze
Mar17-06, 04:00 AM
http://uk.arxiv.org/abs/physics/0505042
This is a paper published in Acta Physica Polonica B36 (2005)
2887-2930.
``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.
This is a paper published in Acta Physica Polonica B36 (2005)
2887-2930.
``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.