芝诺与现代科学相遇
Zeno meets modern science
摘要：
“从来没有人碰过芝诺而不反驳他。我们不会在本文中反驳芝诺。相反，我们回顾芝诺与现代科学的一些意想不到的遭遇。本文首先简要介绍芝诺的埃利亚其次是他著名的运动悖论。对空间和时间连续性的思考将我们引向巴拿赫和塔斯基及其著名的悖论，这实际上根本不是悖论，而是一个严格的数学定理，尽管非常违反直觉。量子力学给芝诺悖论带来了另一种味道。量子芝诺和反芝诺效应确实是自相矛盾的，但现在是实验事实。然后我们讨论了超级任务和分叉超级任务。定域化的概念将我们引向牛顿和维格纳，以及有趣的量子复兴现象。最后，我们注意到古代芝诺和巴门尼德所捍卫的宇宙无时间的悖论观念在量子引力中仍然存在。下面的参考文献清单必然是不完整的，但我们希望它将有助于感兴趣的读者填写细节。
英文摘要：
``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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
