Billiard-ball paradox for a quantum wave packet
| Autor: | Bishop, Lachlan G., Ralph, Timothy C., Costa, Fabio |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Class. Quantum Grav. 39, 175007 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6382/ac8198 |
| Popis: | Past studies of the billiard-ball paradox, a problem involving an object that travels back in time along a closed timelike curve (CTC), typically concern themselves with entirely classical histories, whereby any trajectorial effects associated with quantum mechanics cannot manifest. Here we develop a quantum version of the paradox, wherein a (semiclassical) wave packet evolves through a region containing a wormhole time machine. This is accomplished by mapping all relevant paths on to a quantum circuit, in which the distinction of the various paths is facilitated by representing the billiard particle with a clock state. For this model, we find that Deutsch's prescription (D-CTCs) provides self-consistent solutions in the form of a mixed state composed of terms which represent every possible configuration of the particle's evolution through the circuit. In the equivalent circuit picture (ECP), this reduces to a binomial distribution in the number of loops of time machine. The postselected teleportation prescription (P-CTCs) on the other hand predicts a pure-state solution in which the loop counts have binomial coefficient weights. We then discuss the model in the continuum limit, with a particular focus on the various methods one may employ in order to guarantee convergence in the average number of clock evolutions. Specifically, for D-CTCs, we find that it is necessary to regularise the theory's parameters, while P-CTCs alternatively require more contrived modification. Comment: 18 pages, 9 figures |
| Databáze: | arXiv |
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