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In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given space-time passes through an event horizon, a property which can be called chronological censorship, then that space-time with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.
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References
- ↑ "Rhodes Scholars Announced; a First for Hispanic Women". New York Times. 3 December 1983.
- ↑ Farrell, Joseph; Monroe, Hunter; Saloner, Garth (February 1998). "The Vertical Organization Of Industry: Systems Competition versus Component Competition". Journal of Economics & Management Strategy. 7 (2): 143–182. doi:10.1162/105864098567380.
- ↑ Monroe, Hunter (June 21, 1990). European Developments and the U.S. Economy (PDF). United States Congress Joint Economic Committee.
- ↑ Lenz, Allen; Monroe, Hunter; Parsell, Bruce (1992). Narrowing the U.S. Current Account Deficit: A Sectoral Assessment. Peterson Institute for International Economics. ISBN 9780881321036.
- ↑ "Statement at the Conclusion of an IMF Visit to El Salvador" (Press release). International Monetary Fund. November 2014. Retrieved 2020-02-06.
- ↑ "FMI recomienda crear un fondo de liquidez a El Salvador". San Salvador: Contrapunto. November 2014. Archived from the original on 2020-02-06. Retrieved 2020-02-06.
- ↑ Monroe, Hunter (2011). "Speedup for natural problems and noncomputability". Theoretical Computer Science. 412 (4–5): 478–481. arXiv: 0906.3765 . doi:10.1016/j.tcs.2010.09.029. ISSN 0304-3975. S2CID 6829092.
- ↑ Monroe, Hunter (2008). "Are Causality Violations Undesirable?". Foundations of Physics. 38 (11): 1065–1069. arXiv: gr-qc/0609054 . Bibcode:2008FoPh...38.1065M. doi:10.1007/s10701-008-9254-9. ISSN 0015-9018. S2CID 119707350.