梯子悖論
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梯子悖論（英語：Ladder Paradox；或稱為竿與穀倉悖論，英語：Barn-pole Paradox）是狹義相對論的思想實驗。
其內容如下。假設有一個梯子，和一個有前門與後門的穀倉。其中梯子的靜止長度比穀倉前、後門間的靜止長度要長。如果梯子不移動的話，其是無法容納進整個穀倉裏的。
此時如果有一個人，拿着這個梯子，以接近光速的速度，向穀倉運動的話。對於站在穀倉，一名靜止旁觀者而言，因為收縮效應，當梯子高速移動經過穀倉時，可以完美地容納進穀倉。也就是說，對於這名旁觀者而言，梯子的長度小於穀倉前、後門間的長度。
但是另一方面，對於拿着梯子的人而言，由於與梯子沒有相對速度，因此梯子並不會縮短。反而是觀察到穀倉以接近光速的速度巷自己移動，因為收縮效應，穀倉會收縮。也就是說，對於拿着梯子的人而言，梯子的長度大於穀倉前、後門間的長度。
由此可見，兩位觀察者對於所見到的事實有着明顯的差異。
這明顯的悖論是來自於錯誤地假設同時性是絕對的。如果梯子的兩端能夠同時在穀倉裏面，則會認為梯子能夠容納進穀倉裏。因此這個悖論可以由考慮到在相對論中，同時性對每位觀察者是相對的來解決。換句話說，梯子是否能夠容納進穀倉裏是取決於觀察者的。
參見
[編輯]參考資料
[編輯]- Wells, Willard H. Length paradox in relativity. American Journal of Physics. 1961, 29 (12): 858. Bibcode:1961AmJPh..29..858W. doi:10.1119/1.1937641.
- Shaw, R. Length contraction paradox. American Journal of Physics. 1962, 30 (1): 72. Bibcode:1962AmJPh..30...72S. doi:10.1119/1.1941907.
- Martins, Roberto De A. Length paradox in relativity. American Journal of Physics. 1978, 46 (6): 667–670. Bibcode:1978AmJPh..46..667M. doi:10.1119/1.11227.
- Sastry, G. P. Is length contraction really paradoxical?. American Journal of Physics. 1987, 55 (10): 943–946. Bibcode:1987AmJPh..55..943S. doi:10.1119/1.14911.
- Grøn, Øyvind; Johannesen, Steinar. Computer simulation of Rindler's length contraction paradox. European Journal of Physics. 1993, 14 (3): 97–100. Bibcode:1993EJPh...14...97G. S2CID 250879672. doi:10.1088/0143-0807/14/3/001.
- van Lintel, Harald; Gruber, Christian. The rod and hole paradox re-examined. European Journal of Physics. 2005, 26 (1): 19–23. Bibcode:2005EJPh...26...19V. S2CID 121888743. doi:10.1088/0143-0807/26/1/003.
- Iyer, Chandru; Prabhu, G. M. Reversal in the time order of interactive events: the collision of inclined rods. European Journal of Physics. 2008, 27 (4): 819–824. Bibcode:2006EJPh...27..819I. S2CID 117711286. arXiv:0809.1721
. doi:10.1088/0143-0807/27/4/013. - Pierce, Evan. The lock and key paradox and the limits of rigidity in special relativity. American Journal of Physics. 2007, 75 (7): 610–614. Bibcode:2007AmJPh..75..610P. doi:10.1119/1.2711827.
- Iyer, Chandru; Prabhu, G. M. Differing observations on the landing of the rod into the slot. American Journal of Physics. 2008, 74 (11): 998–1001. Bibcode:2006AmJPh..74..998I. S2CID 55801261. arXiv:0809.1740 . doi:10.1119/1.2346686.
- McGlynn, Enda; van Kampen, Paul. A note on linking electric current, magnetic fields, charges and the pole in a barn paradox in special relativity. European Journal of Physics. 2008, 29 (6): N63–N67. Bibcode:2008EJPh...29...63M. S2CID 121939564. doi:10.1088/0143-0807/29/6/N03.
延伸閱讀
[編輯]- Edwin F. Taylor and John Archibald Wheeler, Spacetime Physics (2nd ed) (Freeman, NY, 1992)
- - discusses various apparent SR paradoxes and their solutions
- Rindler, Wolfgang. Relativity: Special, General and Cosmological. Oxford University Press. 2001. ISBN 0-19-850836-0.
- Ferraro, Rafael. Einstein's space-time: an introduction to special and general relativity. Springer. 2007. ISBN 978-0-387-69946-2.
外部連結
[編輯]
- Special Relativity Animations from John de Pillis.This inter-active animated train-and-tunnel paradox is an analog of the pole (train) and barn (tunnel) paradox.