梯子悖論
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。實驗中牽涉到一個平行於地面放置，行進方向與地面平行且速度接近於光速因此感受到長度收縮的梯子。假想此梯子會經過一個其靜止長度比梯子短的車庫或穀倉的前門與後門，因此如果梯子不移動的話，其是無法容納進整個穀倉裡的。一方面，對於一個靜止的觀察者而言，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。另一方面，對於一個與梯子一起運動的觀察者而言，梯子長度不會收縮，反而穀倉會收縮到更短的長度。因此，當梯子經過穀倉時，無法完美地容納進穀倉裡。由此可見，兩位觀察者對於所見到的事實有著明顯的差異。
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裡面，則會認為梯子能夠容納進穀倉裡。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裡是取決於觀察者的。
參見
编辑參考資料
编辑- 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
编辑- 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
编辑
- 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.