梯子悖论

梯子悖论（英语：Ladder Paradox；或称为竿与谷仓悖论，英语：Barn-pole Paradox）是狭义相对论的思想实验。

其内容如下。假设有一个梯子，和一个有前门与后门的谷仓。其中梯子的静止长度比谷仓前、后门间的静止长度要长。如果梯子不移动的话，其是无法容纳进整个谷仓里的。

此时如果有一个人，拿著这个梯子，以接近光速的速度，向谷仓运动的话。对于站在谷仓，一名静止旁观者而言，因为收缩效应，当梯子高速移动经过谷仓时，可以完美地容纳进谷仓。也就是说，对于这名旁观者而言，梯子的长度小于谷仓前、后门间的长度。

但是另一方面，对于拿著梯子的人而言，由于与梯子没有相对速度，因此梯子并不会缩短。反而是观察到谷仓以接近光速的速度巷自己移动，因为收缩效应，谷仓会收缩。也就是说，对于拿著梯子的人而言，梯子的长度大于谷仓前、后门间的长度。

由此可见，两位观察者对于所见到的事实有著明显的差异。

这明显的悖论是来自于错误地假设同时性是绝对的。如果梯子的两端能够同时在谷仓里面，则会认为梯子能够容纳进谷仓里。因此这个悖论可以由考虑到在相对论中，同时性对每位观察者是相对的来解决。换句话说，梯子是否能够容纳进谷仓里是取决于观察者的。

参见

• 贝尔太空船悖论
• 埃伦费斯特悖论
• 物理学悖论
• 相对同时
• Supplee悖论
• 双生子佯谬

参考资料

• 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. 

延伸阅读

• 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. 

外部链接

• 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.