相对性原理与时空线性变换THE PRINCIPLE OF RELATIVITY AND THE SPACE-TIME LINEAR TRANSFORMATION
戴又善
摘要(Abstract):
惯性系具有任何方向时空平移不变的特性,依据相对性原理和时空平移不变性证明了惯性系的时空变换必须为线性变换。相对性原理是时空线性变换的真正必要条件。除了伽利略变换具有"同时的绝对性"外,其他的惯性系时空线性变换都具有"同时的相对性"。利用相对性原理还可以证明惯性系的速度变换为单调递增函数,因而存在速度上限,惯性系除伽利略变换外的所有时空线性变换都存在有限的极限速度,进而可以推导出惯性系时空线性变换的广义洛伦兹变换公式,其中极限速度的取值可以通过实验来确定。
关键词(KeyWords): 相对性原理;时空平移不变性;时空线性变换;同时的相对性;极限速度;广义洛伦兹变换
基金项目(Foundation): 浙江省自然科学基金,相对论理论的研究与改进(LY17A050001)
作者(Author): 戴又善
参考文献(References):
- [1]EINSTEIN A.Zur Elektro-dynamik Bewegter K9rper[J].Annalen der Physik,1905,17:891-921.
- [2]LEVY-LEBLOND J M.One more derivation of the Lorentz transformation[J].American Journal of Physics,1976,44(3):271-277.
- [3]王笑君,关洪.关于洛伦兹变换的推导[J].大学物理,1998,17(8):18-20.WANG X J,GUAN H.On the derivation of Lorentz transformation[J].College Physics,1998,17(8):18-20.(in Chinese)
- [4]关洪.再谈洛伦兹变换的推导[J].大学物理,2007,26(11):11-12.GUAN H.Ferther discussions on the derivation of Lorentz transformation[J].College Physics,2007,26(11):11-12.(in Chinese)
- [5]冯胜奇.惯性系之间的时空变换是线性变换的充分与必要条件[J].广西物理,2009,30(3):47-49.FENG S Q.The sufficient and necessary conditions for the linear time-space transform between inertial frames[J].Guangxi Physics,2009,30(3):47-49.(in Chinese)
- [6]陈奎孚.为什么时空变换必须是线性的[J].物理与工程,2017,27(6):31-36.CHEN K F.Why the time-space transformations must be linear[J].Physics and Engineering,2017,27(6):31-36.(in Chinese)
- [7]郭长贵.保持匀速直线运动规律不变的时空坐标变换一定是线性变换吗[J].大学物理,1993,12(4):28-29.GUO C G.Is the time-space transformations preserved uniform linear motion only by linear transformation[J].College Physics,1993,12(4):28-29.(in Chinese)
- [8]郭汉英,黄超光,田雨,等.Beltrami-de Sitter时空和de Sitter不变的狭义相对论[J].物理学报,2005,54(6):2494-2503.GUO H Y,HUANG C G,TIAN Y,et al.Beltrami-de Sitter spacetime and de Sitter invariant special relativity[J].Acta Physica Sinica,2005,54(6):2494-2503.(in Chinese)
- [9]张元仲.爱因斯坦建立狭义相对论的关键一步——同时性定义[J].物理与工程,2015,25(3):3-8.ZHANG Y Z.A key step in the development of the special relativity by Einstein——Definition of simultaneity[J].Physics and Engineering,2015,25(3):3-8.(in Chinese)
- [10]张元仲.狭义相对论教学中不该出现的错误[J].物理与工程,2017,27(4):3-9.ZHANG Y Z.The mistakes that should not appear in the teaching materials of special relativity[J].Physics and Engineering,2017,27(4):3-9.(in Chinese)
- [11]戴又善.狭义相对论与运动速度上限[J].北京大学学报(自然科学版),2013,49(3):356-364.DAI Y S.Special relativity and upper limit for speed[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2013,49(3):356-364.(in Chinese)
- [12]戴又善,戴亮.普遍的质速关系和狭义相对论[J].北京大学学报(自然科学版),2014,50(3):403-410.DAI Y S,DAI L.Universal mass-velocity relation and special relativity[J].Acta Scientiarum Naturalium Universitatis Pekinensis,2014,50(3):403-410.(in Chinese)
- [13]戴又善,宋孝同.无需光速不变假设的狭义相对论新推导[J].浙江大学学报(理学版),2016,43(2):247-252.DAI Y S,SONG X T.New derivation of special relativity without assumption of constant speed of light[J].Journal of Zhejiang University(Science Edition),2016,43(2):247-252.(in Chinese)
- [14]ADLER C G.Connection between conservation of energy and conservation of momentum[J].American Journal of Physics,1976,44(5):483-484.
- [15]DAI Y S,DAI L.Deriving mass-energy equivalence and mass-velocity relation without light[J].American Journal of Physics,2018,86(4):284-289.