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Open AccessArticle

Lorentz Transformations from Intrinsic Symmetries

Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan
Academic Editor: Roman M. Cherniha
Symmetry 2016, 8(9), 94; https://doi.org/10.3390/sym8090094
Received: 20 June 2016 / Revised: 31 August 2016 / Accepted: 1 September 2016 / Published: 9 September 2016
We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination with the principle of relativity and the presumed nature of Euclidean space and time, the symmetry principle is employed to derive the proper orthochronous Lorentz transformation without assuming the constancy of the speed of light and specific mathematical requirements (such as group property) a priori. We explicitly demonstrate that the constancy of the speed of light in all inertial frames can be derived using the velocity reciprocity property, which is a deductive consequence of the space–time homogeneity and the space isotropy. The FESI or the FETI symmetry remains to be preserved in the Galilean transformation at the non-relativistic limit. Other similar symmetry operations result in either trivial transformations or improper and/or non-orthochronous Lorentz transformations, which do not form groups. View Full-Text
Keywords: symmetry principle; Lorentz transformation; special relativity symmetry principle; Lorentz transformation; special relativity
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MDPI and ACS Style

Chao, S.D. Lorentz Transformations from Intrinsic Symmetries. Symmetry 2016, 8, 94. https://doi.org/10.3390/sym8090094

AMA Style

Chao SD. Lorentz Transformations from Intrinsic Symmetries. Symmetry. 2016; 8(9):94. https://doi.org/10.3390/sym8090094

Chicago/Turabian Style

Chao, Sheng D. 2016. "Lorentz Transformations from Intrinsic Symmetries" Symmetry 8, no. 9: 94. https://doi.org/10.3390/sym8090094

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