Lorentz Transformations in 1+1 Dimensional Spacetime: Mainly the Superluminal Case
Main Article Content
Abstract
We discuss the most general form of the Lorentz transformation in 1+1 dimensional spacetime, focusing mainly on its superluminal branch. For this purpose, we introduce the 2-velocity of a reference frame and the clockwork postulate. Basic special relativity effects are discussed in the proposed framework. Different forms of the superluminal Lorentz transformation, which were studied in the literature, are critically examined from the perspective of our formalism. Counterintuitive features of the superluminal Lorentz transformation are identified both in our approach and in earlier studies.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
G. Feinberg, Phys. Rev. 159, 1089 (1967), https://doi.org/10.1103/PhysRev.159.1089
R.C. Tolman, The Theory of Relativity of Motion, University of California Press, 1917
R. Ehrlich, Symmetry 14, 1198 (2022), https://doi.org/10.3390/sym14061198
A. Dragan, A. Ekert, New J. Phys. 22, 033038 (2020), https://doi.org/10.1088/1367-2630/ab76f7
A. Grudka, A. Wójcik, New J. Phys. 24, 098001 (2022), https://doi.org/10.1088/1367-2630/ac924e
A. Grudka, J. Stempin, J. Wójcik, A. Wójcik, Phys. Lett. A 487, 129127 (2023), https://doi.org/10.1016/j.physleta.2023.129127
R. Horodecki, New J. Phys. 25, 128001 (2023), https://doi.org/10.1088/1367-2630/ad10ff
F.D. Santo, S. Horvat, New J. Phys. 24, 128001 (2022), https://doi.org/10.1088/1367-2630/acae3b
A. Dragan, A. Ekert, New J. Phys. 24, 098002 (2022), https://doi.org/10.1088/1367-2630/ac90e3
A. Dragan, A. Ekert, New J. Phys. 25, 128002 (2023), https://doi.org/10.1088/1367-2630/ad100e
A. Dragan, A. Ekert, New J. Phys. 25, 088002 (2023), https://doi.org/10.1088/1367-2630/acec62
L. Parker, Phys. Rev. 188, 2287 (1969), https://doi.org/10.1103/PhysRev.188.2287
R. Goldoni, Nuovo Cim. A 14, 501 (1973), https://doi.org/10.1007/BF02756272
R.N. Henriksen, How might tachyons appear?, 2020, https://arxiv.org/abs/2004.04045
L. Marchildon, A.F. Antippa, A.E. Everett, Can. J. Phys. 61, 256 (1983), https://doi.org/10.1139/p83-035
K. Lorek, J. Louko, A. Dragan, Class. Quantum Gravity 32, 175003 (2015), https://doi.org/10.1088/0264-9381/32/17/175003
R.S. Vieira, Rev. Bras. Ensino Fís. 34, 3306 (2012), https://doi.org/10.1590/S1806-11172012000300006
R.I. Sutherland, J.R. Shepanski, Phys. Rev. D 33, 2896 (1986), https://doi.org/10.1103/PhysRevD.33.2896
A. Dragan, Unusually Special Relativity, World Scientific, 2022
L.M. Sokołowski, Elementy szczególnej teorii względności, Wydawnictwo Uniwersytetu Warszawskiego, 2023
P. Moylan, Am. J. Phys. 90, 126 (2022), https://doi.org/10.1119/10.0009219
A. Dragan, Why devil plays dice?, 2008, https://arxiv.org/abs/0806.4875
O.M.P. Bilaniuk, V.K. Deshpande, E.C.G. Sudarshan, Am. J. Phys. 30, 718 (1962), https://doi.org/10.1119/1.1941773
A. Dragan, K. Dębski, S. Charzyński, K. Turzyński, A. Ekert, Class. Quantum Grav. 40, 025013 (2022), https://doi.org/10.1088/1361-6382/acad60