Why and How Special Relativity Fails in the Second Spatial Dimension? An Introduction to the Preferred Frame Theory

Maciej Rybicki^1,

¹Independent researcher, Kraków, Poland

Cite this paper:
Maciej Rybicki. Why and How Special Relativity Fails in the Second Spatial Dimension? An Introduction to the Preferred Frame Theory. International Journal of Physics. 2024; 12(4):175-195. doi: 10.12691/ijp-12-4-5

Abstract

It is demonstrated by means of a thought experiment that the special theory of relativity (STR) leads to contradiction when applied to a spacetime with more than one spatial dimension. The underlying cause of inconsistency proves to be the symmetry of relativistic effects, in particular the symmetry of Lorentz contraction due to the relativity of simultaneity. In this context, the preferred frame theory (PFT) is proposed and discussed. PFT bases on the assumptions different from the two postulates of STR (principle of relativity and constancy of the velocity of light), relating instead to the ideas originated and developed mainly by FitzGerald, Lorentz, Larmor, Voigt and Poincaré, before the advent of Einstein’s theory. However, contrary to the belief shared by the mentioned scholars, these ideas do not comply with the Lorentz transformation, but with the more than half a century later Tangherlini transformation, connecting time dilation and length contraction with the inconstant speed of light and the absolute simultaneity. Despite the fundamental differences, PFT and STR prove to be largely equivalent with each other as to the observational predictions; a significant albeit hardly detectable (on Earth) exception concerns energy. Unlike in the case of STR, in PFT the magnitude of the ratio between particular energies remains constant in all inertial frames (although specific values of energy vary from frame to frame), being thus an invariant of the Tangherlini transformation. This property makes PFT a Lorentz violating theory in a clearly defined way restricted to energy, which opens new perspectives in searching for an effective theory of quantum gravity.

Keywords:
special relativity Lorentz transformation relativity of simultaneity Lorentz contraction Tangherlini transformation preferred inertial frame quantum gravity

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Einstein, A., Zur Elektrodynamik bewegter Körper (On the electrodynamics of moving bodies), Annalen der Physik, 17, 891-921, 1905, https://www.fourmilab.ch.
[2]	Einstein, A., Ist die Trägheit eines Körpers von seinem Energienhalt abhängig? (Does the inertia of a body depend upon its energy-content?), Annalen der Physik, 18, (13) 639-643, 1905 https://www.fourmilab.ch.
[3]	Minkowski, H., Raum und Zeit (Space and time), Physikalische Zeitschrift, 10, 75-88, 1909.
[4]	Roberts, T.; Schleif, S., What is the experimental basis of Special Relativity? 2007, https://math.ucr.edu, University of California, Riverside.
[5]	Russel, N., Framing Lorentz symmetry, CERN Courier, 2004-11-24. Retrieved 2019-11-08.
[6]	Einstein, A., Relativität und Gravitation. Erwiderung auf eine Bemerkung von M. Abraham (Relativity and gravitation. Reply to the comment by M. Abraham), Annalen der Physik, 38, 10, 1059-1064, 1912.
[7]	Bluhm. R., Breaking Lorentz symmetry, Physics World 17 (3) 41, 2004, https://physicsworld.com.
[8]	Colladay, D.; Kostelecky, V.A., Lorentz violating extension of the standard model, Phys. Rev. D. 55 (11), 6760-6774, 1998 arXiv:hep-ph/9703464.
[9]	Coleman, S.; Glashow, S. L., High energy tests of Lorentz invariance, Phys. Rev. D. 59 (11) 116008, 1999.
[10]	Kostelecky, V.A.; Russel, N., Data tables for Lorentz and CPT violation, Rev. Mod. Phys., 83 (1) 11-31, 2011, arXiv: 0801.0287.
[11]	FitzGerald, G.F., The ether and Earth’s atmosphere, Science 13, 328, 390, 1889, https://ui.adsabs.harvard.edu.
[12]	Lorentz, H.A., The relative motion of the Earth and ether, in: Collected Papers, Vol. IV, the Hague 1937, 219-223, 1892
[13]	Larmor, J., Aether and Matter, Cambridge University Press, 1900, https://archive.org.
[14]	Cohn, E.G., Zur Elektrodynamik bewegter Systeme II (On the electrodynamics of moving systems II), Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, 1904/2, 43, 1404-1416, 1904, https://en.wikisource.org.
[15]	Poincaré, H., La mesure du temps (The Measure of Time), 1898, The Foundations of Science, New York: The Science Press, 223-234. 1913, https://en.wikisource.org.
[16]	Poincaré, H., The Principles of Mathematical Physics, Congress of arts and science, Universal Exposition, St Louis, 1, Boston and New York: Houghton, Muffin & Co., 604-622, 1904.
[17]	Rothman, T., Was Einstein the first to invent E=mc²?, Scientific American, August 24, 2015, https://www.scientificamerican.com
[18]	Roberts, T.J., An explanation of Dayton Miller’s anomalous “ether drift” result, 2006, arXiv:physics/0608238
[19]	Reichenbach, H., The Philosophy of Space and Time, Dover, New York, 1930.
[20]	Tangherlini, F.R. Nuovo Cimento Suppl. 20, 351, 1961.
[21]	Selleri, F., Noninvariant one-way velocity of light, Found. Physics., 26 (5), 641-664, 1996.
[22]	Selleri, F., Noninvariant one-way velocity of light and locally equivalent reference frames, Found. Phys. Lett. (10) 73-83, 1997.
[23]	Mansouri, R.; Sexl, U., A test theory of special relativity I: Simultaneity and clock synchronization, Gen. Relativity Gravitation, 8 (7) 497-513, 1977.
[24]	Rybicki, M., Mansouri-Sexl test theory: The question of equivalence between special relativity and ether theories, Progress in Physics, 12 (3), 204, 2016, https://www.ptep-online.com.
[25]	Rybicki, M., Errata to “Mansouri-Sexl test theory: The question of equivalence between special relativity and ether theories”, Progress in Physics, 12 (1), 89-92, 2016, https://www.ptep-online.com.
[26]	Dewan, E.M.; Beran, M.J., Note on stress effects due to relativistic contraction, American Journal of Physics, 27 (7) 517-518, 1959.
[27]	Bell, J.S., How to teach special relativity, in: Speakable and Unspeakable in Quantum Mechanics: papers on quantum philosophy, Cambridge University Press, 1987.
[28]	Thomas, L.H., Motion of the spinning electron, Nature 117 (2945) 514, 1926.
[29]	Rhodes, J.A.; Semon, M.D., Relativistic velocity space, Wigner rotation and Thomas precession, Am. J. Phys. 72 (7) 943-960, 2005, arXiv:gr-qc/0501070v1.
[30]	Rybicki, M., Failure of special relativity as a theory applied to more than one of spatial dimensions, Int. J. Theor. Math. Phys., 9 (3) 81-96, 2019, http://article.sapub.org.
[31]	Rybicki, M., Inconsistency of Minkowski space endowed with more than one spatial dimension, 2022, obtainable on request at: maciej.rybicki@icloud.com).
[32]	Taylor, E.F.; Wheeler, J.A., Spacetime Physics, W.H. Freeman and Co., San Francisco & London, 1966.
[33]	Rybicki, M., Inertial transformation extended to the general case, Galilean Electrodynamics, 21 (1), 8-11, 2010.
[34]	Janis, A. Conventionality of Simultaneity > Transport of Clocks, Stanford Encyclopedia of Philosophy, 2018 https:// plato.stanford.edu > entries.