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Degree of freedom in the Lorentz transformation

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Lorentz pointed out in 1899 that a relativistic space-time transformation which leaves Maxwell's equations invariant could only be defined to within a common factor on the basis of then-existing experimental data. The present work calls attention to the fact that Einstein's subsequent derivation of the Lorentz transformation (LT) is based on an undeclared assumption regarding the functional dependence of this factor. Consequently, many of the unconfirmed predictions of Einstein's special theory of relativity (STR), such as the remote nonsimultaneity of events and the symmetric relationship of measurements made by observers in different inertial systems, would lose their validity if the above assumption is shown to be incorrect. At the same time, any other choice for Lorentz's common factor is seen to be consistent with the relativistic velocity transformation (VT). Accordingly, predictions of STR that are derived exclusively from the VT would not be affected by such a change in relativity theory. On this basis, an alternative Lorentz transformation is defined that also satisfies Einstein's two postulates of relativity, but incorporates the strict proportionality of the rates of moving clocks assumed in the operation of the Global Positioning System (GPS) rather than invoking the inextricable mixing of space and time coordinates predicted by the LT.
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Keywords: Alternative Lorentz Transformation (ALT); Lorentz Transformation (LT); Postulates of Special Relativity; Velocity Transformation (VT)

Document Type: Research Article

Publication date: December 30, 2013

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  • Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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