Discrete and continuous representations of the same motion
We have defined slowness (v′=1/v) as the reciprocal of velocity v. Einstein's postulate (v≤c) sets a lower limit to slowness (v′≥c′). We have shown that the lower bound condition together with the group property (that the difference between two slownesses is also slowness) implies that slowness is discrete. We have, then, shown that the same physics can be described by a continuous quantity (like velocity) and by a discrete quantity (like slowness). This shows the equivalence between continuity and discreteness. We have also represented a distance traveled by a moving body in continuous representation and in discrete representation. We have considered motion in one space dimension only.
Keywords: Continuous; Discrete; Distance; Galilean Velocity; Lorentz-Algebraic Velocity; Reciprocal Distance; Reciprocal Lorentz-Algebraic Velocity
Document Type: Research Article
Affiliations: Email: [email protected]
Publication date: 01 March 2009
- 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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