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The imaginary unit i as the temporal directional component of the complex position vector

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Some interpretations of modern physics reject imaginary numbers as having physical significance. They are considered a convenient mathematical tool for calculation of phase or probability. Their presence in equations of modern physics is, however, indispensable. An examination of the definition of the square root operation shows that its definition is suggestive of time. With this information and the axioms of the complex plane, it is shown that i can be defined as the temporal directional component of the complex position vector. i and −i are here considered forward and reverse time direction numbers which are derived differently than the direction numbers of standard Euclidean vector analysis.
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Keywords: Complex Numbers; Direction Numbers; Imaginary Numbers; Schrodinger Equation; Time Symmetry; Vector Analysis; Wave Function Realism; Wheeler‐DeWitt Equation; Wigner Theorem

Document Type: Research Article

Publication date: 18 June 2015

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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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