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Directional emissions from a moving light-source: Coincidence and simultaneity

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Directional emissions of light-pulses from a point-source (which is stationary at the origin of a moving inertial reference-frame) towards detectors which are all stationary at a constant radial-distance from the light-source (within the latter's inertial reference-frame) are transformed into another time-synchronized inertial reference-frame relative to which the source is moving with a speed v. Both the Galilean-transformation and the Lorentz-transformation are used. Light-pulses along different directions are compared to the equivalent situation when a spherical wavefront is emitted from the same source. The Galilean-transformation gives transformed coordinates of points on this wavefront that remain coincident on this wavefront; which, in turn, remains centered at the origin of the moving inertial reference-frame. In contrast, the Lorentz-transformation mandates that the same spherical wavefront must be observed as twin wavefronts, each of which remains centered at one of the origins of the moving and the stationary reference-frames, respectively. Here it is found that the Lorentz-transformation of simultaneous-instantaneous position-coordinates, of points on the wavefront within the moving inertial reference-frame, does not result in points which are simultaneously situated on its twin wavefront within the stationary inertial reference-frame. This is a compelling proof that an event which occurs at nonzero position-coordinates and at a nonzero time within the moving inertial reference-frame is not observed coincidently from the origin of another time-synchronized inertial reference-frame relative to which the reference-frame of the source is moving.
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Keywords: Cosmic-Ray Muon; Galilean-Transformation; Light-Clock; Lorentz-Transformation; Minkowski’s Space‐Time; Simultaneity; Speed of Light; Time-Dilation; Twin Paradox

Document Type: Research Article

Publication date: March 5, 2014

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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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