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Cranks and special relativity

October 2, 2011

Last month a paper (which I use in its vaguest sense) was put on viXra, the website for cranks and nuts who can’t can’t meet arXiv’s basic requirements of sanity and science, pertaining to special relativity. Of course this isn’t a new thing, SR is a favourite topic of people who slept through science class and never made it to university level physics. However, it’s on a specific thing all too often brought up on forums (in my particular experience that being Sciforums), light spheres.

As such I spent a bit of yesterday evening knocking up a refutation of the article, based on posts I made on Sciforums here. The pdf can be found here. The fatal mistake the author makes is that he doesn’t transform into the second frame properly. He doesn’t explicitly compute the Lorentz images of the two points in question, nor the Lorentz image of the light sphere. If he had done this then it would become clear why the Lorentz image of the second point is hit first, despite being hit second in the initial frame.

More formally, we denote p_{1},p_{2} as the points in frame S such that (p_{1})^{x} < (p_{2})^{x}. Since (p_{1})^{y} = (p_{2})^{y} and the Lorentz boost \Lambda is by speed v in the x direction we need only consider the x' components of q_{i} = \Lambda(p_{i}). While it is true (q_{1})^{x'} < (q_{2})^{x'} for sufficiently large values of v the boost is such that \vert (q_{1})^{x'}\vert > \vert(q_{2})^{x'}\vert and thus (q_{1})^{t'} > (q_{2})^{t'} as both frames see the light sphere as centred on the origin and emitted at time 0.

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