How can one derive the equations for a Lorentz transformation? Is there a paper by Lorentz in which it is done? I think it is related to considering motion with respect to a beam of light. I am trying to understand how the scaling factor called $\beta$ arises.
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Qmechanic
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Christina Daniel
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4Does this answer your question? Derivation of Lorentz Transformations – BioPhysicist Dec 09 '19 at 02:58
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Do you mean gamma? "gamma" is the Lorentz factor, $\gamma = 1/\sqrt{1-v^2/c^2}$ (or its inverse). "beta" is usually used to represent the velocity of something as fraction of the velocity of light, $\beta=v/c$. So $\gamma = 1/\sqrt{1 - \beta^2}$ – Eric Baird Dec 09 '19 at 03:23
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In Einstein's original 1905 paper (e.g. https://en.wikisource.org/wiki/Translation:On_the_Electrodynamics_of_Moving_Bodies ), he uses the symbol $\beta$ for the time-dilation factor. – robphy Dec 09 '19 at 05:52
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(looks at p.48 of the Dover Press reprint translation) Oh. So he does.Well pointed out. But nowadays this would be considered nonstandard. – Eric Baird Dec 09 '19 at 06:05
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Here's a nice set of lecture notes that derives the Lorentz transformations: http://physics.mq.edu.au/~jcresser/Phys378/LectureNotes/VectorsTensorsSR.pdf – Charlie Dec 09 '19 at 03:12