Adventures in Thought Space

In the last post, I discussed relativistic time dilation, length contraction, and the twin parado x. Unlike that post, however, the following is not just conceptual; tricky algebraic and kinematic calculations are required.   The Lorenz kinematic transforms are a collection of general formulae to transform kinematical calculations from one frame to another: the distance transforms, the time transforms, the velocity/velocity-addition transforms, and the acceleration transforms. They are the relativistic equivalent of the Gallian kinematic transforms, the technical term for the formulas that convert kinematic measurements from one frame to another in simple distance-rate and (constant) acceleration problems. Older than relativity itself, the transforms were originally—and ironically—derived to account for the antiquated “ether wind.”     This post consists of semi-original derivations of the inertial formulas (excluding acceleration), each detailing the steps of their ...

  Caveat: Misconceptions could be accrued if one hasn’t either read the post " Frame of Reference vs. Observer: Where Relativity Pedagogy Goes Wrong" before OR after reading this, or studied special relativity from other sources offering additional rigor.       Many popular science sources have “attempted” to teach special relativistic phenomena without mathematical and conceptual rigor. Although this is achievable in theory, this may or may not be realistic in practice. Moreover, even if successful, since it’d be unlikely the student would be able to solve any relativity problems without additional learning, it would be difficult to verify, especially if required to avoid instilling misconceptions about OTHER aspects of relativity (which popular science generally seems indifferent to). Most of the explanations are pseudo-pedagogical, designed to create the illusion of understanding. This post is an (actual) attempt to achieve where most others have failed....