Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 8. Time intervals. Next Document: 10. A word about intervals. See reader questions & answers on this topic!  Help others by sharing your knowledge When we return to Einstein's derivations of the transform formulas with a wellfocused eye, we find he was a wee bit confused  or at least selfcontradictory. When he set up his (at first unknown) tau=moving system time formulas, he created three particular instances of tau. Tau.0 is the time at which light is emitted at the moving origin toward a mirror to the right that is moving at rest wrt that moving origin and at a constant distance from that origin. He lets the stationary time slot have the value t, a constant, the stationary system starting time. Tau.1 is the time at which the light is reflected. He lets the stationary time be t+x'/(cv); t is still a constant and x'/(cv) is the time interval since t. Tau.2 is the time at which the light gets (back) to the moving origin. The stationary time value is put as t + x'/(cv) + x'/(c+v); t is still a constant and x'/(cv) + x'/(c+v) is the time interval since t. On the thesis that the moving observer sees the time to the mirror as the same as the time back to the origin, he sets .5[ tau.0 + tau.2 ] = tau.1. Tau.0 completely drops out of the analysis and leaves no trace, and has no effect. Further, the t you see in tau.0, tau.1, and tau.2 also completely drops out with no trace and no effect, leaving us with exactly what you'd get if you had explicilty said t' is an interval and so is t. What doesn't drop out in the stationary time values is x'/(cv) and x'/(c+v), the time interval it takes for light to get to the fleeing mirror, and the time interval it takes for light to get back to the approaching origin. Thus, his resultant t' formula is strictly based on time intervals in the stationary system. Time intervals since some starting time, yes, but time intervals. There is absolutely nothing in the derived formulas that depends on arbitrary coordinates like the constant t in the stationary time arguments. Let's look at the x dimension; it is x'=xvt [as x increases by vt, the effect over time is x'=(x+vt)vt)], which Einstein explicitly sets up as a constant stationary distance. He uses that x' not just in the time interval parts of the stationary time arguments, but also in the x (distance) stationary system argument for the tau at the time light is reflected. x' can't be the stationary system coordinate of the mirror at that time. That value is x'+vt. x' is explicitly an interval, distance. Thus, the whole tau derivation of the t' formula is fully and explicitly based on x'  a spatial length/distance/interval  and the two time interals x'/(cv) and x'/(c+v). While we're at it, if the starting t is not zero, his x'=xvt formula is complete nonsense also. Given that there was some L that was the mirror xlocation and length when the light is emitted, if t was already, say, 500, then x'=Lvt could have been a very negative length. User Contributions:Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 8. Time intervals. Next Document: 10. A word about intervals. Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: Thnktank@concentric.net (Eleaticus)
Last Update March 27 2014 @ 02:12 PM

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