Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 7. Distances and moving coordinate axes. Next Document: 9. Einstein's (1905) derivations. See reader questions & answers on this topic!  Help others by sharing your knowledge Instead of using our sticks, let's get out two clocks. Mind you, we're not going to deal with different clock rates here, just establish the same basics as for distance. Your clock says 9:00 Eastern Standard Time (EST) and we note that t=540 minutes when we put down the clock. Blindly, let's turn the setting knob of your twin's Pacific Standard Time clock and put it down before us. According to what we see, EST's 540 minutes (9:00) corre sponds to PST's 14:30; t'=870. We know the formula relating PST to EST is t' (pacific) = t (eastern)  180 (minutes). Thus, it is not correct that the second clock can have an arbitrary setting, because 870 <> 540180. We know that the two clocks are related by t' = t/1 since both are using the same second, hour, etc units. But 870 (14:30 in minutes) is not 540/1180, so once again we know something is wrong. However, t'=t.z' + t/1 works. EST midnight equals PST 0.0 (midnite)  180, so t.z' = 180, and t' = 180 + 540/1 = 360. Since EST180=PST, 9:00 EST is 6:00 PST = 360 minutes. We see thus that like distance measures/coordinates, time axis origins (zero points) must either be 'lined up' or adjusted for. So, the Lorentz/Einstein t'=t/sqrt(1vv/cc) must be the moving system elapsed time interval since the time axes were both at a common zero. There is no t.z' adjustment: t' = (t  vx/cc)/sqrt(1vv/cc) (Eq 1t) Make sure you understand that in the clock case, if the EST is showing a good number for elapsed time since the travelling observer passed NYC, then the PST clock is silliness. t.z' must be zero or must be taken out of time lapse calculations for the PST clock to be used intelligently, just as was true for x.z'. What is lacking as yet for Lorentz t' is the vx/cc term that corresponds to the x' formula vt term. Break it up into two parts: v/c and x/c. v/c is a scaling factor that changes velocity from whatever kind of unit you are using over to fractions of c. x/c is distance divided by velocity, which is time. x/c is thus the time interval since the two time axes had a common zero point  which they have to have in the Lorentz transforms which do not have the t.z' term we learned to use above. Thus, (vx/cc)/sqrt(1vv/cc) is the interval amount the moving system clock has been changed  since the common/ adjusted time  over and beyond the elapsed time interval represented by x/sqrt(1vv/cc). We have discovered that the only way for t' to be t/g is for t' and t to have a common zero point, just as for x' and x. It would be otherwise if the t' formula contained an adjustment t.z' under some name or other, but the necessity to include such a term correlates 100% with t' numbers that aren't directly usable. As for x and x', our knowledge of how to setup a proper formula relating t and t' is of no use unless we use the knowledge in scientific formulas; (t't.z'+xv/gcc) gives us the only directly useful value: t/g. User Contributions:Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 7. Distances and moving coordinate axes. Next Document: 9. Einstein's (1905) derivations. 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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