Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 6. Relating two coordinate measures/systems. Next Document: 8. Time intervals. See reader questions & answers on this topic!  Help others by sharing your knowledge We discovered x'=x.z' + x/g as the correct formula for relating one coordinate to another system's. But the Lorentz transform contains another term, vt/sqrt(1vv/cc). What is it? Let's start with our x'=51 cm, x=3.5", x.z'=42.11 example. Every minute, let's move the meterstick one inch to our right. At minute 0, the cm reading was 51 cm. At minute 1, the cm reading is now 50 cm. At minute 2, the cm reading is now 49 cm. In this instance, v=1 inch/minute. And t was 0, 1, 2. What has happened is that we have made our x.z' a lie, and increasingly so. vt/.3937 is the change in x.z'. x' = (x.z  vt/.3937) + x/.3937. Obviously, vt/.3937 is not a coordinate; even most SRians wouldn't imagine it was. It is an interval, the distance over which the moving system has moved since t=0. And, of course, x/.3937 is the distance of our brave little ant from the point where x=0 and the centimeter reading is x.z'vt/.3937. Yes, every minute the meter stick moves to the right and the meterstick coordinate of the spot where x=0 gets less and less  and eventually negative. Make sure you understand that every minute the x' coordinate, because of vt/g, becomes a better measure of, say, the 3.5" paper we might be measuring with the yardstick, given that 51 was too big a number and vt is negative. That is, until the two origins coincide at x'=x=0, and then it gets worse and worse. With vt positive (because v<0) the situation is different. With 51 and vt positive, x' just gets worse and worse over time. Quite obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x' coordinate even when the x' axis is moving, does not mean that x'is anything more than nonsense for use in any scientific formula. Unless we were smart enough to put the x zero point in a useful location, and use (x'x.z'+vt/.3937) in the scientific formula. (x'x.z'+vt/.3937) equals the useful, Ratio Scale value x/.3937. User Contributions:Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 6. Relating two coordinate measures/systems. Next Document: 8. Time 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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