Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 5. Singlesystem, littlepurpose ambiguity. Next Document: 7. Distances and moving coordinate axes. See reader questions & answers on this topic!  Help others by sharing your knowledge Taking care to not damage our brave little ant, I place my yardstick onto the table, zero end to the left, 36" end to the right. Now I place the 'just coordinate' meterstick on the table in the same orientation, in a random location, and find that the ant's coordinate on the meterstick is 51. The formula relating centimeters to inches is cm=i*2.54 but we want a formula similar to x'=(xvt)/sqrt(1vv/cc). That would be c=i/.03937 approximately, but let's use x' for the meterstick reading, and x for the inch reading: x'=x/.3937. 3.5/.3937 = 8.89 Wait a minute. It's not just science but definition that says c=i/.3937=8.89, so something is wrong. 8.89 is not 51. We already knew that 51 cm was just an arbitrary coordinate. Arbitrary not because that point isn't 51 cm from the zero end of the meterstick, but because the zero point was in an arbitrary position. Let's put the meterstick in a position where it's zero point is at the yardstick zero point. What is the centimeter coordinate now? Hey. 8.89, just like the formula says. The only way for a 'transform' like x'=x/g to work, whatever g might be, is for both coordinate systems to have their zero points aligned, in which case saying the two measures are not intervals is pure idiocy. Noe that with both zero points at the same position both x' and x are great measures for scientific purposes, in any and every case where we were smart enough to put those zero points at a useful location. There is one extension of x'=x/g that will let us use the meterstick in arbitrary position. When the cm reading was 51, the zero point of the yardstick read (518.89=) 42.11 cm. If we call that point x.z' we get x' = x.z' + x/.3937. = 42.11 + 3.5/.3937 = 42.11 + 8.89 = 51. Obviously, in this formula x/.3937 is the distance from the x' coordinate of the location where x=0. An interval. Just as obviously, the fact that we now have the correct formula for relating an x interval to an arbitrary x' coordinate, 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') in the scientific formula. (x'x.z') equals the useful, Ratio Scale value x/.3937. So, we have discovered a basic fact: a transformation formula like x'=x/g works only if the two zero points of the coordinate systems coincide. That makes it non sense to say the two coodinates are only coordinates and not intervals. Both must be values that represent distances from their respective zero points unless you take the proper steps to adjust for the discrepancy. Make sure you understand that although the inclusion of x.z' made it possible to correctly calculate x', the result is nonsense when it comes to use of x' for general length/distance purposes; it is x'x.z' that is a useful number in such cases. It could be that we're measuring a sheet of paper with one end at x=0 and the other at x=3.5; x'=51 is nonsense as a centimeter measure of the paper. But, you say, the Lorentz transform contain a vt term. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: (SR) Lorentz t', x' = Intervals Previous Document: 5. Singlesystem, littlepurpose ambiguity. Next Document: 7. Distances and moving coordinate axes. 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
