Top Document: Einstein (1905) Absurdities Previous Document: 7. Simultaneity and Measurement Prologue. Next Document: 9. The absolute simultaneity SR transforms. See reader questions & answers on this topic!  Help others by sharing your knowledge The SR transforms and the Galilean transforms both convert good, ratio scale data to inferior interval scale data. The effect is corrected, allowed for, when the transforms are conducted on the generalized coordinate forms specified by analytic geometry  and vector algebra, for that matter  but SR refuses to do it right. The consequence is the appearance that simultaneity does not hold across inertial frames, and the consequence of that is the Twins Paradox absurdity. Both sets of transforms are 'translations'  lateral movements of an axis, increasing over time in these caes  but with the SR transform also containing a rescaling. It is the translation term, vt in the x transform to x', and xv/cc in the t transform to t', that degrades the ratio scale data to interval scale data. SR likes to consider its transforms just rotations, however, and in the case of 'good' rotations, ratio scale data quality is indeed preserved, but SR violates the conditions of good rotations; they are not rigid rotations and they don't appropriately rescale all the axes that must be rescaled to preserve compati bility. The proof is in the pudding, and the pudding is the combination of simple tests of the transformations. We can tell if the transformed data are ratio scale or interval. Ratio scale data are like absolute Kelvin. A measure ment of zero means there is zero quantity of the stuff being measured. Ratio scale data support add ition, subtraction, multiplication, and division. The test of a ratio scale is that if one measure looks like twice as much as another, the stuff being measured is actually twice as much. With absolute Kelvin, 100 degrees really is twice the heat as 50 degrees. 200 degrees really is twice as much as 100. Interval scale data are like relative Celsius, which is why your science teacher wouldn't let you use it in gas law problems. There is only one mathematical operation interval scales support, and that has to be between two measures on the same scale: subtraction. 100 degrees relative (household) Celsius is not twice as much as 50; we have to convert the data to absolute Kelvin to tell us what the real ratio of termperatures is. However, whether we use absolute Kelvin or relative Celsius, the difference in the two temperature readings is the same: 50 degrees. Thus, if we know the real quantities of the 'stuff' being measured, we can tell if two measures are on a ratio scale by seeing if the ratio of the two measures is the same as the ratio of the known quant ities. If a scale passes the ratio test, the interval scale test is automatically a pass. If the scale fails the ratio test, the interval scale test becomes the next in line. It isn't just the bare differences on an interval scale that provides the test, however. Differences in two interval scale measures are ratio scale, so it is ratios of two differences that tell the tale. Let's do some testing, and remember as we do that our concern is for whether or not the data are messed up, not with 'reasons', excuses, or avoidance.  Are we going to take a transformed length and see whether that length fits ratio or interval scale definitions? Of course, not. Interval scale data are ratio after one measure is subtracted from another. That is the major reason the SR transforms can be used in science. Let there be three rods, A, B, C, of length 10, 20, 40, respectively. These lengths are on a known ratio scale, our original xaxis, with one end of each rod at the origin, where x=0, and the other end at the coordinate that tells us the correct lengths. Note that these xvalues are ratio scale only because one end of each rod is at x=0. That may remind you of the correct way to use a ruler or yard/meterstick: put the zero end at one end of the thing you are measuring. Put the one mark there instead of the zero, and you have interval scale measures. Let a,b,c be x' at v=.7071c, t=0. Let A',B',C' be x' at v=.7071c, t=10. g=sqrt(1(.7071)^2)=.7071. A B C a b c A' B' C'    10 20 40 14.14 28.28 56.57 4.14 18.28 46.57    B/A = 2 b/a = 2 B'/A' = 4.42 C/A = 4 c/a = 4 C'/A' = 11.25 C/B = 2 c/b = 2 C'/B' = 2.55 CA = 10 ba = 14.14 B'A' = 14.14 CA = 30 ca = 32.52 C'A' = 42.42 CB = 20 cb = 28.28 C'B' = 28.28 (CA)/(BA) = 3 (ca)/(ba) = 3 (C'A')/(B'A') = 3 (CB)/(BA) = 2 (cb)/(ba) = 2 (C'B')/(B'A') = 2. The results show that the primed data (a,b,c) are ratio scale as we'd expect since the vt term is zero. The ratios b/a, etc, are the same as the known ratio scale ratios, B/A, etc. When vt=0 the data are still ratio scale, but the rescaling is why the differences (ba, etc) are not the same as before transform. The simple ratios prove the data still ratio, and the ratios of differences [(ca)/(ba), etc] just support that finding. When vt<>0, the data (A',B',C') are no longer ratio scale, which is why the simple ratios now differ from both the original and vt=0 data. However, the ratios of differences show us that the data do satisfy the one mathematical operation of subtraction, the differences thus being shown to be ratio scale. If you do not understand that the above data table proves that the SR transforms did indeed degrade the ratio scale to interval scale, please study it until you understand.  If we remember that the only effect of gamma=g is to rescale the data, we realize that the above results and conclusions also apply to the galilean transform. As we said in the introduction of this Subject, use of the generalized cartesian coordinate form corrects the interval scale problem. Using this form for the galilean transformation upgrades the traditional, incompetent, noninvariant transform of laws/equations up to invariant (so to speak) invariance. To test the results of the use of the generalized cartesian coordinate form, with (xx0) instead of just (x), we can again let the SR version stand in for both the galilean and SR results. Here, our unprimed data were with x0=0. Let a,b,c be x' at v=.7071c, t=0. Let A',B',C' be x' at v=.7071c, t=10. g=sqrt(1(.7071)^2)=.7071. a'= b'= c'= A B C x0 (Ax0)' (Bx0)' (Cx0)' x0'   10 20 40 0 14.14 28.28 56.57 10   B/A = 2 b'/a' = 2 C/A = 4 c'/a' = 4 C/B = 2 c'/b' = 2 CA = 10 b'a' = 14.14 CA = 30 c'a' = 42.42 CB = 20 c'b' = 28.28 (CA)/(BA) = 3 (c'a')/(b'a') = 3 (CB)/(BA) = 2 (c'b')/(b'a') = 2. The above data table shows us that focusing on (xx0), instead of just plain x, will give us ratio scale data in any equation the transforms are applied to. Use of the generalized coordinate form verifies the interval nature of the transforms. Just as one x' subtracted from another on the same scale is a ratio scale result, just so does subtracting x0' from every x' create a ratio scale result. There is absolutely nothing about the SR transform derivation that says to not use the generalized coordinate form, absolutely nothing to gain by insisting  so to speak  on using interval scale data in your equations. To do so is absolutely absurd. Doing so is a sufficient cause of the obvious simultaneity problem of Special Relativity, which is itself the cause of the absurd Twins Paradox mess. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Einstein (1905) Absurdities Previous Document: 7. 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Last Update March 27 2014 @ 02:12 PM
