Spacetime diagrams
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What follows next is an article that I posted to the sci.physics.relativity newsgroup in August, 1998. Dealing with the fascinating but elusive special theory of relativity, the text below demonstrates, in my opinion, that not all is well in the realm of Einstein's relativity. This shouldn't really be a surprise, since from the outset the special theory has been surrounded with an atmosphere of controversy and dispute. The reaction of established science to this is usually one of mockery and condescending comment about those who "just don't understand this simple theory". One must however distinguish between simple and easy. Simple the special theory may be, intuitively applying it to our world of experience is not easy and it is probably true that in trying to do so one is liable to device constructions incompatible with the second postulate (of SR). Established science, fully embracing Einsteins exposition, has, as far as I know, been challenged only by people forwarding erroneous arguments while remaining insensitive to the criticism of established science. My posting has received no comment, let alone criticism,
so I can only assume it to be correct. I am quite aware of the fact that many people claim that their "revolutionary" theories remain unchallenged by established science, also when this is not the case (in other words:they are lying), but this can't keep me from expressing my views in all sincerity. I do not however, claim my view to be revolutionary, since I don't dispute what can be seen as "the outcome" of special relativity, namely the Lorentz transformations. Although I think I am correct, I don't claim to possess absolute wisdom either and appreciate your comment and criticism.
I would like to point your attention towards some mistakes frequently made in established (special) relativity textbooks. One of the most popular ones will be a statement of the kind: "....A is running to meet the (light) signal pulse whereas C is running away from it."
Strictly speaking this is wrong because this defies the second postulate. The principle of relativity doesn't apply to the relationship between observers and observables on the one hand and the propagation of light on the other. If it did, then it would be fair to say that an object can be regarded as traveling at the speed of light, with "light stationary". Therefore any object under consideration must be regarded as stationary with respect to the propagation of light, which means that it is not possible to "run to meet" a lightsignal.
 I have included a "low K" picture from a well-known textbook, which shows how one can come to the misconception described above. The picture shows the x- and t-axes from frame K together with the worldlines of points A',B' and C' (which are stationary in K') as seen from K. It certainly looks as if A' is running to meet the light pulse from B, but it doesn't if you set up a complete spacetime diagram, that is with the x'-axis included. The picture below only shows lines parallel to the t'-axis.
Summarizing, I think it is fair to say that Einstein was a man of genius in spite of, or maybe because he was able to be right without being absolutely precise. Furthermore I propose that anything that looks like a spacetime diagram should include an even number of axes (x,t,x' and t' , for two observers with relative non-zero velocity), and that diagrams as below be removed from the literature. It is a shame that the more instructive an SR-textbook is, the more mistakes it generally contains. The author that sticks to deriving the Lorentz transformations is far less likely to go wrong, but that provides a rather slim intuitive basis for the undergraduate student. In the practice of interpreting and illustrating the Lorentz transformations, relativity-texts are still a messy business, depriving the student of, indeed, the beauty of relativity.
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