ABSTRACT

At this point it is important to keep in mind the meaning of the symbols (x, t), (x ′, t′), (x′′, t′′),…as relative measures, in the sense of using different calibrations in the relatively moving frames of reference. These coordinate notations do not at all refer to physical properties other than their use in facilitating a description of the latter. In the Lorentz transformation formulas above, x′ stands for an abstract spatial coordinate used by one observer, in her own frame of reference, relative to some convenient point in that reference frame, such as her telescope at the site of a rocket launching pad. On the other hand, x is a spatial coordinate determined by the same observer but in a different frame of reference, for example the rocket ship —as the observer watches it travel away from her at the speed v. Similarly, t′ stands for the observer’s time measure, calibrated with reference to some physical clock in her own frame, say her wrist watch, while t stands for her

measure of the time passing in the moving frame of reference (the rocket ship). In classical physics, the latter two time measures would be the same; in relativity physics they are not, . The coordinates (x, t) and (x′, t′) of the relatively moving reference frames (the launch pad and the rocket) are both defined from the given observer’s point of reference-whichever frame is chosen for this is strictly arbitrary. That is to say, we assumed above that the observer (on the launch pad) is the stationary one. But we could have equally represented the frame of the rocket as stationary, with the launch pad moving relative to it (backwards) at −v cm/sec, in all of the transformation formulae above. According to the principle of relativity, such an alteration should not change the forms of the laws of nature-be they expressed from the reference frame of either the launch pad or the rocket.