Elementary relativity with 'everyday' clock synchronization

Abstract

Although the importance of clock synchronization for relativity is discussed from time to time in the educational literature, the fact that different synchronization conventions imply different coordinizations of spacetime with ensuing changes of the form of possibly all coordinate-dependent quantities, has neither entered textbooks nor undergraduate physics education. As a consequence, there is a widespread belief among students that the familiar form of coordinate-dependent quantities like the measured velocity of light, the Lorentz transformation between two observers, 'addition of velocities', 'time dilation', 'length contraction', 'E=mc2 gamma ', which they assume under the standard clock synchronization, is relatively proper. In order to demonstrate that this is by no means so, the paper studies the consequences of a non-standard synchronization, and it is shown that drastic changes in the appearance of all these quantities are thus induced. For example, the phrases 'moving clocks go slow', and 'simultaneity is relative', which are usually considered as intrinsic features of relativity, turn out to be no longer true, whereas all coordinate-independent quantities remain of course indifferent to such a change in coordinization. Although Einstein's standard convention of clock synchronization enjoys distinct advantages over the 'everyday' method, the message clearly conveyed is that in the teaching of elementary relativity much more stress should be laid on the intrinsic (coordinate-independent) features of spacetime.