100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

12 J. Stachelupon by no (net) external forces moves in a straight line with constantvelocity with respect to an inertial frame of reference. o This equivalenceof all inertial frames has been called the relativity principle of Newtonianmechanics. There is a three-fold infinity of inertial frames, each of which isin a state of uniform motion with respect to all the others, and in each ofwhich Newton’s laws of mechanics are equally valid.With the abandonment of absolute space, the concept ‘at the same place’loses its absolute significance, and must be replaced by the concept ‘at thesame place relative to some inertial frame of reference.’ pIn summary, whether or not adherents of the mechanical worldviewwere aware of it, Newtonian mechanics properly understood does requirea universal or absolute concept of time, but leads to abandonment of theconcept of absolute position in favor of a concept of relative position withrespect to some reference frame, usually chosen to be inertial.The concepts of absolute time and relative space may be given operationalsignificance in terms of the measurement of temporal and spatialintervals with (ideal) measuring clocks and rods, respectively. For example,the temporal interval (’time’) between two events, as measured bytwo clocks is independent of the inertial frame of reference in which theclocks are at rest (and therefore, they need not both be at rest in the sameframe). On the other hand, the spatial interval (distance) between two nonsimultaneousevents, as measured by a rigid measuring rod for example, isnot absolute, but depends on the inertial frame of reference in which themeasuring rod is at rest. Since there is no preferred inertial frame of reference(no ‘absolute space’), none of these relative distances can claim thetitle of ‘the (absolute) distance’.For simultaneous events, of course, the distance between them is independentof the inertial frame in which the measuring rod is at rest: Itmakes no difference whether the rod is at rest or in motion relative to thetwo events. When one speaks of ‘the length’ of an extended object, what iso The phrase ‘with constant velocity’ implies that an appropriate definition of distantsimultaneity must be adopted when, as in the special theory of relativity, the conceptof absolute time is abandoned. When we come to consider gravitation, we shall have toexamine the phrase: ‘acted on by no (net) external forces’ more critically.p One might be tempted to generalize, and say: ‘with respect to any arbitrary frame ofreference’. But in both Galilei-Newtonian and special-relativistic theories, the inertialframes maintain their privileged role: The laws of physics take their simplest form whenexpressed relative to these frames – as long as gravitation is disregarded. As we shallsee, when gravitation is taken into account, the inertial frames lose their privileged roleeven in Galilei-Newtonian theory.