Special Relativity: Kinematics

Physics
Summary

Postulates and the Loss of Simultaneity

Summary Postulates and the Loss of Simultaneity

The Loss of Simultaneity

The most fundamental effect of the postulates of Special Relativity is to demonstrate that simultaneity (the notion of events occurring at the same time) is relative (dependent on frame of reference). This concept is best understood by way of example. Consider an observer OA standing equidistant between two light sources. OA has measured the distance to each source and found it to be lA. The sources each emit an instantaneous flash; the flashes reach OA at the same time, so he concludes that the flashes were emitted at the same time.

Now consider observer OB, moving past the sources and OA at speed v from the right (see ). In OB's rest frame (that is the reference frame in which OB is at rest) they see the sources whizzing past to the left at speed v. OB has measured the distance between the sources and found it to be 2lB, and also that OA is standing exactly half way between the sources (a distance lB from each). From OB's point of view, the light from the right source travels at a speed c (from our second postulate) with respect to OB, but with speed c + v with respect to the source. Similarly the light from the left source travels at a speed c - v with respect to its source. Thus the time the light takes to reach OA from the right source is tr = and from the left source it is tl = . If v 0, then these times are different, and OB concludes that the light emitted by the sources reached OA at different times and so the flashes could not possibly have been simultaneous.

Figure %: Observers in different reference frames have different concepts of simultaneity.

Thus the whole concept of 'things happening at the same time' is relative. One must specify a reference frame to say that events are simultaneous. This will have especially important consequences for the measurement of length. Different symbols are used for the distance measured by each observer between the sources because the distances are indeed different, as we will see in Section 3, but this is not important in the example above. Finally, it is important to point out that the different times taken for the light to reach OA in OB's frame has nothing to do with the time taken for light to reach an observers eye; rather the sources really emit their flashes at different time in OB's frame (his frame is just as good as OA's according to our first postulate). The time taken for light to reach an observer's eye will never be taken into consideration in this topic (it would be trivial to calculate them: simply add on an amount of time distance/c, but this just complicates things unnecessarily).