10 - Time dilation and length contraction

Summary

Einstein concentrated on changing the traditional notions of absolute space and absolute time, replacing them by one absolute: the speed of light.

Anthony J. Adams, Wesley an '91, essay in Physics 104, fall 1988.

Time dilation

The relativity of simultaneity tells us that observers in different frames of reference may disagree on the time interval between two events. One observer may find the time interval to be zero and hence the events to be simultaneous; another may not.

Let us try to make the comparison of time intervals more quantitative. We suppose that Alice is baking brownies. She puts the tray in the oven and sets the timer for 30 minutes. This is the first event. When the timer rings, Alice takes out the brownies; that is the second event. For Alice, the time interval between the two events is 30 minutes, and the events occur at the same location: the oven, stationary in her frame.

As in chapter 9, Alice moves with speed ν relative to Bob, and so do the oven and brownies. What time interval between the two events does Bob perceive?

To answer the question, we need somehow to introduce light, for all that we are sure of is that both Alice and Bob always measure the speed of light to be c, 3x 10⁸ meters/second. So let us imagine a mirror on the ceiling over the oven, as sketched in figure 10.1.