Simple Nature - Light and Matter

f / The correspondence principlerequires that the relativisticdistortion of time become smallfor small velocities.until section 7.4, and that means that what we want to focus onright now is the distortion of time due to motion, not gravity.We can now see in more detail how to apply the correspondenceprinciple. The behavior of the three clocks in the Hafele-Keatingexperiment shows that the amount of time distortion increases asthe speed of the clock’s motion increases. Newton lived in an erawhen the fastest mode of transportation was a galloping horse, andthe best pendulum clocks would accumulate errors of perhaps aminute over the course of several days. A horse is much slowerthan a jet plane, so the distortion of time would have had a relativesize of only ∼ 10 −15 — much smaller than the clocks were capableof detecting. At the speed of a passenger jet, the effect is about10 −12 , and state-of-the-art atomic clocks in 1971 were capable ofmeasuring that. A GPS satellite travels much faster than a jet airplane,and the effect on the satellite turns out to be ∼ 10 −10 . Thegeneral idea here is that all physical laws are approximations, andapproximations aren’t simply right or wrong in different situations.Approximations are better or worse in different situations, and thequestion is whether a particular approximation is good enough in agiven situation to serve a particular purpose. The faster the motion,the worse the Newtonian approximation of absolute time. Whetherthe approximation is good enough depends on what you’re tryingto accomplish. The correspondence principle says that the approximationmust have been good enough to explain all the experimentsdone in the centuries before Einstein came up with relativity.By the way, don’t get an inflated idea of the importance of theHafele-Keating experiment. Special relativity had already been confirmedby a vast and varied body of experiments decades before 1971.The only reason I’m giving such a prominent role to this experiment,which was actually more important as a test of general relativity, isthat it is conceptually very direct.7.2 Distortion of Space and Time7.2.1 The Lorentz transformationRelativity says that when two observers are in different frames ofreference, each observer considers the other one’s perception of timeto be distorted. We’ll also see that something similar happens totheir observations of distances, so both space and time are distorted.What exactly is this distortion? How do we even conceptualize it?The idea isn’t really as radical as it might seem at first. Wecan visualize the structure of space and time using a graph withposition and time on its axes. These graphs are familiar by now,but we’re going to look at them in a slightly different way. Before, weused them to describe the motion of objects. The grid underlyingthe graph was merely the stage on which the actors played their384 Chapter 7 Relativity