Simple Nature - Light and Matter

system, velocities are always unitless. This sort of thing happensfrequently in physics. For instance, before James Joule discoveredconservation of energy, nobody knew that heat and mechanical energywere different forms of the same thing, so instead of measuringthem both in units of joules as we would do now, they measuredheat in one unit (such as calories) and mechanical energy in another(such as foot-pounds). In ordinary metric units, we just need anextra conversion factor c, and the equation becomes1γ = √1 − ( ).v 2ck / The γ factor.Here’s why we care about γ. Figure k defines it as the ratio of twotimes: the time between two events as expressed in one coordinatesystem, and the time between the same two events as measured inthe other one. The interpretation is:Time dilationA clock runs fastest in the frame of reference of an observerwho is at rest relative to the clock. An observer in motionrelative to the clock at speed v perceives the clock as runningmore slowly by a factor of γ.l / The ruler is moving in frame1, represented by a square, butat rest in frame 2, shown as aparallelogram. Each picture ofthe ruler is a snapshot takenat a certain moment as judgedaccording to frame 2’s notionof simultaneity. An observer inframe 1 judges the ruler’s lengthinstead according to frame 1’sdefinition of simultaneity, i.e.,using points that are lined upvertically on the graph. The rulerappears shorter in the frame inwhich it is moving. As provedin figure m, the length contractsfrom L to L/γ.m / This figure proves, as claimed in figure l, that the length contractionis x = 1/γ. First we slice the parallelogram vertically like a salamiand slide the slices down, making the top and bottom edges horizontal.Then we do the same in the horizontal direction, forming a rectangle withsides γ and x. Since both the Lorentz transformation and the slicingprocesses leave areas unchanged, the area γx of the rectangle mustequal the area of the original square, which is 1.As proved in figures l and m, lengths are also distorted:Length contractionA meter-stick appears longest to an observer who is at restrelative to it. An observer moving relative to the meter-stickat v observes the stick to be shortened by a factor of γ.self-check AWhat is γ when v = 0? What does this mean? ⊲ Answer, p. 924390 Chapter 7 Relativity