Free The Elegant Universe by Brian Greene Page A

compensates for the slowness of her clock.” George’s realization that there are competing effects—the slowness of Gracie’s clock vs. the travel time of his signal—inspires him to sit down and quantitatively work out their combined effect. The result he finds is that the travel time effect more than compensates for the slowness of Gracie’s clock. He comes to the surprising conclusion that Gracie will receive his signals proclaiming the passing of an hour on his clock after the appointed hour has passed on hers. In fact, since George is aware of Gracie’s expertise in physics, he knows that she will take the signal’s travel time into account when drawing conclusions about his clock based on his cell phone communications. A little more calculation quantitatively shows that even taking the travel time into account, Gracie’s analysis of his signals will lead her to the conclusion that George’s clock ticks more slowly than hers.
    Exactly the same reasoning applies when we take Gracie’s perspective, with her sending out hourly signals to George. At first the slowness of George’s clock from her perspective leads her to think that he will receive her hourly messages prior to broadcasting his own. But when she takes into account the ever longer distances her signal must travel to catch George as he recedes into the darkness, she realizes that George will actually receive them after sending out his own. Once again, she realizes that even if George takes the travel time into account, he will conclude from Gracie’s cell phone communications that her clock is running slower than his.
    So long as neither George nor Gracie accelerates, their perspectives are on precisely equal footing. Even though it seems paradoxical, in this way they both realize that it is perfectly consistent for each to think the other’s clock is running slow.
    Motion’s Effect on Space
    The preceding discussion reveals that observers see moving clocks ticking more slowly than their own-that is, time is affected by motion. It is a short step to see that motion has an equally dramatic effect on space. Let’s return to Slim and Jim on the drag strip. While in the showroom, as we mentioned, Slim had carefully measured the length of his new car with a tape measure. As Slim is speeding along the drag strip, Jim cannot apply this method to measure the length of the car, so he must proceed in an indirect manner. One such approach, as we indicated earlier, is this: Jim starts his stopwatch just when the front bumper of the car reaches him and stops it just as the rear bumper passes. By multiplying the elapsed time by the speed of the car, Jim can determine the car’s length.
    Using our newfound appreciation of the subtleties of time, we realize that from Slim’s perspective he is stationary while Jim is moving, and hence Slim sees Jim’s clock as running slow. As a result, Slim realizes that Jim’s indirect measurement of the car’s length will yield a shorter result than he measured in the showroom, since in Jim’s calculation (length equals speed multiplied by elapsed time) Jim measures the elapsed time on a watch that is running slow. If it runs slow, the elapsed time he finds will be less and the result of his calculation will be a shorter length.
    Thus Jim will perceive the length of Slim’s car, when it is in motion, to be less than its length when measured at rest. This is an example of the general phenomenon that observers perceive a moving object as being shortened along the direction of its motion. For instance, the equations of special relativity show that if an object is moving at about 98 percent of light speed, then a stationary observer will view it as being 80 percent shorter than if it were at rest. This phenomenon is illustrated in Figure 2.4.4
    Motion through Spacetime
    The constancy of the speed of light has resulted in a replacement of the traditional view of space and time as rigid and objective structures with a new