1 1 Ne an mc in thi tic Special do ur Relativity ce sp Space and Time sp veryone knows that we move in time. at the rate of 24 hours per day. And everyone Eknows that we can move through space. at rates ranging from a snails pace to those of super- sonic aircraft and space shuttles. But relam eh few people know that motion through space is related to motion in time. Space and time are related. The first person to understand the relationship between space and time was Albert Einstein.* Einstein went beyond common sense when he stated in 1905 that in moving through space we also change our rate of proceeding into the future—time itself is altered This view was introduced to the world in his special theory of relativity. This theory describes how time is affected by motion in space at constant velocity, and how mass and energy are related. Ten years later Einstein announced a similar theory, called the general theory of relativity, which encompasses accelerated motion as well. These theories have enormously changed the way scientists view the work- ings of the universe. This book discusses only the special theory and leaves the general theory for follow-up study later in your education. This chapter will serve merely to acquaint you with the basic ideas of special relativity as they relate to space and time. Chapter 16 will continue with the relationship between mass and energy. These ideas, for the most part, are not common to your everyday experi- ence. As a result, they don't agree with common sense. So please be patient -will: yoursolf At you fiod that you do nui -lind,,,— ,d- Perhaps your children or grandchildren will find them very much a part of their everyday experience. If so, they should find an under- standing of relativity considerably less difficult. " The concerns of Albert Einstein (1879-1955) were not limited to physics. As a German citizen in Nazi Germany he spoke out against Hitler's racial and political policies, which prompted his resignation from the University of Berlin. He fled Germany in 1933 and became an American citizen in 1940. 212 Chapter 15 Special Relativity—Space and Time rrrerrrwrwri 15.1 Space-Time Newton and other investigators before Einstein thought of space as an infinite expanse in which all things exist. We are in space, and we move about in space. It was never clear whether the universe exists in space, or space exists within the universe. Is there space outside the universe? Or is space only within the universe? The same ques- tion could be raised for time. Does the universe exist in time, or does time exist only within the universe? Was there time before the ;Jr:lye:caeca= to be? Will-there Le rime if arid ;A:licit ullivcrac ceases to exist? Einstein's answer to these questions is that both space and time exist only within the universe. There is no time or space "outside." Figure 15.1 The universe does not exist in a certain part of infinite space, nor does it exist during a certain ne era in time. It is the other way , at around: space and time exist wer- within the universe. y few lated , ace iense lange is thy. it ars eory iese work- y and .ation. ;lc )ter 16 [hese eri- se be Einstein reasoned that space and time are two parts of one em. whole called space-time. To begin to understand this, consider your ach a present knowledge that you are moving through time at the rate of der- 24 hours per day. This is only half the story. To get the other half, convert your thinking from "moving through time" to "moving through space-time." From the viewpoint of special relativity, you travel through a combination of space and time. You travel through German space-time. When you stand still, then all your traveling is through as, which time. When you move a bit, then some of your travel is through 33 and spac-e and most of it is still through time. If you were somehow able to travel through space at the speed of light, what changes would you experience in time? The answer is that all your traveling would be through space, with no travel through time! You would be as age- less as light, for light travels through space only (not time) and is timeless. From the frame of reference of a photon traveling from one part of the universe to another, the journey takes no time at all! Motion in space affects motion in time. Whenever we move through space, we to some degree alter our rate of moving into the future. This is time dilation, a stretching of time that occurs ever so slightly for everyday speeds, but significantly for speeds approaching the speed of light. If spacecraft of the future reach sufficient speed, people will be able to travel noticeably in time. They will be able to jump centuries ahead, just as today people can jump from Earth to . M•1•11. Figure 15.2 A the moon. To understand time dilation and how this can be, you first When you stand still, you are need to understand several ideas: the relativity of motion and the traveling at the maximum rate in time: 24 hours per day. If you fundamental assumptions (postulates) of special relativity traveled at the maximum rate through space (the speed of light), time would stand still. 15.2 Motion Is Relative Recall from Chapter 2 that whenever we discuss motion, we must specify the position from which the motion is being observed and measured. For example, you may walk along the aisle of a moving frit: bus at a speed of 1 km/h relative to your seat, but at 100 km/h rela- at a; tive to the road outside. Speed is a relative quantity. Its value min depends upon the place—the frame of reference—where it is the observed and measured. An object may have different speeds rela- thai tive to different frames of reference. Suppose your friend always pitches a baseball at the same speed and of 60 km/h. Neglecting air resistance and other small effects, the ball this is moving at 60 km/h when you catch it. Now suppose your friend relz pitches the ball to you from the flatbed of a truck that moves toward you at 40 km/h. How fast does the ball meet you? You'll have to be sure to wear a catcher's mitt, because the speed of the ball will be 100 km/h (the 60 km/h relative to the truck plus the 40 km/h relative Figure 15.3 A 11 The bag of groceries has an to the ground). Speed is relative. appreciable speed in the frame of reference of the building, but Su. in the frame of reference ot the in freely falling elevator it has no tio speed at all. 60 an ca all sp in re Figure 15.4 A Your speed is 1 km/h relative to your seat, and 100 km/h relative to the road. 214 Chapter 15 Special Relativity—Space and Time 4 Figure 15.5 The ball is always pitched at 60 km/h relative to the truck. (a) When both you and the truck are at relative rest the ball is TRUCK AT REST traveling at 60 km/h when you catch it. (b) When the truck moves toward you at 40 km/h, the ball is traveling at 100 km/h when you catch it. (c) When the truck moves away from you at ; Artsvil," the same speed, the ball is travel- ing at 20 km/h when you catch it. TRUCK MOVES TOWARD YOU ASSIVINIrThres. TRUCK- MOVES 114,4Y ROM YOU Suppose the truck moves away from you at 4(1 km/h and your Mend again pitches the ball to you. This time you will need no glove at all, for the ball will reach you at a speed nt 3) km :h (since 60 km/h minus 40 km/h is 20 km/h,. This is not surprising, for you expect that the ball will be traveling faster when the truck approaches you and that the ball will be traveling more slowly when the truck recedes. The idea that speed is a relative quantity goes back to Galileo and was known lOng before the time of Einstein. As you will learn in this chapter, Einstein expanded the relativity of speed to include the relativity of things that seem unchangeable. 15.3 The Speed of Light Is Constant Suppose you actually caught baseballs thrown off a moving truck out in a parking lot and found that no matter what the speed or direc- tion Lilo 'truck, the Lmill 14/,1,3 - - 60 km/h. That is to say, if the truck zoomed toward you at 50 km/h and your friend pitched the ball at his speed of 60 km/h, you would catch the ball with the same speed as if the truck were not moving at all. Furthermore, if the truck moved away from you at whatever speed, the ball would still get to you at 60 km/h. This all seems quite impossible, for it is contrary to common experience. And if you did experience this, you would have to reevaluate your whole notion of reality To put it mildly, you would be quite confused. Baseballs do not behave this way. But it turns out that light does! Every measurement of the speed of light in empty space gives the 215 same value of 300 000 km/s, regardless of the speed of the smiit the speed of the receiver.*We do not ordinarily notice this beea light travels so incredibly fast.