Spacetime and Gravity LEARNING GOALS 53.1 Einstein's 5econd Revolution 53.4 Testing General Relativity • What are the major ideas of • How do we test the predictions general relativity? of the general theory of relativity? • Is all motion relative? • What are gravitational waves? 53.2 Understanding 5pacetime 53.5 Hyperspace, Wormholes, • What is spacetime? and Warp Drive • What is curved spacetime? • Where does science end and science 53.3 A New View of Gravity fiction begin? • What is gravity? • What is a black hole? • How does gravity affect time? ~i?A The eternal mystery of the world is its comprehensibility. The fact that it is comprehensible is a miracle. Albert Einstein hat is gravity! Newton considered gravity to be a mysterious force that somehow reaches W across vast distances of space to hold the Moon in orbit around Earth and the planets in orbit around the Sun. His law of gravity explained the actions and conse­ a Travelers goi ng in opposite b Two space probes launched quences of this mysterious force but said nothing about directions along paths that are in opposite di rections in Earth how the force is transmitted through space. as straight as possibl e will meet orbit will meet as they orbit Einstein removed the mystery of how gravity acts at a as they go around the Earth, a Earth. a fact that we usuailly distance. As he extended his theory of relativity, Einstein fact that we attribute to the attribute to the mysterious curvature of Earth's su rface. fo rce of gravity. found that he could explain gravity in terms of the struc­ ture of space and time. In his view, the orbits of the Moon Figure 53 .1 Travelers on Earth's surface and orbiting objects follow similar-shaped paths. but we usually explain these paths in and the planets are as natural as motion in a straight line. very different ways. As we investigate Einstein's revolutionary view of grav­ ity, we will see that the consequences of his discoveries abound in astronomy and explain phenomena ranging from posite directions and neither has ever fired its engines, the the peculiar orbit of Mercury to black holes. We will probes have somehow met. This might at first sound sur­ also see how space and time merge into a four-dimensional prising, but in fact this situation arises quite naturally with spacetime that determines the overall structure of the orbiting objects. If you launch two probes in opposite di­ universe. rections from a space station, they will meet as they orbit Earth (Figure S3. 1b). Since the time of Newton, we've generally explained 53.1 Einstein's Second the curved paths of the two probes as an effect caused by the Revolution force of gravity. However, by analogy with the explorers journeying in opposite directions on Earth, might we in­ Imagine that you and everyone around you believe the Earth stead conclude that the probes meet because space is some­ to be flat. As a wealthy patron of the sciences, you decide to how curved? The idea that space could be curved certainly sponsor an ex pedition to the far reaches of the world. You sounds strange at first. While it's easy to visualize a surface select two fearless explorers and give them careful instruc­ curving through space, our minds cannot visualize three­ tions. Each is to journey along a perfectl y straight path, but dimensional space itself as being curved. The idea that they are to travel in opposite directions. You provide each space can be curved lies at the heart of Einstein's second with a caravan for land-based travel and boats for water revolution-a revolutio nary view of gravity contained in crossings, and you tell each to turn back only after discov­ his general th eory of relativity, published in 1915. ering "something ex traordinary." Some time later, the two explorers return. You ask, "Did • What are the major ideas you discover something extraordinary?" To your surprise, they answer in unison, "Yes, but we both discovered the of general relativity? same thing: We ran into each other, despite having traveled Recall that the special theory of relativity applies only to in opposite directions along perfectly straight paths." situations in which we are not concerned with the effects Although this outcome would be extraordinarily sur­ of gravity. From this theory, we already know that space prising if you truly believed the Earth to be flat, we are not and time are inextricably linked. More specifically, special really surprised because we know that Earth is ro und (Fig­ relativity tells us that the three dimensions of space and the ure S3.1a) . In a sense, the explorers followed the straightest one dimension of time together form an inseparable,four­ possible paths, but these "straight" lines follow the curved dimensional combination called spacetime. When Einstein surface of the Earth. extended the theory of relativity to the general case that in­ Now let's consider a somewhat more modern scenario. cludes gravity, he discovered that matter shapes the "fabric" You are floating freely in a spaceship somewhere out in of spacetime in a manner analogous to the way heavy weights space. Hoping to learn more about space in your vicinity, distort a taut rubber sheet or trampoline (Figure S3.2). Of you launch two small probes along straight paths in oppo­ course, we cannot place weights "upon" spacetime because site directions. Each probe is equipped with a camera that all matter exists within spacetime, and we cannot visualize transmits pictures back to your spaceship. Imagine that, to distortions of spacetime. However, using a rubber sheet your astonishment, the probes one day transmit pictures as an analogy, we can begin to appreciate the principles of of each other! That is, although you launched them in op­ general relativity. chapter S3 • Spacetime and Gravity 435 you accelerating away, with your speed growing ever faster, so she sends you a radio message saying, "Good-bye, have .~~.~":- ......... .,...I'~.Y'!."!r.'!r .". ......,- • I ~I­ ,.. _. .' a nice trip!" . I . ...Lr~, I~ .. i I ·1 THINK ABOUT_IT .:, .' ~kg .~.. ... ...... f :. Suppose you start from rest in Jackie's re ference frame an d ~g j.' she se es you accelerate at Ig (= 9.8 m/s2). ApprOXimat ely ,." .. .. ~ - __ ~~~I~~.~ how fast w ill Jackie see you going after I second? After 10 sec ­ Figure 53.2 A rubber sh eet analogy to spacetime: Matter dis­ onds? A fter a minute? (Hint See Section 4. I t o review the torts the "fabric" of four- dimensiona l spacetime in a mann er analo­ meaning of acceleration.) gous to the w ay heavy weights distort a ta ut, two-dimensional r ub­ ber sheet The greater the mass. the greater the distortion of If all motion is relative, you should be free to claim that spacetime. you are still stationary and that it is Jackie who is receding into the distance at ever-faster speeds. You might therefore It is difficult to overstate the significance of general rela­ wish to reply: "Thanks, but I'm not going anywhere. You're tivity to our understanding of the universe. For example, the one accelerating into the distance." However, this situa­ the following ideas all come directly from Einstein's general tion has a new element that was not present when we dealt theory of relativity: with constant velocities: Because your rocket engines are firing, you feel a force inside your spaceship (Figure S3 .3). • Gravity arises from distortions of spacetime. It is not a In fact, because the engines are giving you an acceleration mysterious force that acts at a distance. The presence of of 1g, you'll feel a force holding you to the floor of your mass causes the distortions, and the resulting distortions spaceship that is the same as the force you fe el when you determine how other objects move through spacetime. stand on Earth's surface. In other words, you'll no longer be • Time runs slowly in gravitational fields. The stronger weightless but instead will be able to walk on the spaceship the gravity, the more slowly time runs. floor with your normal Earth weight Thus, Jackie may re­ • Black holes can exist in spacetime, and falling into a spond back: "Oh, yeah? If you're not going anywhere, why black hole means leaving the observable universe. are you stuck to the floor of your spaceship, and why do • The universe has no boundaries and no center, yet it you have your engines turned on? Furthermore, if I'm accel­ might still have a finite volume. erating, why am I weightless?" • Large masses that undergo rapid changes in motion or You must admit that Jackie is asking very good questions. structure emit gravitational waves that travel at the speed It certainly looks as if you really are the one who is acceler­ of light ating, in which case you cannot legitimately claim to be sta­ tionary. In other words, it seems that motion is no longer • Is all motion relative? relative when we introduce acceleration. This idea did not sit well with Einstein, because he believed that all motion Special relativity tells us that there is no single, absolute should be relative, regardless of whether the motion was answer to the question, "Who is moving?" when two people at constant velocity or included an acceleration. Einstein pass each other at a constant velocity in free-float frames. Each individual can claim to be at rest, and each claim is equally valid. However, the situation seems quite different if one of the reference frames is accelerating rather than F!fIny ,'(Jur ruckels Iilil ill:;u flJakes vou Iccl traveling at constant velocity.