The Fabric of the Cosmos: Space, Time, and the Texture of Reality (9 page)

At this point you might think we've reached the end of the bucket story, with Mach's ideas having been discredited and Einstein's radical updating of Newton's absolute conceptions of space and time having won the day. The truth, though, is more subtle and more interesting. But if you're new to the ideas we've covered so far, you may need a break before pressing on to the last sections of this chapter. In Table 3.1 you'll find a summary to refresh your memory when you've geared up to reengage.

Okay. If you're reading these words, I gather you're ready for the next major step in spacetime's story, a step catalyzed in large part by none other than Ernst Mach. Although special relativity, unlike Mach's theory, concludes that even in an otherwise empty universe you would feel pressed against the inside wall of a spinning bucket and that the rope tied between two twirling rocks would pull taut, Einstein remained deeply fascinated by Mach's ideas. He realized, however, that serious consideration of these ideas required significantly extending them. Mach never really specified a mechanism whereby distant stars and other matter in the universe might play a role in how strongly your arms splay outward when you spin or how forcefully you feel pressed against the inner wall of a spinning bucket. Einstein began to suspect that if there were such a mechanism it might have something to do with gravity.

This realization had a particular allure for Einstein because in special relativity, to keep the analysis tractable, he had completely ignored gravity.

Maybe, he speculated, a more robust theory, which embraced both special relativity and gravity, would come to a different conclusion regarding Mach's ideas. Maybe, he surmised, a generalization of special relativity that incorporated gravity would show that matter, both near and far, determines the force we feel when we accelerate.

Einstein also had a second, somewhat more pressing, reason for turning his attention to gravity. He realized that special relativity, with its central dictum that the speed of light is the fastest that anything or any disturbance can travel, was in direct conflict with Newton's universal law of gravity, the monumental achievement that had for over two hundred years predicted with fantastic precision the motion of the moon, the planets, comets, and all things tossed skyward. The experimental success of Newton's law notwithstanding, Einstein realized that according to Newton, gravity exerts its influence from place to place, from the sun to the earth, from the earth to the moon, from any-here to any-there, instantaneously, in no time at all,
much faster than light.
And that directly contradicted special relativity.

To illustrate the contradiction, imagine you've had a really disappointing evening (hometown ball club lost, no one remembered your birthday, someone ate the last chunk of Velveeta) and need a little time alone, so you take the family skiff out for some relaxing midnight boating. With the moon overhead, the water is at high tide (it's the moon's gravity pulling up on bodies of water that creates the tides), and beautiful moonlight reflections dance on its waving surface. But then, as if your night hadn't already been irritating enough, hostile aliens zap the moon and beam it clear across to the other side of the galaxy. Now, certainly, the moon's sudden disappearance would be odd, but if Newton's law of gravity was right, the episode would demonstrate something odder still. Newton's law predicts that the water would start to recede from high tide, because of the loss of the moon's gravitational pull, about a second and a half
before
you saw the moon disappear from the sky.
Like a sprinter
jumping the gun, the water would seem to retreat a second and a half
too soon.

The reason is that, according to Newton, at the very moment the moon disappears its gravitational pull would
instantaneously
disappear too, and without the moon's gravity, the tides would immediately start to diminish. Yet, since it takes light a second and a half to travel the quarter million miles between the moon and the earth, you wouldn't immediately see that the moon had disappeared; for a second and a half, it would seem that the tides were receding from a moon that was still shining high overhead as usual. Thus, according to Newton's approach, gravity can affect us before light—gravity can outrun light—and this, Einstein felt certain, was wrong.
¹²

And so, around 1907, Einstein became obsessed with the goal of formulating a new theory of gravity, one that would be at least as accurate as Newton's but would not conflict with the special theory of relativity. This turned out to be a challenge beyond all others. Einstein's formidable intellect had finally met its match. His notebook from this period is filled with half-formulated ideas, near misses in which small errors resulted in long wanderings down spurious paths, and exclamations that he had cracked the problem only to realize shortly afterward that he'd made another mistake. Finally, by 1915, Einstein emerged into the light. Although Einstein did have help at critical junctures, most notably from the mathematician Marcel Grossmann, the discovery of
general relativity
was the rare heroic struggle of a single mind to master the universe. The result is the crowning jewel of pre-quantum physics.

Einstein's journey toward general relativity began with a key question that Newton, rather sheepishly, had sidestepped two centuries earlier. How does gravity exert its influence over immense stretches of space? How does the vastly distant sun affect earth's motion? The sun doesn't touch the earth, so how does it do that? In short, how does gravity get the job done? Although Newton discovered an equation that described the effect of gravity with great accuracy, he fully recognized that he had left unanswered the important question of how gravity actually works. In his
Principia,
Newton wryly wrote, "I leave this problem to the consideration of the reader."
¹³
As you can see, there is a similarity between this problem and the one Faraday and Maxwell solved in the 1800s, using the idea of a magnetic field, regarding the way a magnet exerts influence on things that it doesn't literally touch. So you might suggest a similar answer: gravity exerts its influence by another field, the gravitational field. And, broadly speaking, this is the right suggestion. But realizing this answer in a manner that does not conflict with special relativity is easier said than done.

Much easier. It was this task to which Einstein boldly dedicated himself, and with the dazzling framework he developed after close to a decade of searching in the dark, Einstein overthrew Newton's revered theory of gravity. What is equally dazzling, the story comes full circle because Einstein's key breakthrough was tightly linked to the very issue Newton highlighted with the bucket: What is the true nature of accelerated motion?

In special relativity, Einstein's main focus was on observers who move with constant velocity—observers who feel no motion and hence are all justified in proclaiming that they are stationary and that the rest of the world moves by them. Itchy, Scratchy, and Apu on the train do not feel any motion. From their perspective, it's Martin and everyone else on the platform who are moving. Martin also feels no motion. To him, it's the train and its passengers that are in motion. Neither perspective is more correct than the other. But accelerated motion is different, because you
can
feel it. You feel squeezed back into a car seat as it accelerates forward, you feel pushed sideways as a train rounds a sharp bend, you feel pressed against the floor of an elevator that accelerates upward.

Nevertheless, the forces you'd feel struck Einstein as very familiar. As you approach a sharp bend, for example, your body tightens as you brace for the sideways push, because the impending force is inevitable. There is no way to shield yourself from its influence. The only way to avoid the force is to change your plans and not take the bend. This rang a loud bell for Einstein. He recognized that exactly the same features characterize the gravitational force. If you're standing on planet earth you are subject to planet earth's gravitational pull. It's inevitable. There is no way around it. While you can shield yourself from electromagnetic and nuclear forces, there is no way to shield yourself from gravity. And one day in 1907, Einstein realized that this was no mere analogy. In one of those flashes of insight that scientists spend a lifetime longing for, Einstein realized that gravity and accelerated motion are two sides of the same coin.

Just as by changing your planned motion (to avoid accelerating) you can avoid feeling squeezed back in your car seat or feeling pushed sideways on the train, Einstein understood that by suitably changing your motion you can also avoid feeling the usual sensations associated with gravity's pull. The idea is wonderfully simple. To understand it, imagine that Barney is desperately trying to win the Springfield Challenge, a monthlong competition among all belt-size-challenged males to see who can shed the greatest number of inches. But after two weeks on a liquid diet (Duff Beer), when he still has an obstructed view of the bathroom scale, he loses all hope. And so, in a fit of frustration, with the scale stuck to his feet, he leaps from the bathroom window. On his way down, just before plummeting into his neighbor's pool, Barney looks at the scale's reading and what does he see? Well, Einstein was the first person to realize, and realize fully, that Barney will see the scale's reading drop to zero. The scale falls at exactly the same rate as Barney does, so his feet don't press against it at all.
In free fall, Barney experiences the same weightlessnessthat astronauts experience in outer space.

Indeed, if we imagine that Barney jumps out his window into a large shaft from which all air has been evacuated, then on his way down not only would air resistance be eliminated, but because every atom of his body would be falling at exactly the same rate, all the usual external bodily stresses and strains—his feet pushing up against his ankles, his legs pushing into his hips, his arms pulling down on his shoulders—would be eliminated as well.
¹⁴
By closing his eyes during the descent, Barney would feel exactly what he would if he were floating in the darkness of deep space. (And, again, in case you're happier with nonhuman examples: if you drop two rocks tied by a rope into the evacuated shaft, the rope will remain slack, just as it would if the rocks were floating in outer space.) Thus, by changing his state of motion—by fully "giving in to gravity"— Barney is able to simulate a gravity-free environment. (As a matter of fact, NASA trains astronauts for the gravity-free environment of outer space by having them ride in a modified 707 airplane, nicknamed the
Vomit
Comet,
that periodically goes into a state of free fall toward earth.)

Similarly, by a suitable change in motion you can create a force that is essentially identical to gravity. For example, imagine that Barney joins astronauts floating weightless in their space capsule, with the bathroom scale still stuck to his feet and still reading zero. If the capsule should fire up its boosters and accelerate, things will change significantly. Barney will feel pressed to the capsule's floor, just as you feel pressed to the floor of an upward accelerating elevator. And since Barney's feet are now pressing against the scale, its reading is no longer zero. If the captain fires the boosters with just the right oomph, the reading on the scale will agree precisely with what Barney saw in the bathroom. Through appropriate acceleration, Barney is now experiencing a force that is indistinguishable from gravity.

The same is true of other kinds of accelerated motion. Should Barney join Homer in the outer space bucket, and, as the bucket spins, stand at a right angle to Homer—feet and scale against the inner bucket wall—the scale will register a nonzero reading since his feet will press against it. If the bucket spins at just the right rate, the scale will give the same reading Barney found earlier in the bathroom: the acceleration of the spinning bucket can also simulate earth's gravity.

All this led Einstein to conclude that the force one feels from gravity and the force one feels from acceleration are the same. They are equivalent. Einstein called this the
principle of equivalence.

Take a look at what it means. Right now you feel gravity's influence. If you are standing, your feet feel the floor supporting your weight. If you are sitting, you feel the support somewhere else. And unless you are reading in a plane or a car, you probably also think that you are stationary—that you are not accelerating or even moving at all. But according to Einstein you actually are accelerating. Since you're sitting still this sounds a little silly, but don't forget to ask the usual question: Accelerating according to what benchmark? Accelerating from whose viewpoint?

With special relativity, Einstein proclaimed that absolute spacetime provides the benchmark, but special relativity does not take account of gravity. Then, through the equivalence principle, Einstein supplied a more robust benchmark that does include the effects of gravity. And this entailed a radical change in perspective.
Since gravity and acceleration
are equivalent, if you feel gravity's influence, you must be accelerating.
Einstein argued that only those observers who feel no force at all—including the force of gravity—are justified in declaring that they are not accelerating. Such force-free observers provide the true reference points for discussing motion, and it's this recognition that requires a major turnabout in the way we usually think about such things. When Barney jumps from his window into the evacuated shaft, we would ordinarily describe him as accelerating down toward the earth's surface. But this is not a description Einstein would agree with. According to Einstein, Barney is
not
accelerating.
He
feels no force.
He
is weightless.
He
feels as he would floating in the deep darkness of empty space.
He
provides the standard against which all motion should be compared. And by this comparison, when you are calmly reading at home,
you
are accelerating. From Barney's perspective as he freely falls by your window—the perspective, according to Einstein, of a true benchmark for motion—you and the earth and all the other things we usually think of as stationary are
accelerating upward.
Einstein would argue that it was Newton's head that rushed up to meet the apple, not the other way around.

Clearly, this is a radically different way of thinking about motion. But it's anchored in the simple recognition that you feel gravity's influence only when you resist it. By contrast, when you fully give in to gravity you don't feel it. Assuming you are not subject to any other influences (such as air resistance), when you give in to gravity and allow yourself to fall freely, you feel as you would if you were freely floating in empty space—a perspective which, unhesitatingly, we consider to be unaccelerated.

In sum, only those individuals who are freely floating, regardless of whether they are in the depths of outer space or on a collision course with the earth's surface, are justified in claiming that they are experiencing no acceleration. If you pass by such an observer and there is relative acceleration between the two of you, then according to Einstein,
you
are accelerating.

As a matter of fact, notice that neither Itchy, nor Scratchy, nor Apu, nor Martin was truly justified in saying that he was stationary during the duel, since they all felt the downward pull of gravity. This has no bearing on our earlier discussion, because there, we were concerned only with horizontal motion, motion that was unaffected by the vertical gravity experienced by all participants. But as an important point of principle, the link Einstein found between gravity and acceleration means, once again, that we are justified only in considering stationary those observers who feel
no
forces whatsoever.

Having forged the link between gravity and acceleration, Einstein was now ready to take up Newton's challenge and seek an explanation of how gravity exerts its influence.