Read The Fabric of the Cosmos: Space, Time, and the Texture of Reality Online
Authors: Brian Greene
Tags: #Science, #Cosmology, #Popular works, #Astronomy, #Physics, #Universe
The Fabric of the Cosmos: Space, Time, and the Texture of Reality (7 page)
The relativity of space and of time is a startling conclusion. I have known about it for more than twenty-five years, but even so, whenever I quietly sit and think it through, I am amazed. From the well-worn statement that the speed of light is constant, we conclude that
space and time are in the eye
of the beholder.
Each of us carries our own clock, our own monitor of the passage of time. Each clock is equally precise, yet when we move relative to one another, these clocks do not agree. They fall out of synchronization; they measure different amounts of elapsed time between two chosen events. The same is true of distance. Each of us carries our own yardstick, our own monitor of distance in space. Each yardstick is equally precise, yet when we move relative to one another, these yardsticks do not agree; they measure different distances between the locations of two specified events. If space and time did not behave this way, the speed of light would not be constant and would depend on the observer's state of motion. But it
is
constant; space and time
do
behave this way. Space and time adjust themselves in an exactly compensating manner so that observations of light's speed yield the same result, regardless of the observer's velocity.
Getting the quantitative details of precisely how the measurements of space and time differ is more involved, but requires only high school algebra. It is not the depth of mathematics that makes Einstein's special relativity challenging. It is the degree to which the ideas are foreign and apparently inconsistent with our everyday experiences. But once Einstein had the key insight—the realization that he needed to break with the more than two-hundred-year-old Newtonian perspective on space and time—it was not hard to fill in the details. He was able to show precisely how one person's measurements of distances and durations must differ from those of another in order to ensure that each measures an identical value for the speed of light.
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To get a fuller sense of what Einstein found, imagine that Bart, with heavy heart, has carried out the mandatory retrofitting of his skateboard, which now has a maximum speed of 65 miles per hour. If he heads due north at top speed—reading, whistling, yawning, and occasionally glancing at the road—and then merges onto a highway pointing in a northeasterly direction, his speed in the northward direction will be
less
than 65 miles per hour. The reason is clear. Initially, all his speed was devoted to northward motion, but when he shifted direction some of that speed was diverted into eastward motion, leaving a little less for heading north. This extremely simple idea actually allows us to capture the core insight of special relativity. Here's how:
We are used to the fact that objects can move through space, but there is another kind of motion that is equally important: objects also move through time. Right now, the watch on your wrist and the clock on the wall are ticking away, showing that you and everything around you are relentlessly moving through time, relentlessly moving from one second to the next and the next. Newton thought that motion through time was totally separate from motion through space—he thought these two kinds of motion had nothing to do with each other. But Einstein found that they are intimately linked. In fact,
the
revolutionary discovery of special relativity is this: When you look at something like a parked car, which from your viewpoint is stationary—not moving through space, that is
—all
of its motion is through time. The car, its driver, the street, you, your clothes are all moving through time in perfect synch: second followed by second, ticking away uniformly. But if the car speeds away, some of its motion through time is
diverted
into motion through space. And just as Bart's speed in the northward direction slowed down when he diverted some of his northward motion into eastward motion, the speed of the car through
time
slows down when it diverts some of its motion through time into motion through
space.
This means that the car's progress through time slows down and therefore
time elapses more slowly for the moving car
and its driver than it elapses for you and everything else that remains stationary.
That, in a nutshell, is special relativity. In fact, we can be a bit more precise and take the description one step further. Because of the retrofitting, Bart had no choice but to limit his top speed to 65 miles per hour. This is important to the story, because if he sped up enough when he angled northeast, he could have compensated for the speed diversion and thereby maintained the same net speed toward the north. But with the retrofitting, no matter how hard he revved the skateboard's engine, his total speed—the combination of his speed toward the north and his speed toward the east—remained fixed at the maximum of 65 miles per hour. And so when he shifted his direction a bit toward the east, he necessarily caused a decreased northward speed.
Special relativity declares a similar law for all motion:
the combined
speed of any object's motion through space and its motion through time is
always precisely equal to the speed of light.
At first, you may instinctively recoil from this statement since we are all used to the idea that nothing but light can travel at light speed.
But that familiar idea refers solely to
motion through space.
We are now talking about something related, yet richer: an object's combined motion through space and time. The key fact, Einstein discovered, is that these two kinds of motion are always complementary. When the parked car you were looking at speeds away, what really happens is that some of its light-speed motion is diverted from motion through time into motion through space,
keeping their combined
total unchanged.
Such diversion unassailably means that the car's motion through time slows down.
As an example, if Lisa had been able to see Bart's watch as he sped along at 500 million miles per hour, she would have seen that it was ticking about two-thirds as fast as her own. For every three hours that passed on Lisa's watch, she would see that only two had passed on Bart's. His rapid motion through space would have proved a significant drain on his speed through time.
Moreover, the maximum speed through space is reached when all light-speed motion through time is fully diverted into light-speed motion through space—one way of understanding why it is impossible to go through space at greater than light speed. Light, which always travels at light speed through space, is special in that it always achieves such total diversion. And just as driving due east leaves no motion for traveling north, moving at light speed through space leaves no motion for traveling through time! Time stops when traveling at the speed of light through space. A watch worn by a particle of light would not tick at all. Light realizes the dreams of Ponce de León and the cosmetics industry: it doesn't age.
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As this description makes clear, the effects of special relativity are most pronounced when speeds (through space) are a significant fraction of light speed. But the unfamiliar, complementary nature of motion through space and time always applies. The lesser the speed, the smaller the deviation from prerelativity physics—from common sense, that is— but the deviation is still there, to be sure.
Truly. This is not dexterous wordplay, sleight of hand, or psychological illusion. This is how the universe works.
In 1971, Joseph Hafele and Richard Keating flew state-of-the-art cesium-beam atomic clocks around the world on a commercial Pan Am jet. When they compared the clocks flown on the plane with identical clocks left stationary on the ground, they found that less time had elapsed on the moving clocks. The difference was tiny—a few hundred billionths of a second—but it was precisely in accord with Einstein's discoveries. You can't get much more nuts-and-bolts than that.
In 1908, word began to spread that newer, more refined experiments were finding evidence for the aether.
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If that had been so, it would have meant that there was an absolute standard of rest and that Einstein's special relativity was wrong. On hearing this rumor, Einstein replied, "Subtle is the Lord, malicious He is not." Peering deeply into the workings of nature to tease out insights into space and time was a profound challenge, one that had gotten the better of everyone until Einstein. But to allow such a startling and beautiful theory to exist, and yet to make it irrelevant to the workings of the universe, that would be malicious. Einstein would have none of it; he dismissed the new experiments. His confidence was well placed. The experiments were ultimately shown to be wrong, and the luminiferous aether evaporated from scientific discourse.
This is certainly a tidy story for light. Theory and experiment agree that light needs no medium to carry its waves and that regardless of the motion of either the source of light or the person observing, its speed is fixed and unchanging. Every vantage point is on an equal footing with every other. There is no absolute or preferred standard of rest. Great. But what about the bucket?
Remember, while many viewed the luminiferous aether as the physical substance giving credibility to Newton's absolute space, it had nothing to do with
why
Newton introduced absolute space. Instead, after wrangling with accelerated motion such as the spinning bucket, Newton saw no option but to invoke some invisible background stuff with respect to which motion could be unambiguously defined. Doing away with the aether did not do away with the bucket, so how did Einstein and his special theory of relativity cope with the issue?
Well, truth be told, in special relativity, Einstein's main focus was on a special kind of motion: constant-velocity motion. It was not until 1915, some ten years later, that he fully came to grips with more general, accelerated motion, through his general theory of relativity. Even so, Einstein and others repeatedly considered the question of rotating motion using the insights of special relativity; they concluded, like Newton and unlike Mach, that even in an otherwise completely empty universe you would feel the outward pull from spinning—Homer would feel pressed against the inner wall of a spinning bucket; the rope between the two twirling rocks would pull taut.
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Having dismantled Newton's absolute space and absolute time, how did Einstein explain this?
The answer is surprising. Its name notwithstanding, Einstein's theory does not proclaim that everything is relative. Special relativity does claim that
some
things are relative: velocities are relative; distances across space are relative; durations of elapsed time are relative. But the theory actually introduces a grand, new, sweepingly absolute concept:
absolute spacetime.
Absolute spacetime is as absolute for special relativity as absolute space and absolute time were for Newton, and partly for this reason Einstein did not suggest or particularly like the name "relativity theory." Instead, he and other physicists suggested
invariance theory,
stressing that the theory, at its core, involves something that everyone agrees on, something that is not relative.
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Absolute spacetime is the vital next chapter in the story of the bucket, because, even if devoid of all material benchmarks for defining motion, the absolute spacetime of special relativity provides a something with respect to which objects can be said to accelerate.
To see this, imagine that Marge and Lisa, seeking some quality together-time, enroll in a Burns Institute extension course on urban renewal. For their first assignment, they are asked to redesign the street and avenue layout of Springfield, subject to two requirements: first, the street/avenue grid must be configured so that the Soaring Nuclear Monument is located right at the grid's center, at 5th Street and 5th Avenue, and, second, the designs must use streets 100 meters long, and avenues, which run perpendicular to streets, that are also 100 meters long. Just before class, Marge and Lisa compare their designs and realize that something is terribly wrong. After appropriately configuring her grid so that the Monument lies in the center, Marge finds that Kwik-E-Mart is at 8th Street and 5th Avenue and the nuclear power plant is at 3rd Street and 5th Avenue, as shown in Figure 3.2a. But in Lisa's design, the addresses are completely different: the Kwik-E-Mart is near the corner of 7th Street and 3rd Avenue, while the power plant is at 4th Street and 7th Avenue, as in Figure 3.2b. Clearly, someone has made a mistake.
After a moment's thought, though, Lisa realizes what's going on. There are no mistakes. She and Marge are both right. They merely chose different orientations for their street and avenue grids. Marge's streets and avenues run at an angle relative to Lisa's; their grids are rotated relative to each other; they have sliced up Springfield into streets and avenues in two different ways (see Figure 3.2c). The lesson here is simple, yet important. There is freedom in how Springfield—a region of space—can be organized by streets and avenues. There are no "absolute" streets or "absolute" avenues. Marge's choice is as valid as Lisa's—or any other possible orientation, for that matter.
Hold this idea in mind as we paint time into the picture. We are used to thinking about space as the arena of the universe, but physical processes occur in some region of space
during some interval of time.
As an example, imagine that Itchy and Scratchy are having a duel, as illustrated in Figure 3.3a, and the events are recorded moment by moment in the fashion of one of those old-time flip books. Each page is a "time slice"—like a still frame in a filmstrip—that shows what happened in a region of space at one moment of time. To see what happened at a different moment of time you flip to a different page.
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(Of course, space is three-dimensional while the pages are two-dimensional, but let's make this simplification for ease of thinking and drawing figures. It won't compromise any of our conclusions.) By way of terminology, a region of space considered over an interval of time is called a region of
spacetime;
you can think of a region of spacetime as a record of all things that happen in some region of space during a particular span of time.
Figure 3.2
(
a
)
Marge's street design.
(
b
)
Lisa's street design.
Figure 3.2
(
c
)
Overview of Marge's and Lisa's street/avenue designs. Their grids differ by a rotation.
Now, following the insight of Einstein's mathematics professor Hermann Minkowski (who once called his young student a lazy dog), consider the region of spacetime as an entity unto itself: consider the complete flip book as an object in its own right. To do so, imagine that, as in Figure 3.3b, we expand the binding of the flip-card book and then imagine that, as in Figure 3.3c, all the pages are completely transparent, so when you look at the book you see one continuous block containing all the events that happened during a given time interval. From this perspective, the pages should be thought of as simply providing a convenient way of organizing the content of the block—that is, of organizing the events of spacetime. Just as a street/avenue grid allows us to specify locations in a city easily, by giving their street and avenue address, the division of the spacetime block into pages allows us to easily specify an event (Itchy shooting his gun, Scratchy being hit, and so on) by giving the time when the event occurred—the page on which it appears—and the location within the region of space depicted on the pages.
Figure 3.3
(
a
)
Flip book of duel.
(
b
)
Flip book with expanded binding.
Here is the key point: Just as Lisa realized that there are different, equally valid ways to slice up a region of space into streets and avenues,
Figure 3.3
(
c
)
Block of spacetime containing the duel. Pages, or "time slices," organize the events in the block. The spaces between slices are for visual clarity only; they are not meant to suggest that time is discrete, a question we discuss later.
Einstein realized that there are different, equally valid ways to slice up a region of spacetime—a block like that in Figure 3.3c—into regions of space at moments of time.
The pages in Figures 3.3a, b, and c—
with, again, each page denoting one moment of time
—provide
but one of the
many possible slicings.
This may sound like only a minor extension of what we know intuitively about space, but it's the basis for overturning some of the most basic intuitions that we've held for thousands of years. Until 1905, it was thought that everyone experiences the passage of time identically, that everyone agrees on what events occur at a given moment of time, and hence, that everyone would concur on what belongs on a given page in the flip book of spacetime. But when Einstein realized that two observers in relative motion have clocks that tick off time differently, this all changed. Clocks that are moving relative to each other fall out of synchronization and therefore give different notions of simultaneity. Each page in Figure 3.3b is but one observer's view of the events in space taking place at a given moment of his or her time. Another observer, moving relative to the first, will declare that the events on a single one of these pages
do not
all happen at the same time.
This is known as the
relativity of simultaneity,
and we can see it directly. Imagine that Itchy and Scratchy, pistols in paws, are now facing each other on opposite ends of a long, moving railway car with one referee on the train and another officiating from the platform. To make the duel as fair as possible, all parties have agreed to forgo the three-step rule, and instead, the duelers will draw when a small pile of gunpowder, set midway between them, explodes. The first referee, Apu, lights the fuse, takes a sip of his refreshing Chutney Squishee, and steps back. The gunpowder flares, and both Itchy and Scratchy draw and fire. Since Itchy and Scratchy are the same distance from the gunpowder, Apu is certain that light from the flare reaches them simultaneously, so he raises the green flag and declares it a fair draw. But the second referee, Martin, who was watching from the platform, wildly squeals foul play, claiming that Itchy got the light signal from the explosion before Scratchy did. He explains that because the train was moving forward, Itchy was heading toward the light while Scratchy was moving away from it. This means that the light did not have to travel quite as far to reach Itchy, since he moved closer to it; moreover, the light had to travel farther to reach Scratchy, since he moved away from it. Since the speed of light, moving left or right from anyone's perspective, is constant, Martin claims that it took the light longer to reach Scratchy since it had to travel farther, rendering the duel unfair.
Who is right, Apu or Martin? Einstein's unexpected answer is that they both are. Although the conclusions of our two referees differ, the observations and the reasoning of each are flawless. Like the bat and the baseball, they simply have different perspectives on the same sequence of events. The shocking thing that Einstein revealed is that their different perspectives yield different but equally valid claims of what events happen at the same time. Of course, at everyday speeds like that of the train, the disparity is small—Martin claims that Scratchy got the light less than a trillionth of a second after Itchy—but were the train moving faster, near light speed, the time difference would be substantial.
Think about what this means for the flip-book pages slicing up a region of spacetime. Since observers moving relative to each other do not agree on what things happen simultaneously, the way each of them will slice a block of spacetime into pages—with each page containing all events that happen at a given moment from each observer's perspective— will not agree, either. Instead, observers moving relative to each other cut a block of spacetime up into pages, into time slices, in different but equally valid ways. What Lisa and Marge found for space, Einstein found for spacetime.