Decoding the Universe, page 14
Three different relativistic supercops
Strangely, neither of the moving cops notices his meterstick shrink or his clock slow down. In fact, when each moving cop looks at his meterstick and clock, everything looks normal, but when each looks at the other cops’ metersticks and clocks, he sees that the metersticks have shrunk and the clocks have slowed down. So each of the moving cops thinks, “Aha! Here’s the problem!” and blames his colleagues’ messed-up metersticks and clocks for getting the right answer in the wrong way.
Shrinking metersticks? Slowing clocks? It seems silly, but it has been observed. For example, particle physicists see clocks slowing all the time. Certain subatomic particles, like the muon or the tau particle, heavier siblings of the electron, only have a short time to live before they spontaneously decay into other, more stable particles. (The muon, for example, lives, on average, about two-millionths of a second.) In a particle accelerator, though, a muon often travels at more than 99 percent of the speed of light, and as a result its internal clock is slowed relative to the laboratory’s clock. This means that the muon lives a lot longer than it would if it were at rest. Global Positioning System receivers, which sense clock signals from satellites orbiting the Earth, have to take into account relativistic clock slowing when figuring out position. Even more directly, in 1971 two scientists flew four atomic clocks aboard commercial jetliners. Because of their motion relative to the Earth, the clocks disagreed after the trip. Length contraction and time dilation, as well as other strange relativistic effects, such as an increase in mass at high speeds, are a fact. They have been observed, and they agree wonderfully with Einstein’s theory.
Einstein’s two assumptions, the principle of relativity and a constant speed of light, had lots of weird consequences, but there is a beautiful symmetry to the theory. Observers might have very different views of the world—they might disagree about length, time, mass, and many other fundamental things—but at the same time, all the observers are correct.
In other words, Einstein’s theory, at its root, says that you cannot divorce perception—the information you gather from your environment—from reality. If an observer collects accurate information about something (how fast a speeder is moving, for example), that information will be correct, but with a catch: it is correct only from his point of view. Different observers, making the same measurement and gathering the same information, will often get different answers. They may all get different numbers for how fast an object is moving, how long an object is, how much it weighs, or how fast its clock is ticking. However, no observer’s information is more or less correct than any of the other observers’ information. Everyone’s information is equally correct, even though the answers to the questions about mass, length, speed, and time seem to contradict one another. It seems hard to accept, but the equations of general relativity work out beautifully. If you know how each observer is moving, you can use the equations to predict exactly what each observer sees; in other words, you are able to take the information you gathered and use the equations to figure out what the other observers are seeing. This is the key to understanding relativity. Different observers can ask the same questions about the same phenomena and get seemingly different answers. But the laws of relativity govern the laws of how information is transferred from observer to observer and tell you how different observers will interpret the same phenomenon in different ways.
The elegant way the equations worked out, not to mention the observations that they explained, convinced physicists that Einstein was correct. In the early 1920s, a rumor spread that a more sensitive Michelson-Morley–type experiment had detected the faint hints of a luminiferous ether, thereby disproving the theory of relativity. Einstein’s famous response was, “Subtle is the lord, but malicious he is not.” Einstein, like many other physicists of the day, was absolutely convinced that the theory was right. Relativity was too beautiful to be wrong.
However, there is one thing that physicists enjoy more than building a beautiful theory—and that’s smashing someone else’s beautiful theory. Plenty of people tried to destroy Einstein’s. Since experimental tests of relativity are hard to do (and some predictions of general relativity haven’t yet been tested because of that difficulty), theorists attacked Einstein’s theory with a different tool: the thought experiment.
In a thought experiment, a physicist sets up a scenario and tries to solve it using the laws of the theory he is testing. If the theory has a hole and if the physicist is clever enough, he can set up a scenario that causes an internal contradiction, a point where the theory disagrees with itself. If this happens, if the theory is inconsistent, then it must be wrong. If the theory is sound, however, the seemingly paradoxical scenario will have a consistent explanation, and everything works out in the end. (Maxwell’s demon was essentially a thought experiment, and it caused no end of problems for thermodynamics.)
Einstein himself loved thought experiments and used them to try to tear down other people’s theories (as the next chapter will demonstrate). With relativity, the situation was reversed. Einstein had to contend with other scientists’ thought experiments. One of the most tricky was what we will call the spear-in-the-barn paradox.
Imagine a sprinter with a fifteen-meter-long spear. He runs toward a fifteen-meter-long barn with two doors—a front door and a back door. To start off with, the front door is open and the back door is shut.
Now this sprinter is really good. In fact, he can sprint at 80 percent of the speed of light, and he runs into the barn. From the point of view of a stationary observer sitting in the rafters, the sprinter’s spear is contracted (because of the relativistic effect on the runner’s meterstick). In fact, the fifteen-meter spear is only nine meters long. If the observer in the rafters were to take a snapshot of the spear or measure it in some other way, he would see that it is only nine meters in length, even while the stationary barn stays at its original size of fifteen meters.
In other words, if a stationary observer tries to get information about the length of the spear, he will discover that it is nine meters long. And as Einstein’s theory says, information is reality. If your (accurate) measuring instrument gathers information about the spear and that information reveals that the spear is nine meters long, then it is nine meters long—never mind that it started off as a fifteen-meter-long spear.
A nine-meter-long spear fits nicely in the fifteen-meter-long barn; an electronic sensor can shut the front door as soon as the spear is fully inside the barn. For a moment, the spear is entirely enclosed in the barn, which has both doors shut. Then, just as the tip of the spear reaches the end of the barn, another sensor opens the rear door, letting the sprinter out. So far, so good.
The spear-in-the-barn paradox from a stationary point of view
But things really get weird when you look at the events from the sprinter’s point of view. From his perspective, the barn is rushing at him at 80 percent of the speed of light. If he were to gather information about how long the barn is, he would see that it’s only nine meters long—and perception is reality. Even though his spear appears to be the full fifteen meters long, the sprinter’s information says that the barn is only nine meters long, so the spear doesn’t fit into the barn! How, then, could both doors be shut at the same time?
The answer is hidden in the last word of the question. The solution to the paradox has to do with time, but it is a little more complicated than the mere slowing of a clock. One of the side effects of relativity is that the concept of simultaneity—that two things can happen at the same time—breaks down. Different observers can disagree about whether two events happen at the same time, or whether one occurs before the other or vice versa.
In this case, the events in question are (1) the front door’s shutting and (2) the back door’s opening. From the point of view of the stationary observer in the rafters, the sprinter runs into the barn, (1) the front sensor shuts the front door, with the sprinter inside, and then (2) the rear sensor opens the back door, letting the sprinter out. But from the point of view of the sprinter, the order of events is reversed. He runs into the barn and (2) the back door opens when the tip of the spear reaches the end of the barn and triggers the rear sensor. He continues on, and then (1) the front door shuts as soon as the butt of his spear passes the threshold of the front door, triggering the front sensor.
The sprinter and the observer in the rafters disagree about the order of events, but mathematically the two observations are consistent with each other. The two sensors are independent, and there is no particular reason why one has to be triggered before the other. In one frame of reference, the front sensor triggers first, and in the other frame of reference the rear sensor triggers first. Once again, it is all a matter of information transfer.
Information doesn’t get from place to place instantly; at most, it can travel at the speed of light. This means that the concept of “simultaneous” doesn’t really mean anything, because you have to take into account the fact that it takes time for information to travel to your observers. And an observer’s motion will affect the order in which information reaches him. The information that the front door is shut and the information that the back door is open might reach one observer at the same time; to another observer, the “front door is shut” information might arrive first. To yet another, the information that the back door is open might come first. The three observers will disagree about whether the front door shut first, the back door opened first, or both events occurred at the same time. Which one is correct? They all are.
The spear-in-the-barn paradox from a moving point of view
Einstein’s theory of relativity says that an event only “occurs” from your perspective when the information about that event’s occurrence reaches you. An event doesn’t really happen until that information (traveling at the speed of light) traverses the distance from the event to you. Once again, perception—and information—is reality. This is what causes simultaneity to break down; since the three observers get information in a different order, then in truth the events they were observing occur in a different order for each of the three observers. It’s a strange concept, but the breakdown of simultaneity in relativity theory is just something that physicists have come to live with; it doesn’t violate any principles any more than do length contraction and time dilation. Crisis averted.
Or is it? Can we use this breakdown of simultaneity to come up with an impossible scenario? We can certainly try. For example, we can modify the thought experiment slightly to try to force a contradiction. Instead of having two sensors, one at the front of the barn and one at the rear, each triggering its respective door, imagine that there is only one sensor at the front. When the sensor senses that the butt end of the spear has passed the threshold, it slams the front door and only then signals the back door to open. For a split second, both the front door and the back door must be shut at the same time before the back door opens. No longer are the events independent, because, in a sense, the shutting of the front door causes the back door to open. Swapping the order of these two events would be a violation of the laws of physics.
This is because causality must be preserved, even in the upside-down world of relativity. Imagine that an assassin shoots a general with a bullet. The bullet strikes the general and kills him; had the gun not been fired, the general would not die. But if there were a nearby, fast-moving observer whose motion saw the bullet strike before the gun was fired, he might be able to knock the gun out of the assassin’s hand before the gun is fired. He might be able to prevent the assassination he just saw! It’s as if he traveled back in time and changed the past. This makes no sense, even in the strange domain of modern physics.
There is a limit to the reordering of events in relativity. If an event(1) causes an event (2), there is no way that an observer can see (2) before he sees (1). These two events are said to be causally connected. Even taking into account relativity’s distortion of time, a traveler moving near the speed of light will never see a reversal of causally connected events. He would never see your birth before he sees your mother’s; your mother’s birth must come before yours, because your mother’s existence causes your birth. Similarly, in the modified spear-in-the-barn paradox, the front door’s closure causes the back door’s opening. Therefore, from any point of view—from a stationary observer’s or the sprinter’s—the back door must open after the front door. With this modified sensor, let’s rerun the scenario.
From the sprinter’s point of view, the back door only opens when the front sensor is triggered—when the butt end of his spear crosses the threshold. The front part of his spear, which is fifteen meters long, will smash through the back door before it triggers the sensor that closes the front door. The outcome is a collision, at least from the sprinter’s point of view.
Aha! Now it looks like we’ve got Einstein in a tight spot because, as before, from the stationary observer’s point of view it seems possible that the spear fits well within the barn, giving enough time to open the door and avert the collision. In one frame of reference, there’s a smack-up, and in the other, nothing! That’s a contradiction. Or so it would seem. There is a way out, an additional subtlety that we have to take into account. And this is where information theory begins to reveal itself.
The sensor at the front of the barn has to signal the back door to open. It has to transmit information—the command to open—from the front of the barn to the rear of the barn. At least one bit of information must travel from the front of the barn to the back, and information cannot travel from place to place instantly, because information has a physical presence. Transmitting this bit takes time. In the stationary observer’s frame of reference, the front sensor slams the door shut and sends a message to the back door. However, the tip of the sprinter’s pole has a nine-meter head start and is zooming toward the rear door at 80 percent of the speed of light. That’s a tough headstart to overcome. In fact, unless the message travels faster than the speed of light, there is no way it can make up the distance fast enough. The signal to the back door gets there too late: the spear strikes the door before the message arrives. So, even from the point of view of the stationary observer there’s a jarring collision. Both observers agree; a smack-up occurs. Paradox averted. Averted, that is, so long as information can travel no faster than the speed of light.
Einstein’s theory holds firm—but only when there is a limit on how fast information can travel. If, somehow, information could travel faster than the speed of light, causality would break down; you would be able to send a message into the past and affect the future. So long as information behaves itself and moves at light speed or below, Einstein’s theory is completely consistent.
This is what is behind the famous “nothing can go faster than the speed of light” dictum, but in fact, that dictum is an oversimplification. Some things can go faster than the speed of light. Even light itself can break light speed, in a sense. The true rule is that information can’t travel faster than the speed of light. You cannot take a bit of information, transmit it, and have it get to a recipient faster than a beam of light can make the same trip, otherwise causality will break down. The ordering of events in the universe would no longer make sense; you might be able to build a time machine and be born before your mother.
The seeming paradoxes in relativity hinge upon the transfer and motion of information; relativity, deep down, is a theory about information. Sometimes its rules are incredibly subtle, but they have held, despite legions of scientists who for the past century have tried to find loopholes. The puzzle of faster-than-light travel is a puzzle of information. So is the problem of time travel.
In an unassuming laboratory in New Jersey, scientists built the first time machine. Lijun Wang, a physicist at NEC Research Institute outside Princeton, sent a pulse of light faster than light speed—and forced it to exit a chamber before it ever entered.
This is no joke. It was published in the peer-reviewed journal Nature in 2000 and has been replicated by a handful of labs across the country. It is not that difficult an experiment to perform: all it requires is a chamber full of gas, a laser, and a very precise stopwatch. And while Wang’s work is the most dramatic example of breaking the speed of light, it is not the only one. Barely a month before Wang’s experiment, Italian physicists used a clever geometric construction to get a laser beam to exceed c, the speed of light. Half a decade before that, Raymond Chiao, a physicist at the University of California at Berkeley, used a bizarre quantum-mechanical property called tunneling to make a light pulse go faster than c.
The easiest faster-than-light experiment to understand is one that was performed in Italy in 2000. In it, Anedio Ranfagni and colleagues at the Italian National Research Council in Florence took a beam of microwaves, passed it through a ring, and then bounced it off a curved mirror to create what is called a Bessel beam of microwave light. Viewed from above, a Bessel beam has planes of waves that intersect like an X. The scientists watched as the intersection of that X moved more than 7 percent faster than the speed of light; it looked as if they were sending something—the intersection—faster than c. (An easy way to see what’s going on is to make an X with your two index fingers nearly parallel to each other. Move your hands apart slowly and you’ll see that the intersection moves up your fingers at a speed that’s much greater than the speed at which your hands are moving apart.) But what happens if you try to send a message with this scheme? Can it go faster than light?
