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Dance of the Photons
From Einstein to Quantum Teleportation
By Anton Zeilinger
Farrar, Straus and Giroux Copyright © 2010 Anton Zeilinger
All rights reserved.
When we hear of teleportation, we often think it would be an ideal means of traveling. We would simply disappear from wherever we happened to be and reappear immediately at our destination. The tantalizing part is that this would be the fastest possible way of traveling. Yet, a warning might be in order here: teleportation as a means of travel is still science fiction rather than science.
Thus far, people have only been able to travel to the Moon, which on a cosmic scale is extremely close, the equivalent of our backyard. Within our solar system, the closest planets, Venus and Mars, are already roughly a thousand times more distant than the Moon, to say nothing of the planets farther out in the solar system.
It is interesting to consider how long it would take to go to other stars. As we all remember from the Apollo program, which put the first men on the Moon, it takes about four days to go from Earth to the Moon. Traveling by spaceship from Earth to the planet Mars would take on the order of 260 days, one way. It is evident that our space travelers would get quite bored during that time, so they might make good use of their time by performing experiments involving quantum teleportation.
In order to get even farther out, we might use the accelerating force of other planets or even of Earth itself, as has been done with some of the unmanned spacecraft exploring outer planets. The idea is simply to have the spaceship pass close by a planet so that, by means of a sort of slingshot action, it can be accelerated into a new orbit that carries it much farther outward. For example, using these methods, the spacecraft Pioneer 10 took about eleven years to travel past the outermost planets of the solar system on its probably unending journey into the space between the stars. We can thus estimate that it will, for example, take Pioneer 10 about 100,000 years to get to Proxima Centauri, the closest star except for the Sun, at its current speed.
Perhaps, therefore, it would be good to have some other way to get around, to cover large distances. What we want is to travel anywhere instantly, without any limitation on how far we can go. Is that possible, at least in principle? This is why science-fiction writers invented teleportation. Magically, you disappear from one place, and, magically, you reappear at another place, just an instant later.CHAPTER 2
THE STUFF CALLED LIGHT
The first teleportation experiments were done with light, but what is light? Humans have always been fascinated by light. Probably long before we learned to write things down, people must have discussed how it is possible that through light, we experience objects close by or even at large distances. There are two basic concepts physicists use to explain how something travels from a light source — say, the Sun, or even a tiny candle — all the way to our eyes so we can recognize the object that emits the light. One concept assumes that light travels to us as particles, pieces of something, just like chunks of matter. The other assumes that light travels to us in the form of waves.
The simplest analog for the particle concept is that light travels just as a bullet or a small marble does. For the wave concept, the simplest pattern we can think of is the pattern of waves spreading out on the surface of water, for example, in a small pond. These two simple images convey the essential features of the particle and the wave concepts.
In the case of the marble, we have something localized — restricted in space — that moves. Similarly, the particle of light moves from place to place — from the light source, to the object we see, to our eye — by following some trajectory. Furthermore, just as marbles or bullets come one by one, the light source, for example the Sun, emits many tiny particles of light that travel toward us. They hit, for example, the tree across the road, some of them are reflected and scattered off that tree, and a few finally are collected by our eyes.
In contrast, the wave on the surface of a pond is not localized at all. If we throw a stone into a quiet pond, we see a wave that eventually spreads out all over the pond (Figure 1). Furthermore, waves do not come in pieces, in chunks, but, rather, a wave can come in any size. There are very tiny waves caused, for example, by the legs of a small insect gliding across the quiet pond, or huge waves created by large stones thrown into the water. So there is continuity to the size of water waves.
So the big question is, What is light? Which concept applies to the phenomenon of light — the wave concept or the particle concept? Which of the features we just listed are actually features of light?
Much of the history of physics can be written as a history of the nature of light. Very early on, people started to carefully investigate which of the criteria for particles or for waves apply to light. In the early 1700s, there was a large battle between adherents of the particle picture, led by Isaac Newton, and followers of the wave picture, led by Robert Hooke. Back at that time, the particle picture triumphed. Many say that the weight and authority of Newton tipped the scales.
LIGHT IS A WAVE
In 1802, the English medical doctor Thomas Young performed an experiment that turned out to be crucial for our understanding of the nature of light. The experiment itself — actually one of the great experiments in the history of science — is extremely simple. Thomas Young just let light pass through two pinholes in a screen.
Behind the pinholes, he observed light and dark stripes (top sketch in Figure 2), called "interference fringes" today.
What happens if we cover one of the two slits? Then we do not see any fringes, but rather a broad patch of light (middle sketch in Figure 2). If we cover the other slit, we get a similar broad patch of light slightly shifted (bottom sketch). There is a large region where the two patches overlap.
From a particle-picture point of view, when we open both slits, we would expect that the light on the screen would be the sum of the two. But this assumption turns out to be wrong. Instead, in the overlap region, Young observed bright and dark stripes — the fringes. So there are positions, the dark fringes, where no light at all arrives when both slits are open. But when either slit is open alone, we have light there. Careful measurement shows that at the bright fringes, the amount of light is more than the sum of the two intensities that we would get with just either slit open. How can that be explained?
The wave picture provides an explanation of the fringes. Let's assume that a light wave comes from a certain direction, say, from the left, as shown in the figure. It hits the two-slit opening. On the other side of each slit a new wave starts. The two waves reach the observation screen. At the center line on that screen, the two paths leading from the slits will be of equal length. In that case, the two waves will oscillate in sync and they will mutually reinforce each other, and a bright stripe results. If we move our observation point, right or left in the figure, one of the paths gets a little shorter while the other one gets longer. The two paths leading from the two slits to any given point on the observation screen are no longer of equal length. There is a difference in path length.
So, depending on where exactly the new observation point is, the two waves will get more and more out of step. At some point, the two waves will be completely out of step. Where one wave is at its maximum, the other one is at its minimum. Where this happens, the two waves cancel each other out. Just consider the same situation for water waves. If two waves meet so that the crest of one meets the trough of the other one, they cancel each other out.
If we move even farther out, the path length difference will keep getting larger. At some point, the path length difference will be exactly one wavelength. In that case, crest meets crest again: the two waves reinforce each other and a bright stripe will be seen.
If we move the observation point even farther out, the pattern repeats. There will again be positions where crest meets trough: the waves cancel each other out, there is no light, and it will be completely dark, and so on. The interference fringes appear because in those places where we have mutual reinforcement, we get more light resulting in the bright fringes, and in those places where crests meet troughs we have the complete extinction of light — the dark fringes, destructive interference. So we see a striped pattern.
After Thomas Young's experiment, physicists no longer doubted that light consists of waves and not particles.
LIGHT IS PARTICLES
Then, in 1905, a completely unknown clerk at the Swiss patent office in Bern published a series of papers that changed the nature of physics. At that time, Albert Einstein was only twenty-six years old. In one of the papers, he proposed his relativity theory. But it is the first paper published in that year on which we focus now. It is the only one of his works that Einstein himself, in a letter to his friend Conrad Habicht, called "very revolutionary." In that paper, Einstein suddenly suggested that light is made of particles.
These particles of light, also called light quanta, later were named photons by the American chemist Gilbert Newton Lewis in 1926. In the face of all the evidence for the wave nature of light existing in Einstein's time, with the double-slit experiment being only one proof, how did this young clerk at the Swiss patent office in Bern dare to come up with the idea that light might be composed of particles, just the opposite concept? To discuss this question in detail, we have to learn something about the way physicists describe order and disorder.CHAPTER 3
SHEEPDOGS AND EINSTEIN'S PARTICLES OF LIGHT
There are many competitions worldwide every year to find out which sheepdog is the best. One of the jobs such dogs must perform is to gather a flock of sheep and move them to one specific place, say, into one corner of a field. From a physicist's point of view, what the sheepdog does is increase the order of the system. Before, the sheep might be scattered all over the field, particularly if they feel safe and no enemy is around. The sheepdog has something in its genes that tells it how to gather the sheep all together into one pack. In sheepdog competitions, that dog wins who herds the flock together in the shortest time, who gathers all the sheep in an orderly way at some place its master specifies.
Actually, the situation is very similar to clearing off the stuff — books, pieces of paper, and brochures — cluttering a desk. Most desks after some time look completely messy, a piece of paper lying here, a newspaper over there, a coffee cup on top of the newspaper, some other piece of paper in another corner, and so on.
Just as the sheepdog puts all the sheep into one corner of the field, one way to increase the order on the desk is simply to make, say, three stacks, one for notes, one for newspapers and journals, and one for books (Figure 3). Suddenly, all these items are in place and the rest of the desk is free. But unless we take care, the stuff will spread all over the desk again after some time. So, in both the case of the sheep and the case of the desk, we have a natural tendency for stuff to spread out evenly over the available space, and we also see that it takes a special effort to gather the stuff together again. The situation where the stuff is gathered together is one of higher order than the situation where it is evenly spread out.
Interestingly, a gas in a container behaves in the same way. Suppose we have a vessel separated into two parts by a wall with an opening that can be shut or not (Figure 4). We start with the valve closed, and all the gas particles are in one half, while the other half is empty. Then, we open the shutter. It's obvious what will happen. The gas will spread out evenly over the whole vessel. There will be a lower density then, since the gas has to thin out. Gas really consists of atoms and molecules. So the situation is just like two fields, one of them full of sheep. If we open a gate to the other, empty field, after some time, the sheep will spread out over both fields. We assume that there is an equal amount of food available on both sides and that there is no danger — and no sheepdog — pushing them either way.
Now, let us assume the opposite. Let's assume we start with the gas filling both sides. Will it ever happen that all the atoms will, of their own accord, move to one half of the vessel, leaving the other half empty? Probably not. Why not? In principle, such behavior is not impossible. If we look closely, we will observe atoms going through the opening in both directions, some from the right to the left, and some from the left to the right. It could happen by sheer coincidence that at some time, all the atoms are assembled on one side and none on the other. But apparently that is very unlikely.
Likewise, it is very unlikely that within one container, all the atoms will move into one corner together, leaving the rest of the container empty. In principle, this is not impossible; since every molecule moves around in its own zigzag fashion, it could simply happen by chance that they, at some instant, end up in one place. But this is extremely unlikely. The contrary obviously happens easily. If we have all the atoms in one corner and let them fly freely, they will immediately fill the available space in a homogeneous way.
This leads us to the observation that the universe tends to increase its disorder. All the atoms in one corner together means a highly ordered situation; all the atoms filling the available volume is a less ordered one. Also, we can see a clear connection between probability and order. The more orderly a situation is, the less probable it becomes.
Physicists like to describe disorder using the notion of entropy. Entropy is just a measure of disorder. More precisely, entropy reflects in how many ways a given situation can be realized. The larger the entropy, the more disordered a situation is, and the larger the entropy, the higher the probability for that situation to exist. For the case of gas filling a certain volume, it turns out that entropy increases with the in-crease in volume. In a sense, putting all the atoms in the smaller volume is like putting them all together in a corner.
In 1905 the young Albert Einstein made an important discovery. He studied the entropy of a gas filling a certain volume and compared it with the entropy of light filling the same kind of volume. What Einstein discovered was an interesting coincidence. He read and compared scientific papers that had already been around for more than five years, so anyone else could have made the same discovery. But Einstein discovered that the entropy — remember, this is the measure for disorder — of radiation in general, or light more specifically, filling a certain volume is very similar to the entropy of gas filling that same volume. Indeed, he found out that the mathematical expression derived by the German physicist Wilhelm Wien for the entropy of radiation filling some volume is the same as the mathematical expression derived earlier by the Austrian physicist Ludwig Boltzmann for a gas filling a container. More precisely, the two mathematical expressions for entropy vary in the same way if one changes the available volume.
Einstein, seeing this analogy, made a very bold conjecture. He knew that the expression for the entropy of gas filling a volume can easily be understood on the basis of how the individual molecules move around, and how improbable it is that they fill only a part of the available space. Because of the analogy of the two mathematical expressions for light and for particles, Einstein assumed that light is also made up of particles, which move around just like molecules and which also don't like to end up in some corner if a large volume is available to them.
Excerpted from Dance of the Photons by Anton Zeilinger. Copyright © 2010 Anton Zeilinger. Excerpted by permission of Farrar, Straus and Giroux.
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