Chapter 16
In This Chapter
Identifying particles of light
Applying the idea of waves to matter
Furthering our understanding of how atoms work
Expanding on wave mechanics
Giving in to quantum physics
R elativity was not Einstein’s only revolutionary theory. He also made possible quantum theory.
Quantum theory was born in March of 1905, with Einstein’s first paper of his year of miracles (see Chapter 3). The title of the paper was “On a heuristic point of view concerning the production and transformation of light.” If you look up heuristic in a dictionary, you’ll find that it means “serving to guide, discover, or reveal; valuable for empirical research, but unproved or incapable of proof.” That definition summarizes Einstein’s feelings about quantum theory.
After helping create quantum theory, Einstein had second thoughts about its implications. He could never accept that “God would play dice with the universe,” as he put it. Throughout his life, Einstein thought that quantum theory was not the final word and that one day it would be replaced by the true theory of the atom.
However, as I show you in this chapter, scientists think that quantum theory is here to stay.
Discovering the Quantum
In 1900, Max Planck applied Ludwig Boltzmann’s ideas on statistical mechanics to the data that physicists were getting for the radiation of hot objects. The problem that physicists hadn’t been able to solve was in the high-energy region, where their equations were giving them nonsense answers.
Planck came up with a solution, but in doing so, he had to split the total energy being absorbed by an object into bundles of energy, each containing the same amount. In Chapter 15, I explain that Planck wasn’t too happy about using statistics in physics, and he didn’t fully understand the implications of what he’d done. But until 1905, when Einstein published his “heuristic” paper, Planck’s paper remained a successful method to reproduce the data.
Revealing Einstein’s “revolutionary idea”
In his March 1905 paper, Einstein started by showing why existing equations couldn’t really be applied to the problem of the radiation of objects. The old equations worked fine in the low energy region, but they failed in the high energy region. Einstein explained why, in the high energy region, the equation solutions indicated there was an infinite amount of energy.
Einstein then set out to study the problem in a way “which is not based on a picture of the generation and propagation of radiation.” In other words, he wasn’t using Planck’s method. He decided to start from basic physics principles. When he was done, he’d shown that the radiation of hot objects behaves as if it were made up of separate quanta (bundles or packets) of energy. Einstein assumed that the energy of each quantum is related to the wavelength of the radiation emitted: The shorter the wavelength, the larger the value of the energy.
Up to this point, there was no revolution. Like Planck and everyone else had assumed, these light quanta could be interpreted as a curious property of the radiation from hot objects. But Einstein took a bold step (which eventually gained him the Nobel Prize in 1922). He declared that matter and radiation can interact only by exchanging these energy quanta.
Here is what Einstein said:
Light (and all electromagnetic radiation) is made up of quanta of energy, bundles or packets with energies that are related to the wavelength of the light.
The shorter the wavelength, the larger the amount of energy of a light quantum, or photon.
These photons cannot be split.
Light isn’t just a wave, as Thomas Young’s experiments had shown (see Chapter 7). Instead, Einstein said, light is made up of quanta of energy, and these quanta (or photons) are like particles. They’re not exactly like little dust particles, but light has particle properties. A photon has a fixed amount of energy, and it exerts pressure on objects. It interacts with other particles in a particle-like way, not in a wavelike way. Light is lumpy.
In Chapter 7, I explain that Young’s experiment showed once and for all that light is a wave, and his famous interference experiment is repeated today in schools all over the world to show students the wave nature of light. Waves aren’t particles. Waves and particles have very different properties. These two ideas are mutually contradictory. It’s like day and night, on and off. If you have one, you can’t have the other. What gives? Is light a wave, or is it a particle?
It’s both. Before Einstein came along, this statement would have been nonsense. But in the quantum physics that Einstein started, it makes sense. However, it would take 20 years for scientists to resolve the seemingly inherent contradiction.
Identifying quanta of various energies
With Einstein’s new view of the nature of light, Planck’s radiation law became the accepted explanation for the radiation of hot objects. This law indicates that the thermal energy emitted by an object comes from charged particles oscillating inside the object and that these oscillations have only some specific energies. Einstein hadn’t been satisfied with Planck’s radiation law before, because it hadn’t made sense. With his new insight, it made sense, and he was ready to embrace it. “Planck’s theory makes implicit use of the . . . light-quantum hypothesis,” he said.
Einstein’s light-quantum idea explained the strange results that physicists were seeing in their study of the radiation from hot objects. They’d been measuring the energy radiated at different lengths and were seeing that at long and intermediate wavelengths, things made sense. But at very short wavelengths, their measurements were showing very little radiation. They couldn’t understand that result. Their equations predicted that as they looked at shorter and shorter wavelengths, the energies should be larger and larger. As Figure 16-1 shows, the results of their equations differed greatly from the results of their experiments.
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Figure 16-1: Not much short-wavelength energy is radiated out of a hot object, but in theory the results should be different. |
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The light quantum idea made the experiment results clear. Planck had proposed that the thermal energy emitted by an object comes from charged particles oscillating inside the object (see Chapter 15). The energy of each photon depends on the wavelength of the oscillating particle (see Figure 16-2). At short wavelengths, the radiation from a hot object is made up of high-energy photons. (Short wavelength photons have larger energies.) Very few oscillators have photons with these energies, so only a few of these high-energy photons are emitted. That’s why the scientists were detecting very little radiation at these short wavelengths.
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Figure 16-2: Low-energy photons have long wavelengths, while high-energy photons have short wavelengths. |
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At long wavelengths, the photons have low energies, and many more oscillators have these energies. Many more of these low-energy photons can be emitted, but because each one has little energy, the total amount of energy from all of them is not too large. At the middle wavelengths, you have quite a few oscillators that emit photons of moderate size. As a result, the largest emission of energy occurs at the middle wavelengths, as the experiments were showing.
Planck’s great insight, validated by Einstein’s generalization, was to realize that the energies are related to the different wavelengths of the light emitted by the oscillators, instead of assuming that the energies are all equally distributed, like previous theories had done. Einstein’s great insight was to make this idea a fundamental property of nature. Light and all electromagnetic radiation are made up of quanta; light is “quantized.”
The step size of these quanta is determined by a constant now called Planck’s constant. As Figure 16-3 shows, radiations of shorter wavelengths carry more energy (larger steps) and are identical to each other. But those radiations are different from the ones that consist of larger wavelengths. Just as you can’t split the steps of a staircase, you can’t split photons.
According to Einstein and Planck, then,
The energy of a light quantum or photon is related to the wavelength of the light; this energy is “quantized” with the step size determined by Planck’s constant.
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Figure 16-3: Light and all electromagnetic radiation is quantized. All the photons radiated at one wavelength have the same energy and are identical. |
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Solving the photoelectric effect
Another nagging problem in physics, called the photoelectric effect, had also resisted all attempts at explanation. Heinrich Hertz had seen this effect in 1887, and physicists were puzzled by it.
What is the photoelectric effect? If you shine a beam of light on a certain material, you can detect electrons that are ejected from the metal. (That’s what happens in the solar cells that power our modern devices, from calculators and swimming pool heaters to the Martian rovers.) The electrons that are ejected form the electric current that runs the device. If you increase the brightness of the light, you get more electricity out of the cell (see the top of Figure 16-4). However,
The speeds of the electrons emitted don’t change when you increase the brightness.
What’s worse, if you increase the wavelength beyond a certain value, you won’t get anything out of the cell, regardless of how bright the light is (see the bottom of Figure 16-4).
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Figure 16-4: Puzzling experiments when shining a light on certain materials. |
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The solution again came from Einstein’s light-quantum idea. How does the light quantum solve the first problem? When you shine a light at the material, you are sending photons of a certain energy. Suppose that the light is monochromatic (of a single color). In this case, the wavelength of light is fixed, and all the photons that strike the surface have the same energy. When one of the photons strikes the material, all of its energy is transmitted to an electron in the material. The electron then takes in one of these photons and uses its energy to get out of the material. When you increase the brightness, you aren’t increasing the energy of each photon, you are simply sending in more photons all of the same energy. The chances of one electron taking in more than one photon are very small, so increasing the brightness releases more electrons. However, it doesn’t affect their speeds.
The solution to the second problem is simpler. It takes energy for the electron to negotiate its way out of the material. The energy that it receives from the light comes in these photons of fixed energy. Each single photon has to provide one electron with enough energy to leave the material. If you shine a light of low-energy photons, ones from a light with long wavelength, these photons may not have the minimum energy needed. Increasing the brightness of the light only increases the number of these low-energy photons, not their energy.
Imagining Waves of Matter
How did physicists react to having these two nagging and long-standing problems solved? Not surprisingly, with skepticism. In 1905, Einstein was an unknown. However, after the barrage of amazing papers he published that year, it was difficult not to know about him. Planck was one of the first physicists to acknowledge his brilliance and one of the early proponents of the theory of relativity.
The light-quantum idea was another matter. Not even Planck accepted it, even though it helped explain his own discovery. As late as 1913, when Einstein was recognized as one of the top European physicists (and at that time, physics was done mostly in Europe), there was strong opposition to his quantum idea. When Einstein was proposed for membership in the Prussian Academy of Sciences in 1913, Planck and other illustrious physicists wrote in their official recommendation as follows:
One can only say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light-quanta, cannot be held too much against him.
For 15 years, Einstein stood alone in his belief of the light-quantum idea. In 1918, Einstein said that he no longer doubted the reality of quanta, “even though I am still alone in this conviction.” After that, things began to change very rapidly.
Finding a new way to count
In June of 1924, Einstein received a letter from a young, unknown Indian physicist by the name of Saryendra Bose, who was a professor at the University of Dacca. With the letter came a paper in which Bose derived Planck’s radiation formula by imagining a gas of photons, applying the statistical methods used with regular gases to count the photons in a new way, and assuming that you couldn’t distinguish the photons. Einstein was immediately interested in Bose’s derivation and translated the paper into German for publication in a journal. Einstein then extended this new counting method and applied it to atoms and molecules. The method is known today as Bose–Einstein statistics.
Again, Einstein made a leap. From these studies, he concluded not only that light has the dual character of being a wave and a particle, but also that matter shows the same duality. Matter should also have wavelike behavior.
Measuring electron waves
That same year, a graduate student at the University of Paris, Louis de Broglie, finished his PhD dissertation in which he proposed to extend Einstein’s dual character of light to particles of matter. Matter, de Broglie said in his thesis, should also have wave properties. “After long reflection,” wrote de Broglie, “I had the idea, during 1923, that the discovery made by Einstein in 1905 should be generalized by extending it to all material particles and especially to electrons.” In his thesis, de Broglie calculated what the wavelength of an electron should be.
Professor Paul Langevin was a good friend of Einstein’s. When his PhD student, de Broglie, gave him the thesis requesting his approval, he wasn’t sure about granting a PhD for research based on an idea that could turn out to be incorrect. He asked his student to make a third copy of the dissertation, and he sent it to Einstein for his comments. “A very notable publication,” Einstein wrote back. De Broglie defended his thesis on November 25, 1924. He received the Nobel Prize in physics in 1929 for his discovery.
De Broglie suggested ways to test his idea of matter waves by trying to observe interference patterns with electrons. Three years later, two U.S. physicists saw an interference pattern with electron beams. Interference patterns are the trademark of waves; only waves can interact in such ways. De Broglie’s matter waves are the basis for the electron microscopes in use today.
Superatoms
The 2001 Nobel Prize in physics was given to three physicists for their experimental creation of the first Bose–Einstein condensate, a new state of matter predicted by Bose and Einstein when they first proposed their theory. The three scientists are Carl E. Wieman of the University of Colorado in Boulder, Eric A. Cornell of the National Institute of Standards and Technology, and Wolfgang Ketterle of MIT.
In a Bose–Einstein condensate, a gas is cooled to temperatures so low that the atoms all share the same quantum energy level. The billion or so atoms in the gas become a single “superatom.” To create this superatom, the three scientists had to bring the gas to temperatures less than a few billionths of a degree above absolute zero, all the while preventing the gas from liquefying or even solidifying. The feat was accomplished by trapping the atoms with lasers.
This new state of matter will give scientists a new window to the quantum world, allowing them to probe further the nature of matter. The condensate also has possible practical applications. In 1997, Ketterle’s group at MIT was able to extract parts of the condensate like drops from a faucet. They hope to be able to create an atom laser that could be used to build better gyroscopes and more accurate atomic clocks. Other scientists have been able to manipulate condensates on microchips, which eventually will allow the creation of new small instruments and electronic gadgets.
Discovering the New Mechanics of the Atom
During the summer of 1922, Niels Bohr gave a series of lectures at the University of Göttingen in Germany about the new advances in physics. A 22-year-old graduate student by the name of Werner Heisenberg from the University of Munich was in the audience. At one of the lectures, the young Heisenberg made a critical remark. Bohr was intrigued by this student and invited him to go hiking in the Hain Mountain to discuss his questions. Bohr was impressed with Heisenberg and invited him to join his institute in Copenhagen after graduation. “My scientific career only began that afternoon,” wrote Heisenberg years later.
In 1924, after getting his PhD, Werner Heisenberg took Bohr up on his offer and joined the Niels Bohr Institute. He was 23 years old. There, he joined a group of young and bright physicists from Europe, the United States, and Russia who were studying the problems of the atom. After about a year, he was invited to return to Göttingen as an assistant to Max Born, the director of the physics institute.
Studying the spectra of atoms
At Göttingen, Heisenberg began to look at the spectra of atoms that scientists were obtaining at the different labs around the world. Scientists had been studying the spectra of atoms for many years.
To observe a particular spectrum, you can place a gas of a particular element (helium, for example) in a glass container and pass a high-intensity light through it (see Figure 16-5). If you then look at this light through a prism, you’ll see the spectrum, the rainbow of colors. If you place the prism right in front of the incoming light, you notice that the rainbow has some gaps, some small dark areas where the light is missing. If you move the prism to the side and look at the light scattered by the gas, you notice that instead of the dark areas, you see bright areas on top of the rainbow.
Each element has its own very specific set of lines. Hydrogen, for example, has a characteristic set of bright red, blue, and purple lines, while helium is easily identified by its two bright yellow lines very close to each other. The sets of lines are the fingerprints of atoms.
Heisenberg was interested in finding a mathematical expression for the lines of the hydrogen spectrum. He couldn’t come up with an equation for them, but in the process he solved another problem.
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Figure 16-5: Taking the spectrum of a gas. |
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In Bohr’s model of the atom (which I explain in Chapter 15), the electrons orbit the atom with very specific energies. These energies are quantized, with the electrons jumping from one of these orbits to another as they absorb or eject a photon with the right energy. But what are the actual orbits of the electrons in the atom? Are they circular or near circular, like those of the planets? Heisenberg discovered that there is no need to answer this question. The only thing that matters is what can be measured, like the wavelengths and brightness of the spectral lines of the atom.
In the spring of 1925, Heisenberg had a bout of spring fever and asked Born for a few days off. He went to Helgoland, a small island in the North Sea. Away from the pollen, Heisenberg could think clearly. He realized that he needed to simplify the problem if he wanted to get anywhere. He started from scratch, modeling the atomic vibrations after the simple back-and-forth motion of a pendulum. In a few days, he had some promising calculations. When he got back to Göttingen, he had discovered the new mechanics of the atom.
By July, he’d finished writing his first paper on the theory of this new mechanics. In it, he described the changes in the energy of the atom using an array of numbers that followed some simple rules. He asked Born to check his paper. Born immediately recognized the arrays as being matrices — devices that mathematicians had invented some time before. (See the sidebar “The matrix” in this chapter.) The rules that Heisenberg had discovered were the rules of matrix algebra. Born sent the paper for publication and, with his student Pascual Jordan, helped Heisenberg to develop the theory further.
Realizing the world is grainy
The important discovery that Heisenberg made is that quantities that can be measured, like position or speed, can’t be represented by plain numbers, like you are used to. They must be represented by these arrays, these matrices, and must follow their special rules.
The matrix
A matrix is a mathematical entity with specific rules on how you must work with it. When Heisenberg discovered that matrices are the correct tools to describe atomic processes, physicists began to take an interest in them. Until then, very few scientists knew that they even existed. Now, the standard college training for scientists in the physical sciences includes a thorough review of matrices. Matrix algebra isn’t difficult and can even be fun. The movie is better, though.
For example, with regular numbers, if you multiply 2 times 3 you get 6. You also get 6 if you flip the order of the multiplication: 3 times 2 is the same as 2 times 3. Not so with matrices. Matrices are finicky about the way you manipulate them. For example, the way you rotate an object in space is described with matrices. Take a look at Scenarios A and B and Figure 16-6 to get an idea of how this works.
Scenario A
Suppose that you start with a book sitting flat on your desk, with the cover facing up so that you can read it (see Figure 16-6). Now make these two rotations:
1. Flip the book toward you holding the far edge, so that the book rests on its bottom edge. The cover should be face up in front of you now.
2. Rotate the book counterclockwise from its present position. You end up with the spine of the book in front of you.
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Figure 16-6: The order in which you rotate a book matters. Atoms have similar properties. |
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Scenario B
Now, return to the original configuration of the book sitting on the table, and reverse the order of the two rotations:
1. Rotate the book counterclockwise from its initial position. The book sits flat on the table with the spine facing you.
2. Flip the far edge toward you. The book is now resting on the spine.
The order in which you perform the two rotations matters. There is a difference in the final position of the book. Heisenberg, Born, and Jordan found out that when you do the same sort of thing to atoms, when you flip the order of the operations that you perform, the final configuration changes. And the difference is related to Planck’s constant.
Planck’s constant measures the “step size” of quanta. If Planck’s constant was zero, it wouldn’t matter which way the operations with atomic quantities are done. But Planck’s constant isn’t zero. Therefore, the world is grainy, quantized — changing by steps, not continuously. The steps are extremely small (Planck’s constant is very small), and in the normal world of our experiences, you don’t see them, not even with precision instruments. (Think of a digital photograph; unless the photo is enlarged substantially, you don’t realize the photograph consists of individual pixels.) The world seems smooth and continuous. The size of the graininess is determined by Planck’s constant.
That Heisenberg discovered all this in a few days, along the way reinventing some of the mathematical tools he needed, can only be explained as the result of a privileged mind.
Contemplating Wave Mechanics
Erwin Schrödinger, a physics professor at the University of Zurich, wrote to Einstein on November 3, 1925: “A few days ago I read with the greatest interest the ingenious thesis of Louis de Broglie, which I finally got a hold of; with it . . . your second paper . . . has now become clear to me for the first time.”
In his thesis, de Broglie stated that a wave must be associated with an electron (see Figure 16-7). The associated wave of an electron orbiting an atom should close in on itself when the electron is in one of the allowed orbits, one of the steps in Bohr’s atomic model. If you were to try to calculate the electron wave for a nonallowed orbit, the wave wouldn’t close in.
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Figure 16-7: De Broglie’s waves for electrons in orbit around the nucleus of an atom. |
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Doing the math
Schrödinger was intrigued with this idea and decided to apply the mathematics of regular waves (waves on a string or sound waves, for example) to calculate the allowed atomic levels. However, the results that he got didn’t agree with the spectral data. Schrödinger decided that this avenue wasn’t worth pur- suing, and he set the calculations aside for several months.
Luckily, Schrödinger was asked to give a seminar on de Broglie’s work at the university. The discussion during the seminar motivated him to return to his work. In a couple of months, he came up with a wave equation that described the wavelike behavior of the electron in space and time and that established the connection between the wave and the particle. With his new equation, Schrödinger calculated the correct light spectrum of hydrogen, matching the experimental data very well.
Schrödinger published a paper on his wave equation in January of 1926, about six months after Heisenberg’s publication of his own theory. The world had not just one atomic theory but two: matrix mechanics and wave mechanics. Some time later, the English physicist Paul Dirac showed that these two versions are equivalent. Both versions survived, and we use them today. Schrödinger’s wave mechanics is the version that physics students learn first, because it’s easier to grasp if you’re familiar with regular waves. In graduate school, students move on to the more abstract and somewhat more powerful matrix mechanics. (There is even a third version, invented by Dirac himself, that’s a bit more sophisticated and powerful. Grad students sometimes use it in their theses.)
Accepting the uncertainty principle
What are the waves in Schrödinger’s wave mechanics? Are the particles themselves moving up and down like a wave? Max Born provided the answer. The waves are waves of probability: the probability of finding the electron at a particular location in space and time.
Are electrons particles or waves? Like light and electromagnetic radiation, electrons are both particles and waves. How can this be? You know the drill already. It’s a quantum physics thing. In Thomas Young’s experiment (see Chapter 7), you pass two coherent light beams (light beams that oscillate in step) through two narrow slits. The two beams overlap, producing bright areas where the waves reinforce each other and dark areas where they cancel each other out. The bright and dark areas form the interference pattern that’s the signature of the wave (see Figure 16-8).
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Figure 16-8: An interference pattern from Young’s double slit experiment. |
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Einstein showed that light also has particle properties, the photons. But can you think of light as being made up of these particle-like photons and still have an interference pattern? You might argue that photons, traveling at the speed of light, are really not quite the same as “real” particles, like electrons. But you’ll see that electrons are also very alien to the ideas we have in our minds about nature and reality. Let’s experiment with an electron and see what happens.
We’ll use the same setup from Young’s experiment: two narrow slits and a screen. The source of electrons is an electron gun from an old television set. The electrons that come out of the gun form the image on the TV screen when each one of them strikes the phosphor of the screen and lights it up. When you leave both holes open and turn the electron gun on, you see an interference pattern on the screen. Fine. The electrons are behaving like waves, and waves interfere like that (see Figure 16-9).
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Figure 16-9: Electrons demonstrate an interference pattern, which is characteris- tic of waves. |
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Now, cover one slit and turn the gun on (see Figure 16-10). No interference this time — just a bright area on the screen, the result of the many electrons that went straight through the hole and the ones that might’ve grazed the edges and got deflected a bit, you think. You get the same result with either hole.
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Figure 16-10: Covering one hole makes the interference pattern disappear. The electrons behave like particles. |
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The electrons are now behaving like particles. How do they know that you covered one hole?
Open both holes again and try to watch the electrons as they go through. To do that, you install small detectors by each hole and observe. (The detectors may shine some light on the electrons and detect the reflected light.) What you see is that single electrons pass through one hole or the other and hit the screen. Nothing strange — this is what you expect particles to do. But now the interference pattern isn’t there. The electrons are acting as particles (see Figure 16-11).
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Figure 16-11: When you watch every single electron that goes by, the interference pattern disappears. |
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Could it be that the detector is disturbing the electrons when you try to observe them? You can reduce the brightness of the detector light. But light is made up of photons. Reducing the brightness is the same as sending fewer photons to interact with the electrons. You can reduce the brightness until you send just one photon for every electron that passes by. (That’s okay, because your detector is very sensitive and can detect single photons.) When you do the experiment, watching every single electron with one single photon, you don’t get any interference patterns. The electrons behave like particles.
Reduce the brightness some more. Now you have fewer photons and some electrons go by undetected. When you observe the screen, you see the bright spots in front of the holes that particles form, but you also see a faint interference pattern overlaid on the bright spots. Reduce the brightness some more, and the interference pattern becomes stronger at the same time that the bright spots in front of the holes get fainter (see Figure 16-12).
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Figure 16-12: When you don’t watch every electron that goes by, the interference pattern begins to reappear. |
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You can’t win. The electrons outsmart any attempt at watching them without disturbing them. The electron is a particle when you try to detect it as a particle, and it’s a wave when you try to observe it as a wave. Heisenberg discovered this phenomenon early on, calling it the uncertainty principle. The problem is not that you aren’t being clever enough or that you lack better instruments. This is just the way the universe is.
Young’s experiment is an experiment to detect waves. When you don’t attempt to watch the electron, it behaves as a wave and forms an interference pattern. When you try to watch it, you are looking for it as a particle, and that’s what you see. Trying to observe the electron changes its behavior.
Succumbing to the New Physics
What is the true nature of the electron? After many years of deep thought and numerous discussions with Einstein, Niels Bohr came to the conclusion that the question doesn’t have any meaning. According to Bohr, it’s meaningless to ask what an electron really is. Physics isn’t about what is; it’s about telling us something about the world.
Heisenberg’s uncertainty principle says that you can’t determine with complete accuracy the position of an electron and at the same time measure where and how fast it’s going. An electron occupies a place in space only when you measure it at that location. If you measure its location again and find it some place else, that’s all you can say. How it got from here to there is a question that has no meaning in physics.
The uncertainty principle doesn’t apply just to electrons and atoms. It applies to everything. However, because it involves Planck’s constant, which is very small, you don’t notice its effects when you are watching baseballs, cars, or planets move.
Einstein didn’t buy it
Einstein, the scientist who started quantum physics, didn’t buy Bohr’s interpretation. He didn’t think that the universe was built on the type of uncertainty that quantum physics brings. “God doesn’t play dice with the universe,” he said once. He couldn’t accept that the universe is made with uncertainties and unpredictabilities.
Einstein believed instead that the uncertainties exist only because we don’t know enough. There are hidden variables that we aren’t seeing yet, but one day we will discover them. In other words, quantum physics isn’t complete.
In 1935, Einstein proposed a very clever experiment to show that the uncertainty principle and the unpredictable nature of quantum physics weren’t correct. He published a paper with his collaborators Boris Podolsky and Nathan Rosen.
In his EPR experiment (as it is called, after the authors’ names), Einstein imagined that a particle at rest in a laboratory splits into two equal pieces that fly away from each other (see Figure 16-13). Einstein proposed letting the fragments fly away for a long distance. Suppose that the original particle was in a laboratory on the ground on Earth. Also suppose that the arrival of the two particles is monitored by two detectors: one on the International Space Station, and a second in the Space Shuttle (see Figure 16-14). An astronaut in the Space Station measures the speed of one fragment when it gets there. That’s also the same speed of the other fragment moving in the opposite direction toward the Shuttle.
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Figure 16-13: EPR thought experiment. A particle initially at rest splits into two pieces that fly away from each other. |
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Figure 16-14: Astronauts in the International Space Station and in the Shuttle perform measurements on the fragments. |
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The astronaut in the Space Shuttle measures the position of the fragment arriving there. At that point, she knows the position, the speed, and the direction of her particle, even though she measured only one quantity. And she knows them accurately. No uncertainties here. Heisenberg’s uncertainty principle says that you can’t know the speed and the location of one of these fragments with complete accuracy. If you know one, you can’t know the other. Here was Einstein proposing a clever experiment to do just that.
Bohr sticks to his interpretation
Was it that easy to dethrone quantum physics? This simple thought experiment was saying that Heisenberg’s uncertainty principle wasn’t right. And the uncertainty principle is at the heart of quantum physics. If the principle doesn’t hold, the whole building comes crashing down.
Bohr’s response to Einstein’s EPR argument was unexpected. He said that because the two fragments were once in contact with each other, they remain linked forever, regardless of how far apart they are. After they break apart, they continue to form the system that you measure.
When the astronaut in the Space Station measures the speed of the fragment arriving there, the position of the fragment arriving at the Shuttle changes in such a way as to make it impossible for the other astronaut to measure it with any accuracy.
Einstein never accepted that idea. He called it “spooky action at a distance.” How can one particle at one location be affected by the measurements that you make to another particle very far away? For that to happen, an instantaneous signal must travel from one particle to the other, and according to relativity, no signal can travel faster than light.
It would’ve been easier to figure out what really happens by performing a real experiment. But an experiment this sophisticated was beyond the technological capabilities when Einstein and Bohr were alive.
The argument was not settled during their lifetimes. Most physicists sided with Bohr. His Copenhagen interpretation of quantum physics, as it is called, was what most scientists followed.
In 1965, ten years after Einstein died, the Scottish physicist John Bell, working at the European particle accelerator in Geneva, began to study the EPR experiment and came up with a powerful mathematical theorem that we know today as Bell’s inequality. This theorem made possible real EPR experiments.
The theorem is statistical in nature, and the reason it’s needed is that Heisenberg’s uncertainty principle applies only to many measurements. It doesn’t apply to a single measurement but to the measurement of many electrons. It’s a statement about a statistical average over many measurements.
Einstein was wrong
In 1982, French physicist Alain Aspect performed the first real EPR experiment with photons. Instead of position and speed, he measured another property called the polarization. Polarization is the orientation of a photon’s electromagnetic field. His results were clear. The world behaves like Bohr said it did. There are no hidden variables to be discovered; there is no theory to be proposed that would change quantum physics at its roots.
Einstein was wrong this time. The electron isn’t a particle or a wave. While you aren’t observing it, it doesn’t occupy a location in space. If you observe the electron, it is where you find it. If you measure it again at another location, that’s where it is. But the electron doesn’t travel from one location to the other. Physicists say that it “tunnels” through space between the two locations. Although not entirely accurate, the term helps scientists to at least talk about the phenomenon. It’s easier than saying that the electron was measured here, then it spread out throughout all space and reappeared at the second location when they made another measurement. This last statement is actually more accurate, but you can see how cumbersome it can become. Physicists working with quantum physics deal with this situation on a daily basis and usually leave it in the mathematical world, where the equations describe it correctly.
Does all of this sound very strange? That’s the way the universe is. What’s interesting is that scientists have come up with real applications that take advantage of this weird behavior. The first one is the Josephson junction, a type of electronic component that uses the “tunneling” of electrons between superconducting materials in actual devices with a variety of applications.
According to quantum physics, electrons, protons, atoms, and all the other particles that have been discovered are the representation in the physicists’ minds of what are really mathematical relationships connecting their observations.
Scientists arrived at this discovery slowly. Initially, they thought that they were dealing with tiny objects, very small particles that were much smaller versions of the tiny dust or smoke particles they had studied. When they finally discovered quantum physics and what it says about the world, the names had stuck.
The conclusion you can take with you after all of this is that on the very small scale of the atom, the world doesn’t look like the world we see every day. This world is impossible to visualize, and only through the mathematics of quantum physics can scientists make sense of it and use it for practical applications. Electrons exist. And they can be manipulated. Watch television tonight and see how amazingly accurate these electrons that you can’t visualize are aimed at all the different places on the screen to form the ever-changing images that give us the illusion of motion.
Teleportation
“Beam me up, Scotty.” The famous command from the Star Trek television series was invented because of budget limitations. During the production of the original series, there wasn’t a good way to land the ship in every episode, so the producer came up with the idea of teleporting people and things. Today, scientists at IBM and at the University of Michigan are getting us a little closer to achieving teleportation.
The first attempt ever at teleportation took place in 1997, when two research teams used a method proposed by Charles Bennett of the IBM Watson Research Center in Yorktown Heights, New York, which was based in the original EPR thought experiment. The first team, in Austria, reported results of the teleportation of a photon. A similar experiment was also done in Italy. In these experiments, two correlated or entangled photons were emitted from the same atom with the same polarization. When the polarization of one photon was changed, the entangled partner immediately polarized itself in the opposite direction. Bennett had proposed going one step further, using the information sent to the entangled partner to reproduce the state of the first particle, which has changed because of the measurements. Because all photons are identical, reproducing the state of the original photon on the second one amounts to transmitting the particle.
Since then, several other groups have attempted similar experiments. In 2004, Boris Blinov and his collaborators at the University of Michigan were able to entangle a photon and an ion (an electrically charged atom). The next step for his team is to entangle two widely separated ions by first entangling each ion and its photon and then entangling the two photons.
