The Amazing Story of Quantum Mechanics
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Consequently, rather than delve into the inner workings of a variety of electronic products, which will not necessarily add much to our discussion of quantum mechanics, I use this final section to describe how quantum physics may continue to shape the future. That is, I would like to describe the concepts and devices that may become part of our world five or ten or twenty years from now. I will not try to make actual predictions, as that is a mug’s game, but will rather explain the relevant quantum mechanics that underlies such phenomena as “quantum computers” and “nanotechnology.” We already understand the basics; now I will discuss some novel advanced applications that may be coming to a consumer electronics store near you the day after tomorrow.
As described in Chapter 18, the greater sensitivity of read-head sensors using the giant magnetoresistance effect and magnetic tunnel junctions means that smaller magnetic bits can be detected, resulting in an increase in the storage capacity of hard drives. These magnetic sensors can also enable faster data retrieval. The polarization and depolarization of the magnetic layers in the sensor happens quickly, so the detector can read the bits even when the hard-drive platters are rotating at speeds of over ten thousand revolutions per minute. But the next generation of “semiconductor spintronic” devices may increase the speed of computers even more, by removing the need for a separate magnetic storage medium.
There has been considerable interest by researchers in developing semiconductor transistor structures that make use of the electron’s internal magnetic field to process information. Using magnetic metals as the electrodes on a semiconductor device, it is possible to inject magnetically polarized electrons, that is, charge carriers whose internal magnetic fields all point in the same direction, into a semiconductor. By varying the magnetic field in the semiconductor device, the current could be controlled without the need to change the concentration of charge carriers, as in the field-effect transistor discussed in Chapter 17. The goal is to construct a device with a steeper on-off transition for the high-low current levels that are used to represent “ones” and “zeros,” with faster switching between these two states that uses less energy to operate.
This last point is important. Each transistor in your computer creates a small amount of heat as it drives a current from low to high values and back again (passing a current through a toaster wire or lightbulb filament generates heat, and the same physics applies inside a semiconductor transistor). When millions and millions of these transistors are packed into a confined space, the resulting temperature rise can be significant, and in turn this consideration can limit the integrated circuit’s performance. Hence the need for multiple cooling fans in most computer towers. “Spin transistors” use less power, thereby allowing a greater number of devices to be placed in close proximity, resulting in more computing power packed onto a microprocessor.
In addition, the ability to both store magnetic information and manipulate ones and zeros as in an integrated circuit suggests that it might be possible to combine both magnetic data storage and computer logic functions on a single chip. In the late 1950s, when the Challengers of the Unknown faced off against a “calculating machine” capable of independent thought, it was believed that such a device would have to be the size of a large room, while in the future, thanks to quantum mechanics, we may all be able to carry our own ULTIVACs in our back pockets.
The need for speed in computation is driving interest in an even more exotic use of quantum mechanical spin in calculators, often referred to as “quantum computers.” Of course, in a sense all computers (aside from an abacus or a slide rule) are quantum computers, in that their fundamental data-processing elements, diodes and transistors, would not have been invented if not for the insights into the properties of matter provided by quantum theory.
A “quantum computer” is a different beast entirely. In short, rather than represent a “one” or a “zero” through a high or low current passing through a transistor, or from a region of magnetic material with its north pole pointing in one direction or the other, the atoms themselves are the ones and zeros. Actually, quantum computers have been proposed that involve atoms, nuclei, ions, photons, or electrons as the basic computing element—I focus my discussion on electrons for simplicity. Electrons have an intrinsic angular momentum of either +ℏ/2 or -ℏ/2, and in a quantum computer these are the elements that will represent the ones and zeros.
While using electrons in this way would indeed shrink the size of the computer’s elements nearly as far as physically possible, this alone is not what motivates research in quantum computers. Proposed quantum computers involve using pairs of identical particles, arranged so that their wave functions overlap. Recall the discussion from Chapter 12 of two electrons brought so close that their de Broglie waves interfered. In this case we represented the new two-electron wave function by a single ribbon, where one side of the ribbon was white and the other was black. In the example in Figure 30, both sides of the ribbon facing out were white. But we could also have held both black sides facing out, or the left side could have been black and the right side white, or the reverse. To represent these four possibilities—white, white; black, black; black, white; white, black—using conventional computer elements would require two transistors, and they could generate these states only one at a time, that is, in series.
With the quantum ribbon from Chapter 12, all four states are possible simultaneously—if the ribbon is in a dark room and we don’t know which sides are facing out. In this case, all four states may be present, and until we turn on the lights and examine the ribbon, the ribbon can represent the four possible states in parallel. Where I need four separate conventional bits to represent these outcomes, I need only two “quantum bits,” or “qubits,” to accomplish the same task. While the ribbon analogy breaks down when dealing with more than two entangled wave functions, the arguments hold, and one needs only three quantum bits to represent eight distinct conventional states, and ten qubits can do the work of 1,024 classical bits.
This parallelism implies that a quantum computer could perform calculations must faster than a conventional computer. Encryption of information for national security, online commerce, or just using a credit card to pay for a purchase at a gas station involves knowledge of the prime-number factors72 of numbers that are so large that even the fastest conventional computers could not determine the factors in a reasonable time. Quantum computers, with the ability to perform multiple tasks at the same time, could change this situation. A small-scale prototype quantum computer has been able to successfully factor a two-digit number (15 = 5 × 3), but a fully operational quantum computer does not exist and is years and years away in the most optimistic scenario. Nevertheless, data security and cryptology will be dramatically changed if such devices are ever constructed. It will be up to all of us to ensure that this technology does not fall into the wrong hands, for who could forget when the evil Decepticons used quantum computers to hack into the Pentagon’s secure computer system in the Transformers movie (2007), cracking a code in ten seconds that would take more than two decades for the most power supercomputer.
Now, to say that two overlapping electrons can represent all four spin combinations, provided we don’t examine them, may seem a bit73 of a cheat—you can argue that any pair of transistors can represent all four states if I do not actually examine whether the currents passing through them are high or low. But there is a fundamental difference in the quantum spin case that gets to the heart of some of the philosophical arguments over the role of measurement in quantum mechanics.
Throughout this entire book I have pulled a fast one on you, Fearless Reader, and its time to come clean. The difference between the quantum case of overlapping electronic wave functions and the conventional situation involving transistors, and the reason that the quantum ribbon can represent all four possible outcomes simultaneously, is that if the ribbon remains in the dark, that is, until I do a measurement and examine it, the very concept of the color of the rib
bon is not well defined.
Let’s return to the real world of electrons for a moment. I have specified that an electron can have only one of two possible values of its intrinsic angular momentum, rotating either clockwise (that is, spin “up”) or counterclockwise (spin “down”). But we never asked the question: Up or down—relative to what? Clockwise or counterclockwise rotations—about what axis?
The intrinsic angular momentum has a small magnetic field associated with it, with a north pole and south pole. If I don’t measure this magnetic field, that is, in the absence of an external magnetic field, then I have no way of knowing where the pole is oriented. If I apply an external magnetic field and measure the electron’s magnetic orientation, it will either line up with the field or be 180 degrees opposite to the external field (as in our discussion of MRI in Chapter 19). If the external magnet I apply has its north pole pointing toward the ceiling of the room you are in, then this defines the “up”/”down” direction. The electron’s magnetic field will point either to the ceiling or to the floor. If the external magnetic field is instead applied pointing toward one of the walls in your room, then this defines the “up”/”down” direction, and the electron’s magnetic field will point either toward the wall or toward the wall opposite it. Once I apply an external field and measure the electron’s magnetic field, that very act defines the axis about which “clockwise” and “counterclockwise” make sense, and until I do, all I can say is that the electron is in some superposition of these possibilities. It is in this way that we can say that a quantum system can represent multiple states simultaneously.74
Einstein smelled a rat in this scenario and spent a considerable fraction of his later years trying to catch it, for the situation just described opens up the possibility for information to travel faster than the speed of light. Say I arrange two electrons so that their wave functions overlap, and they can be described by a two-particle wave function (as in Chapter 12) and with total intrinsic angular momentum together to be zero. One electron has spin = +ℏ/2 and the other has spin = -ℏ/2, but let’s say I don’t know which is which. When I measure the electron on the left and find that its spin is +ℏ/2, not only do I know logically that the other spin must be -ℏ/2 (since I already knew that the total spin was zero), but I also now know what axis the second electron will be anti-aligned with! The process of measuring the first electron’s magnetic field picks a preferred direction not only for that electron, but for the other one as well, since they are both part of the same wave function, which contains all the information about the system.
Now, here’s where it gets fun. Let’s assume I have an infinitely stretchy ribbon representing the two electrons. I hold one end of the ribbon and pull the other end all the way across town, keeping the electrons still connected. Now I measure the spin of one electron, by placing it in an external magnetic field. This not only tells me if this electron is pointing with or against the applied field, but determines what direction the electron’s magnetic field points. As soon as I do this, the properties of the other electron are also determined. After all, both electrons are described by a single wave function and thus behave as a single entity. In this way the entangled quantum state is like the famous twins in fairy tales, joined by a special bond, so that what happens to one is instantly felt by the other. Einstein objected that this would enable information (about the direction of the magnetic field being used in my lab to measure the electron) to be transmitted from one point in space to another, potentially faster than light could cover the same distance. In his famous phrase, this represented “spooky action at a distance,” and he would have none of it.
Books have been written over the question of whether this scenario does indeed provide a mechanism for instantaneous transmission of information, and, if it does, how to reconcile this with the principles of the Special Theory of Relativity that states that nothing, not even information, can travel faster than light. It remains a topic of lively debate among physicists. As the man said when asked by the child about the nature of the afterlife—experts disagree. Now, questions of what “happens” to a quantum system in the moment of observation are fascinating, but a full discussion of these topics is not the focus of this text. I will therefore now exit, stage left, following two brief observations.
First, the issue of faster-than-light transmission of information holds only if the two electrons are described by a single wave function, and that will be true only if the “infinitely stretchy” ribbon does not break as I pull the two ends farther and farther apart. As you might expect, the more the ribbon is stretched, the easier it is for some stray perturbation to disturb the overlapping waves between the two ends. Once the connection between the two ends is severed, then a measurement of the spin of one electron will have no bearing at all on the other electron, as they are now described by two distinct ribbons. The fancy way to describe this is that the two electrons’ wave functions must remain “entangled” in order for this process to hold, and any object or input of energy that disturbs this state (breaks the ribbon) causes “decoherence.” Overcoming the enormous challenges involved in avoiding decoherence keeps experimental physicists busy, and whether a functioning quantum computer is ever constructed that can live up to its potential remains to be seen.
Figure 50: The Atom (who in his secret identity is physics professor Ray Palmer), informs his Justice League of America colleagues about recent experiments involving entangled quantum states of photons in JLA # 19. Professor Palmer is referring to the work of Anton Zeilinger and coworkers, published in Physical Review Letters (1998). The second panel is an illustration of the overinterpretation of the principles of quantum mechanics to matters of spirituality—we will avoid this trap, as we do all such traps into which the Justice League may fall.
The second point is that whenever one reads in the popular science press about recent experiments in “teleportation,” what they are always referring to is the transmission of information concerning a quantum state, similar to the situation described above. They are not dealing with “beaming” people as in Star Trek, or sending atoms or electrons from one point in space to another. You will have to face your daily morning commute for quite some time.
There have recently been experiments that indeed support the notion that information concerning two entangled quantum entities, such as the polarization of photons, can be transmitted even when separated by a great distance. That is, experimental techniques have now advanced such that considerations that previously had been purely theoretical may be put to empirical verification, as shown in Figure 50, from a 1998 issue of the adventures of the Justice League of America. Real science is now inspiring the comic books, and not the other way round!
CHAPTER TWENTY-ONE
Seriously, Where’s My Jet Pack?
As mentioned at the very start of our narrative, science fiction pulp writers expected that the future would bring a new era in energy production and storage. Instead, it was data manipulation that underwent a profound transformation, enabled by the discoveries of quantum mechanics.
Why is a new type of energy-delivery system needed before jet packs and flying cars become commercially viable? Let’s stipulate that we are not invoking any violations of the laws of physics, such as the discovery of “cavorite” or some other miraculous material with antigravity properties. Thus, our jet pack must provide a downward thrust, equal to a person’s weight, in order to lift the person off the ground. Consider how much energy it takes to lift a 180-pound person 330 feet (one-sixteenth of a mile) up in the air. Just to get up there, neglecting any energy needed to jet from place to place, would require an energy expenditure of a little over eighty thousand Joules, which is equivalent to 0.5 trillion trillion electron Volts.
Recall that nearly every chemical reaction involves energy transfers on the order of an electron Volt. Thus, to lift a person over a twenty-story building involves roughly a trillion trillion molecules of fuel. But that’s not actually as much as it seems,
for there are approximately that many atoms in twenty cubic centimeters of any solid (recall that a cubic centimeter is about the size of a sugar cube). A gallon of fuel contains nearly four thousand cubic centimeters, capable of producing over a hundred trillion trillion electron Volts of energy. If this is the case, why are we still driving to work?
The problem is—what goes up must come down. As soon as our jet pack stops expending energy to maintain our large potential energy above ground, back to Earth we return. Thus, every second we spend in the air, we must continue to burn through our stored chemical energy. The rate at which we use up fuel will depend on the particular mechanism by which we achieve an upward thrust, but for most energy supplies, our trip will be over in a minute or two. We can indeed take jet packs to work, provided we live no more than a few blocks from our office.
Note that the largest expenditure in energy is overcoming gravity. It takes more than eighty thousand Joules to get us up in the air. Flying at forty miles per hour, in contrast, calls for a kinetic energy of only thirteen thousand Joules (neglecting the work we must do to overcome air resistance). This is why we don’t have flying cars. Your gas mileage would be nonexistent if the vast majority of the fuel you carried went toward lifting you up off the ground, with hardly any left over to get you to your destination (sort of defeats the whole purpose of a car, flying or otherwise).
There have been improvements in the energy content of stored fuel, and prototype jet packs have been able to keep test pilots aloft for more than a minute, but ultimately, the longer the flight, the more fuel needed (and the heavier the jet pack will be). Of course, there are alternatives to chemical-fuel reactions to achieve thrust and lift. One could use a nuclear reaction, which, as we saw in Section 3, yields roughly a million times more energy per atom than chemical combustion, but the idea of wearing even a licensed nuclear power plant on your back is less than appealing (except possibly for the Ghostbusters).