Fear of Physics (15 page)

Be that as it may, Dirac was not one to do physics by visualization. He felt much more comfortable with equations, and it was only after playing with one set of equations for several years that he discovered a remarkable relation that correctly described the quantum-mechanical and special-relativistic behavior of electrons. It quickly became clear not only that this equation predicted the possible existence of a positive partner of the electron, which could exist as a “virtual” particle produced as part of a virtual pair of particles, but that this new object must also be able to exist on its own as a real particle in isolation.

At that time the only known positively charged particle in nature was the proton. Dirac and colleagues, who saw that his equation correctly predicted a number of otherwise unexplained features of atomic phenomena but did not want to depart too far from current orthodoxy, thus assumed that the proton must be the positive particle predicted by the theory. The only problem was that the proton was almost 2,000 times heavier than the electron, while the most naive interpretation of Dirac’s theory was that the positive particle should have the same mass as the electron.

Here was an example where two known, well-measured theories of the physical world, when pushed to their limits, forced upon us paradoxical conclusions, just as relativity did for the unification of Galileo’s ideas with electromagnetism. Yet, unlike Einstein, physicists in 1928 were not so ready to demand new phenomena to validate their ideas. It was not until 1932 that, quite by accident, the American experimental physicist Carl Anderson, observing cosmic rays—the high-energy particles that continually bombard the Earth and whose origin ranges from nearby
solar flares to exploding stars in distant galaxies—discovered an anomaly in his data. This anomaly could be explained only if there existed a new, positively charged particle whose mass was much closer to that of the electron than the proton. So it was that the “positron,” the “antiparticle” of the electron predicted by Dirac’s theory, was discovered. We now know that the same laws of quantum mechanics and relativity tell us that for every charged particle in nature, there should exist an antiparticle of equal mass and opposite electric charge.

Reflecting on his timidity in accepting the implications of his work amalgamating special relativity and quantum mechanics, Dirac is said to have made one of his rare utterances: “My equation was smarter than I was!” So, too, my purpose in relating this story is to illustrate again how the most remarkable results in physics often arise not from discarding current ideas and techniques, but rather by boldly pushing them as far as you can—and then having the courage to explore the implications.

I think I have pushed the idea of pushing ideas as far as they can be pushed about as far as I can push it. But by entitling this chapter “Creative Plagiarism,” I don’t mean just stretching old ideas to their limits; I also mean copying them over whole hog! Everywhere we turn nature keeps on repeating herself. For example, there are only four forces we know of in nature—the strong, weak, electromagnetic, and gravitational forces—and every one of them exists in the image of any of the others. Begin with Newton’s Law of Gravity. The only other long-range force in nature, the force between charged particles, starts out as a direct copy of gravity. Change “mass” to “electric charge” and that’s largely it. The classical picture of an electron orbiting a proton to make up the simplest atom, hydrogen, is
identical
to the picture of the
moon orbiting the Earth. The strengths of the interactions are quite different, and that accounts for the difference of scale in the problem, but otherwise all of the results built up to describe the motion of the planets around the sun and apply in this case. We find out that the period of an electron’s orbit around a proton is about 10
^–15
seconds, as opposed to one month for the moon around the Earth. Even this straightforward observation is enlightening. The frequency of visible light emitted by atoms is of the order of 10
¹⁵
cycles/second, strongly suggesting that the electron orbiting around the atom has something to do with the emission of light, as is indeed the case.

Of course, there are important differences that make the electric force richer than gravity. Electric charge comes in two different types: positive and negative. Thus, electric forces can be repulsive as well as attractive. In addition, there is the fact that moving electric charges experience a magnetic force. As I described earlier, this leads to the existence of light, as an electromagnetic wave generated by moving charges. The theory of electromagnetism, in which all these phenomena are unified, then serves as a model for the weak interactions between particles in nuclei that are responsible for most nuclear reactions. The theories are so similar that it was eventually realized that they could be unified together into a single theory, which itself was a generalization of electromagnetism. The fourth force, the strong force between quarks that make up protons and neutrons, is also modeled on electromagnetism. This is reflected in its name,
quantum chromodynamics,
a descendant of quantum electrodynamics. Finally, with the experience gained from these theories we can go back to Newtonian gravity and generalize it and, lo and behold, we arrive at Einstein’s general relativity. As the physicist
Sheldon Glashow has said, physics, like the Ouroboros, the snake that eats its tail, returns full circle.

 

 

I want to end this chapter with a specific example that graphically demonstrates how strong the connections are between completely different areas of physics. It has to do with the Large Hadron Collider (LHC), a mammoth particle accelerator being completed in 2007 for a total cost of approximately $5–$10 billion dollars.

Anyone who has ever visited the site of a large particle physics laboratory has experienced the meaning of the words of the eminent physicist/educator Vicki Weisskopf, who has described these facilities as the gothic cathedrals of the twentieth century. In scale and complexity, they are to the twentieth century what the vast engineering church projects were to the eleventh and twelfth centuries (although I doubt they will last as long). The Large Hadron Collider is located about one hundred feet below the Swiss and French countryside, in a large circle 27 kilometers around, with over 6,000 superconducting magnets to guide two streams of protons in opposite directions around the tunnel, causing them to collide together at energies of 7,000 times their rest mass. Each collision can produce on average over one thousand particles, and there can be upwards of 600 million collisions per second.

The purpose of this gargantuan machine is to attempt to discover the origin of “mass” in nature. We currently have no idea why elementary particles have the masses they do, why some are heavier than others, and why some, such as neutrinos, are so light. A number of strong theoretical arguments suggest that the key to this mystery can be probed at energies accessible at the LHC.

The Large Hadron Collider (LHC) depends crucially for its success on the many superconducting magnets that make up its central “engine,” magnets that without the aid of cooling to temperatures so low that the wires in them become superconducting, would otherwise be impossible or at least prohibitively expensive to build. To understand why the phenomenon of superconductivity that makes the LHC technically possible is also appropriate on much deeper grounds, we have to go back some eighty years to a laboratory in Leiden, Holland, where the distinguished Dutch experimental physicist H. Kammerlingh Onnes discovered the amazing phenomenon we now call superconductivity. Onnes was cooling down the metal mercury to a low temperature in his laboratory in order to examine its properties. As you cool any material down, its resistance to the flow of electric current decreases, primarily because the motion of the atoms and molecules in the material that tends to block the flow of current decreases. However, when Onnes cooled the mercury down to 270° below zero (Celsius), he witnessed something unexpected: The electrical resistance vanished completely! I do not mean that there was
hardly
any resistance; I mean there was
none.
A current, once started, would continue to flow unchanged for very long periods in a coil of such material, even after the power source that had started the current flowing was removed. Onnes dramatically demonstrated this fact by carrying along with him a loop of superconducting wire containing a persistent current from his home in Leiden to Cambridge, England.

Superconductivity remained an intriguing mystery for almost half a century until a full microscopic theory explaining the phenomenon was developed in 1957 by the physicists John Bardeen, Leon Cooper, and J. Robert Schrieffer. Bardeen had already made an important contribution to modern science and technology by
being the co-inventor of the transistor, the basis of all modern electronic equipment. The Nobel Prize in Physics that Bardeen shared with Cooper and Schrieffer in 1972 for their work on superconductivity was his second. (Some time ago I read a letter of complaint to a physics magazine which made the ironic point that when Bardeen—the only person to win two Nobel Prizes in the same field and the co-inventor of a device that changed the way the world worked—died in 1992, it was hardly mentioned on TV. It would be nice if people were able to associate the pleasure they get from their transistor-driven stereos, TVs, games, and computers with the ideas that people like Bardeen produced.)

The key idea that led to a theory of superconductivity was in fact proposed by the physicist Fritz London in 1950. He suggested that this weird behavior was the result of quantum-mechanical phenomena, which normally affect behavior on only very small scales, suddenly extending to macroscopic scales. It was as if all the electrons in a conductor normally contributing to the current that flows when you attach this conductor to a power source were suddenly acting as a single, “coherent” configuration with a behavior governed more by the quantum-mechanical laws that control the individual electrons than by the classical laws that normally govern macroscopic objects. If all the electrons that conduct current act as a single configuration that stretches all the way across the conductor, then the flow of current cannot be thought of as being due to the motion of individual electrons that may bounce off obstacles as they move, producing a resistance to their motion. Rather, this coherent configuration, which spans the material, allows charge to be transported through it. It is as if in one state, this configuration corresponds to a whole bunch of electrons at rest. In another state, which is stable and time-independent, the configuration
corresponds to a whole bunch of electrons that are moving uniformly.

This whole phenomenon can take place only because of an important property of quantum mechanics. Because the amount of energy that can be transferred to or from a finite-sized system occurs only in discrete amounts, or “quanta,” the set of possible energy states for any particular particle in a finite system is reduced in quantum mechanics from a continuous set to a discrete set. This is because the particles can only change their energy by absorbing energy. But if energy can only be absorbed in discrete amounts, the set of possible energies the particles can have will also be discrete. Now, what happens if you have a whole bunch of particles in a box? If there are many possible different energy states for the particles, one might expect each of them to occupy a different discrete state, on average. Yet sometimes, under very special circumstances, it is possible that all of the particles might want to occupy a single state.

To understand how this might happen, consider the following familiar experience: You watch a comedy in a crowded movie theater and find it hilarious. You then rent the video to watch at home alone, and it is merely funny. The reason? Laughter is contagious. When someone next to you starts to laugh uproariously, it is difficult not to laugh along. And the more people who are laughing around you, the harder it is to keep from joining them.

The physical analogue of this phenomenon can be at work for the particles in the box. Say that in a certain configuration, two particles in the box can be attracted to each other, and thus lower their total energy by hanging out together. Once two particles are doing this, it may be even more energetically favorable for a third bystander particle to join the pack. Now, say this particular kind of attraction occurs only if the particles are in one out of all the
possible configurations they can have. You can guess what will happen. If you start the particles out randomly, pretty soon they will all “condense” into the same quantum state. Thus, a coherent “condensate” is formed.

But there is more to it. Because the different quantum states in a system are separated into discrete levels, once all the particles in this system are condensed into a single state, there can be a sizable “gap” in total energy between this state and a state of the whole system where, say, one particle is moving around independently and the rest remain grouped. This is precisely the situation in a superconductor. Even though each electron is negatively charged, and therefore repels other electrons, inside the material there can be a small residual attraction between electrons due to the presence of all the atoms in the solid. This in turn can cause the electrons to pair together and then condense in a single, coherent quantum configuration. Now, say I connect this whole system to a battery. All of the electrons want to move together in the presence of the electric force. If any one of them were to scatter off an obstacle, retarding its motion, it would have to change its quantum state at the same time. But there is an “energy barrier” that prevents this, because the electron is so tightly coupled to all of its partners. Thus, the electrons all move together on their merry way, avoiding obstacles and producing no resistance.

Just by the remarkable behavior of this conglomeration of electrons, you can guess that there will be other properties of the material that are changed in this superconducting state. One of these properties is called the Meissner effect, after the German physicist W. Meissner, who discovered it in 1933. He found that if you put a superconductor near a magnet, the superconducting material will make every effort to “expel” the magnetic field due to the magnet. By this I mean that the electrons in the material will
arrange themselves so that the magnetic field outside is completely canceled and remains zero inside the material. In order to do so, little magnetic fields must be created on the surface of the material to cancel the external magnetic field. Thus, if you bring the material near the north pole of a magnet, all sorts of little north poles will be created on the surface of the material to repel the initial field. This can be quite dramatic. If you take a material that isn’t superconducting and put it on a magnet, it may just sit there. If you cool the whole system down so that the material becomes superconducting, it will suddenly rise and “levitate” above the magnet because of all the little magnetic fields created on the surface that repel the initial magnetic field.