Fear of Physics (3 page)

 

 

Unfortunately, in trying to understand things exactly we often miss the important fundamentals and get hung up on side issues. If Galileo and Aristotle seem a little removed, here’s an example that is closer to home. A relative of mine, along with several others—all college-educated individuals, one a high school physics teacher—invested over a million dollars in a project involving the development of a new engine whose only source of fuel was intended to be the Earth’s gravitational field. Driven by dreams of solving the world’s energy crisis, eliminating domestic dependence on foreign oil, and becoming fabulously wealthy, they let themselves be convinced that the machine could be perfected for just a little more money.

These people were not so naive as to believe you could get something for nothing. They did not think they were investing in a “perpetual motion” machine. They assumed that it was somehow extracting “energy” from the Earth’s gravitational field. The device had so many gears, pulleys, and levers that the investors felt they could neither isolate the actual mechanism driving the machine nor attempt a detailed analysis of its engineering features. In actual demonstrations, once a brake on the machine was removed, the large flywheel began to rotate and appeared to gain speed briefly during the demonstration, and this seemed convincing.

In spite of the complexity of the machine’s details, when these very details are ignored, the impossibility of the machine becomes manifest. Consider the configuration of the prototype I have
drawn below at the start and the end of one complete cycle (when all the wheels have made one complete revolution):

Every gear, every pulley, every nut, every bolt, is in exactly the same place! Nothing has shifted, nothing has “fallen,” nothing has evaporated. If the large flywheel were standing still at the beginning of the cycle, how can it be moving at the end?

The problem with trying to perform an “engineering” analysis of the device is that if there are many components, it may be extremely difficult to determine exactly where and when the forces on any specific component cause the motion to cease. A “physics” analysis instead involves concentrating on the fundamentals and not the details. Put the whole thing in a black box, for example (a spherical one if you wish!), and consider only the simple requirement: If something, such as energy, is to be produced, it must come from inside; but if nothing changes inside, nothing can come out. If you try instead to keep track of everything, you can easily lose the forest for the trees.

How do you know in advance what is essential from what you can safely throw out? Often you don’t. The only way to find out is to go ahead as best you can and see if the results make sense. In
the words of Richard Feynman, “Damn the torpedoes, full speed ahead!”
^a

 

 

Consider, for example, trying to understand the structure of the sun. To produce the observed energy being emitted from the solar surface, the equivalent of a hundred billion hydrogen bombs must be exploding every second in its unfathomably hot, dense core! On the face of it, one could not imagine a more turbulent and complex environment. Luckily for the human species, the solar furnace has nevertheless been pretty consistent over the past few billion years, so it is reasonable to assume that things inside the sun are pretty much under control. The simplest alternative and, more important, perhaps the only one that lends itself even to the possibility of an analytical treatment, is to assume the inside of the sun is in “hydrostatic equilibrium.” This means that the nuclear reactions going on inside the sun heat it up until just enough pressure is created to hold up the outside, which otherwise would collapse inward due to gravity. If the outside of the sun were to begin to collapse inward, the pressure and temperature inside the sun would increase, causing the nuclear reactions to happen more quickly, which in turn would cause the pressure to increase still more and push the outside back out. Similarly, if the sun were to expand in size, the core would get cooler, the nuclear reactions would proceed more slowly, the pressure would drop, and the outside would fall in a little. So the sun keeps burning at the same rate over long time intervals. In this sense, the
sun works just like the piston in the engine of your car as you cruise along at a constant speed.

Even this explanation would be too difficult to handle numerically if we didn’t make some further simplifications. First,
we assume the sun is a sphere!
Namely, we assume that the density of the sun changes in exactly the same way as we travel out from its center in any direction—we assume the density, pressure, and temperature are the same everywhere on the surface of any sphere inside the sun. Next, we assume that lots of other things that could dramatically complicate the dynamics of the sun, such as huge magnetic fields in its core, aren’t there.

Unlike the assumption of hydrostatic equilibrium, these assumptions aren’t made primarily on physical grounds. After all, we know from observation that the sun rotates, and this causes observable spatial variations as one moves around the solar surface. Similarly, the existence of sunspots tells us that the conditions on the solar surface are variable—its period of activity varies regularly on an eleven-year cycle at the surface. We ignore these complications both because for the most part they are too difficult to deal with, at least initially, and because it is quite plausible that the amount of solar rotation and the coupling between surface effects and the solar core are both small enough to ignore without throwing off our approximation.

So how good does this model of the sun work? Better than we probably have a right to expect. The size, surface temperature, brightness, and age of the sun can be fit with very high accuracy. More striking, perhaps, just as a crystal wineglass vibrates with sound waves when its rim is excited properly with your finger, just as the Earth vibrates with “seismic waves” due to the stresses released by an earthquake, the sun, too, vibrates with characteristic frequencies due to all the excitement happening inside. These
vibrations cause motions on its surface that can be observed from Earth, and the frequencies of this motion can tell us a great deal about the solar interior, in the same manner that seismic waves can be used to probe the Earth’s composition when searching for oil. What has become known as the Standard Solar Model—the model that incorporates all the approximations I just described—predicts more or less exactly the spectrum of oscillations at the solar surface that we observe.

It thus seems safe to imagine that the sun
really is
a simple sphere—that our approximate picture comes very close to the real thing. However, there was a problem. Besides producing an abundance of heat and light, the nuclear reactions going on inside the sun produce other things. Most important, they produce curious elementary particles, microscopic objects akin to particles such as electrons and quarks that make up atoms, called
neutrinos.
These particles have an important difference from the particles that make up ordinary matter. They interact so weakly with normal matter, in fact, that most neutrinos travel right through the Earth without ever knowing it is there. In the time it takes you to read this sentence, a thousand billion neutrinos originating in the fiery solar furnace have streamed through your body. (This is true day
or
night, since at night the neutrinos from the sun travel through the Earth to pierce you from below!) Since they were first proposed in the 1930s, neutrinos have played a very important role in our understanding of nature on its smallest scales. The neutrinos from the sun, however, caused nothing but confusion.

The same Solar-Model calculations that so well predict all the other observable features of the sun should allow us to predict how many neutrinos of a given energy should arrive at the Earth’s surface at any time. And while you might imagine that these
elusive critters are impossible to detect, large underground experiments have been built with a great deal of ingenuity, patience, and high technology to do just that. The first of these, in a deep mine in South Dakota, involved a tank of 100,000 gallons of cleaning fluid, in which one atom of chlorine each day was predicted to be converted into an atom of argon by a chance interaction with a neutrino streaming from the sun. After twenty-five years, two different experiments sensitive to these highest-energy neutrinos from the sun have now reported their results. Both found fewer neutrinos than expected, between one-half and one-quarter of the predicted amount.

Your first reaction to this might be that it is much ado about nothing. To predict the results that closely could be viewed as a great success, since these predictions rely on the approximations of the sun’s furnace which I have discussed. Indeed, many physicists took this as a sign that at least one of these approximations must be inappropriate. Others, most notably those involved with developing the Standard Solar Model, said this was extremely unlikely, given the excellent agreement with all other observables.

The 1990s, however, produced a heroic series of experiments that have finally resolved this mystery. The first set of experiments involved a gigantic underground 50,000-ton water detector that was able to detect so many neutrino events that it could confirm with very high accuracy that in fact fewer neutrinos appeared to be coming from the sun than expected.

Next, a novel type of underground detector, using heavy water instead of ordinary water, was built in Sudbury, Canada. One thing that I didn’t explain yet is that all the previous neutrino detectors were sensitive primarily to only one kind of neutrino, and it turns out that there are three different types of neutrinos in nature that we know of. Nuclear reactions produce one kind of neutrino,
called electron-neutrinos, so it makes sense that all the original detectors were sensitive to just these electron-neutrinos.

One of the exotic possible ways to resolve the solar neutrino problem, as it became known, would be if somehow the electron-neutrinos emitted by the nuclear reactions in the sun were to convert themselves into some other type of neutrino inside the sun, or on their way to the Earth. This would require some kind of new physical processes that are not a part of what had become known as the Standard Model of particle physics—in particular it would require that neutrinos are not massless particles, but instead have a very small mass. In any case, if electron-neutrinos converted into other kinds of neutrinos before reaching terrestrial detectors then this would explain why fewer were observed than expected.

The heavy water detector was able to simultaneously detect both electron neutrinos and the two other kinds of neutrinos, using two different types of neutrino interactions with neutrons in the heavy water. Lo and behold, when the dust had settled, and all neutrino types were counted, it turned out that the total number of neutrinos coming from the sun was precisely the number predicted by the Standard Solar Model! Neutrinos “oscillations” had been observed, neutrino masses were discovered, and some very happy physicists received the Nobel Prize. Once again, approximating the sun, like a cow, as a simple sphere, had proved to be a powerful approximation that revealed yet another hidden facet of nature’s tapestry.

We can push still farther the approximation that the sun is a sphere, to probe still more of the universe. We can try to understand other stars, both bigger and smaller, younger and older, than the sun. In particular, the simple picture of hydrostatic equilibrium should give us a rough idea of the general behavior of stars
over their entire lifetimes. For example, from the time stars first begin to form from collapsing gas until the nuclear reactions first turn on, the gas continues to get hotter and hotter. If the star is too small, the heat of the gas at prenuclear levels can provide sufficient pressure to support its mass. In this case, the star will never “turn on,” and nuclear reactions will not begin. Jupiter is such an object, for example. For bigger clumps, however, the collapse continues until nuclear ignition begins and the heat released provides additional pressure which can stop further collapse and stabilize the system. Eventually, as the hydrogen fuel for the nuclear reactions begins to deplete, the slow inner collapse begins anew, until the core of the star is hot enough to burn the product of the first set of reactions, helium. For many stars this process continues, each time burning the product of the previous set of reactions, until the core of the star—now called a red or blue giant, because of the change of its surface color as the outside shell expands to great size at the same time as the inner core gets hotter and denser—is composed primarily of iron. Here the process must stop, one way or another, because iron cannot be used as nuclear fuel, due to the fact that the constituents of its nucleus—protons and neutrons—are so deeply bound together that they cannot give up any more binding energy by becoming part of a larger system. What happens at this point? One of two things. Either the star slowly dies down, like a match at the end of its stick or, for more massive stars, one of the most amazing events in the universe occurs: The star explodes!