The First Elements
The formation of nuclei at the three-minute mark lasted for only a short time before the Hubble expansion spread matter too thinly for nuclear reactions to proceed. During this short burst of nucleus building, there was time to create appreciable amounts of deuterium (one proton, one neutron), various forms of helium (two protons, one or two neutrons), a little lithium (three protons, four neutrons), and nothing else. We can calculate the amounts of deuterium, helium, and lithium nuclei produced by estimating the temperature of the three-minute-old universe and the known rates at which nuclear reactions proceed.
When we look at the universe, we find that the predictions for these primordial abundances are remarkably well borne out (once we have corrected for the elements later created in stars). These predictions are exact and unforgiving, since a few percent deviation in helium abundances from predicted values would rule out the standard big bang model. The fact that our predictions have proved to be so accurate probably constitutes the best available evidence in favor of the big bang.
THE STRUCTURE OF THE UNIVERSE
Just as stars are collected into galaxies, galaxies themselves are collected into structures known as groups, clusters, and super-clusters. The Milky Way and the Andromeda galaxy, for example, form the gravitational anchors of what astronomers call the Local Group, which is made up of these two plus a gaggle of twenty or so smaller galaxies. The Local Group, in turn, lies at the edge of the Local Supercluster, which consists of about 100,000 galaxies.
Almost all the known mass of the universe is gathered into superclusters, which can be pictured as groups and clusters strung together like beads on a string. Between the superclusters lie regions known as voids—desert-like volumes where almost no stars shine. These voids, which can be millions of light-years across, were totally unknown until the early 1980s, when modern data-analysis techniques allowed astronomers to pick out the empty areas despite the fact that light from galaxies behind them shines through and reaches the Earth.
The best way to visualize our present picture of the universe is to imagine cutting through a mound of soapsuds. You’d see a series of empty bubbles, each surrounded by soap film. Replace the film by superclusters and the bubbles by voids and you have the universe.
DARK MATTER AND DARK ENERGY
The universe of blazing stars and galaxies we have discussed up to now is all made up of ordinary matter—stuff like us. Scientists call this baryonic matter, since most of its mass is in baryons in the nuclei of atoms. One of the great surprises of the latter half of the twentieth century was the realization that baryonic matter makes up only a small fraction—about 4 percent—of the fabric of the universe. The rest is made up of two components that go by the names of dark matter and dark energy respectively.
Dark Matter
In the 1970s astronomer Vera Rubin of the Carnegie Institution was studying the way that distant galaxies rotate by looking at light emitted by the thin hydrogen gas between stars. Close to the center of the galaxy, all the stars (as expected) were locked together and rotated like a wheel. Farther out (again, as expected) all the stars moved at the same (somewhat slower) speed, which meant that the farther out a star was, the longer it took to make a complete cycle simply because it had farther to go. The surprise came when she looked at hydrogen gas far outside the region where there were stars. The expectation was that each hydrogen molecule would be in effect a miniature planet in orbit around the galaxy, and just as Jupiter moves more slowly than Earth, the speed of these molecules was expected to fall as they got farther from the galactic center. In fact, they did no such thing—they kept moving at the same speed as molecules closer in. The only way to explain this finding (which has been confirmed for many galaxies since) is to assume that the visible galaxy is encased in a large sphere of unseen massive material whose rotation carries the hydrogen molecules along.
Because this sphere doesn’t interact with light (if it did, we could see it), the new material was called dark matter. Evidence for dark matter quickly appeared in other places—it helps to hold galactic clusters together, for example. Astronomers now believe that dark matter makes up about 25 percent of the mass of the universe. We’ll talk about what it might be in the following section.
Dark Energy
In the early 1990s, astronomers discovered another unexpected fact about our universe. Using a special type of supernova to gauge the distance to the farthest galaxies, they were able to show that the rate of expansion of the universe has been increasing for many billions of years. This is, of course, exactly the opposite of what you would expect if gravity was the only force acting on galaxies, since gravity would tend to rein in the outward motion. There seems, in other words, to be some sort of “antigravity” operating in the universe, pushing galaxies apart at an ever-increasing rate. Scientists have given this mysterious force the name of dark energy (which should not be confused with dark matter).
As we will discuss below, we do not know what dark energy is. We do know, however, that it makes up about 70 percent of the mass of the universe.
Between baryonic matter, dark matter, and dark energy, then, we have finally gotten to the point that we know (or at least think we know) the basic ingredients from which the universe is made. Figuring out how these components fit together is our next task on the road to understanding that universe.
The Final Frontier
The main task that this generation of cosmologists faces is to find the laws that governed the first fraction of a second of the big bang, subject to the rather formidable constraints that those laws must produce a universe in which matter is clustered into galaxies, and galaxies are clustered into superclusters separated by voids, but the cosmic microwave background is the same no matter which direction we look. Finding such a theory is no trivial task, and a lot of bright people have tried and failed. It seems as if the more we learn about the universe’s structure, the harder it gets to make all the pieces mesh. This leads some scientists to hope that when we finally do find a theory that works, it will also be the only theory that does so—a true Theory of Everything.
FRONTIERS
What Is Dark Matter?
The concept of dark matter has been around for long enough for scientists to come up with some guesses as to what it might be. The list is long. It could conceivably be heavy neutrinos or any of a number of particles predicted by the Unified Field Theories discussed in Chapter 9 but not yet seen in the laboratory. Part or all of it could also be burned-out stars or other baryonic matter.
A number of experiments are now running to detect dark matter. The basic experimental strategy is based on the fact that if the galaxy is permeated by dark matter, then Earth must be moving through a dark matter “wind,” the way a moving car creates a wind on a calm day. In these experiments a crystal of pure germanium or silicon is kept near absolute zero in a deep underground cave (to shield it from cosmic rays). The material then is monitored in an attempt to detect the extremely rare interactions of the atoms in the block with the dark matter wind.
What Is Dark Energy?
Most cosmologists would say that this is the most important question that can be asked in their discipline, if for no other reason than that dark energy makes up most of the mass of the universe. Most of the work on this question is theoretical in nature, with an important candidate for dark energy being something called the cosmological constant. This hypothetical effect, which was first introduced by Albert Einstein as a way of creating a static universe, would provide precisely the kind of “antigravity” seen by astronomers. In an interesting historical sidelight, Einstein retracted his cosmological constant after Hubble’s discovery of the universal expansion, calling it the worst mistake of his life. It was resurrected after the discovery of the accelerated expansion.
On the observational front, astronomers can measure the history of universal expansion by looking at distant galaxies (remember: when you look at a galaxy 5 billion light-years away you
are looking 5 billion years back in time). It appears that the expansion did indeed slow down in its early stages, when galaxies were closer together and their gravitational attraction was larger than it is now. About 5 billion years after the big bang, however, gravitational attraction had dropped to the point that the effect of dark energy could take over, and the current era of accelerated expansion started.
CHAPTER TWELVE
Relativity
OUR CHAPTER ON RELATIVITY is quite different from the others in this book. You have day-to-day experience with motion and forces, matter and energy. Chemicals, planet Earth, and living organisms are tangible things. But relativity requires an abstract, even philosophical approach to science. Albert Einstein discovered relativity not by performing experiments, but by thinking about the way nature must be. You can follow Einstein’s ideas by doing the same simple thought experiments.
Relativity is a fascinating subject because it gives you a whole new way of looking at the universe. Still, a lot of scientists, ourselves included, would place relativity pretty far down the list of things you need to know to be scientifically literate. But Einstein and his remarkable theory are part of our cultural heritage—scientific folklore, if you will. Relativity is fun—and it’s great for impressing people at parties.
Let’s get one thing straight right from the start. It is absolutely untrue that there are only a dozen people in the world who understand the theory of relativity. This statement may have been true in 1920 (although, to tell the truth, we doubt that it held even then). Today the basics of relativity are routinely taught to college freshmen in “Physics for Poets” courses, and hundreds of graduate students in physics and astronomy learn the full mathematical rigors of relativity every year.
Relativity is not technically difficult. Indeed, the most basic statement of relativity may surprise you by its simplicity:
Every observer sees the same laws of nature.
Relativity has one central precept: there is no “correct” place from which to view the universe—no “God’s-eye” view of things. Every observer, whether sitting in a rocking chair on Earth or traveling near the speed of light in deep space, sees the same laws of nature. The only laws that could possibly govern the universe, according to the theory of relativity, are the same everywhere you look.
This idea seems almost too simple, yet many of the theory’s results violate our intuition about the way the world ought to behave. Relativity requires us to face up to the fact that the world doesn’t always behave the way we expect it to, and many people find it unsettling that nature is so indifferent to our sense of the rightness of things. If you can get used to the idea that the universe is what it is, regardless of what we think it should be, then you’ll have no problem with relativity.
REFERENCE FRAMES
When you sit in a chair at home, you observe the world from a frame of reference that is firmly attached to the solid Earth. If you ride by in a car or a plane or a spaceship, on the other hand, you observe the world from a frame of reference that is moving with respect to Earth. In either case you are an observer in the relativistic sense: in either reference frame you could set up a physics lab and perform experiments. In either frame of reference you could describe physical phenomena and deduce the laws of nature.
No matter what your reference frame, you can think of yourself as being stationary while every other observer is moving. This view may not seem obvious—when you drive you probably don’t think of your car as stationary while the countryside whizzes past. Most of us are accustomed to thinking of Earth as the “right” frame of reference, and we unconsciously put ourselves into the earthbound frame of reference whether we are moving or not. But have you ever, while sitting in an airplane being pushed back from a gate or a bus backing out of a station, thought, just for an instant, that the plane or bus next to you was moving forward? In that moment, before your conscious mind took over and reimposed its prejudice, you were a true relativistic observer. Your frame of reference was your own fixed center of the universe, and everything was moving around you.
Different observers give different descriptions of the same event. If someone riding in a car drops this book, the book falls straight down as far as the passenger is concerned. But watching this event from the side of the highway, you would see the book fall in an arc—the car’s motion carrying it along some distance during the time it takes to fall. You and the person in the car would give different descriptions of the fall.
But now suppose that you and the person in the car each equip yourselves with a physics laboratory and each of you determines the laws that govern the fall of objects in your own frame of reference. When you compared your results, you would find that they were identical—you would both have come up with Newton’s laws of motion. In other words, observers in different frames of reference give different descriptions of specific events but identical descriptions of the laws that govern those events. This is the central idea of the theory of relativity. If we assume that it is a general truth, then we can derive its consequences and test them experimentally. In the end, we shall see that the predictions that follow from this principle meet the test of experiment, and this is why scientists accept the theory.
The principle of relativity can be stated simply as “Every observer sees the same laws of nature,” but in practice, it is easier to break this principle into two parts, based on how the observers and their frames of reference are moving. The easier part we call special relativity, and it deals with the special case of reference frames that do not accelerate. In the Newtonian sense, special relativity is concerned only with observers in uniform motion, with no forces to alter their motion.
On the other hand, general relativity applies to all frames of reference, whether they accelerate or not. General relativity contains special relativity as a special case, but is itself a lot harder to deal with mathematically. We’ll treat special and general relativity separately, tackling the simpler theory first.
One more point should be made about the place of relativity in modern scientific research. Although the theory of relativity has the aura of being in the forefront of modern science, in fact it has been around since 1905 and is regarded by physicists as a familiar and well-verified part of their world.
SPECIAL RELATIVITY
If the laws of nature must be the same for all observers moving at constant speed, then all such observers must agree with Maxwell’s description of the laws of electricity and magnetism. Since the speed of light is a constant built into Maxwell’s equations, it follows that all observers must measure the same value for the speed of light. If they didn’t, different observers would find different sets of Maxwell equations.
This conclusion, in and of itself, already violates our intuition. Think about a simple example: You stand on a railroad car moving 50 miles per hour and throw a baseball forward at 50 miles per hour. Naturally someone on the ground will see the baseball moving at 100 miles per hour—the speed of the train plus the speed of the baseball. But if instead of throwing a baseball you shine a flashlight, the principle of relativity says that someone on the ground must see the light moving at a speed of 186,000 miles per second, not 186,000 miles per second plus 50 miles per hour.
This sort of basic contradiction between the way we think the universe ought to behave and the idea that the laws of nature have universal validity first led Albert Einstein to think about the theory of relativity. In the late nineteenth century, there were three ways in which the problem could have been resolved:
Maxwell’s equations could have been wrong; or,
the principle of relativity could have been wrong; or,
our intuitive ideas about space and time could have been wrong.
The last possibility arises because to calculate speed, we have to divide the distance traveled by the time it takes for the travel to occur. In our intuitive thinking about the problem of the flashlight, for example, we assumed that a clock on the ground and a clock on the railr
oad car would both run at the same speed. In reality, this might or might not be true—you never know until you actually make measurements.
During the 1920s, serious theories proposed modifications to Maxwell’s equations to make the speed of light depend on the motion of the source. When these modifications were tested (for example, by measuring light emitted by a double-star system both when the star is coming toward us and going away), they failed. In fact, we can say that both Maxwell and Einstein have been abundantly supported by the data. That leaves only the third possibility, that there is something wrong about our intuitive notions about the way different observers see things like clocks and yardsticks.
According to Einstein, he came to the realization that moving clocks might not run at the same rate as stationary ones while riding in a streetcar in Bern. Looking at a clock on a tower, he realized that if the streetcar moved away from the clock at the speed of light, it would look to him as if the clock had stopped. Einstein would, in effect, be riding outward from the clock perched on a single crest of a light wave. His pocket watch, on the other hand, would be moving with him and hence would continue to tick along in its usual manner. Thus, he reasoned, it is at least worth considering the possibility that our usual assumption that time is the same for all observers is simply wrong when things move at speeds near the speed of light.
We instinctively think something is wrong with the idea that light travels at exactly the same speed whether from a moving or stationary flashlight. We base our prejudice on a lifetime’s experience with moving objects. But how much of this experience was garnered while moving at speeds close to the speed of light? None of us has ever moved even close to 186,000 miles per second, so, strictly speaking, we have no experience whatsoever about how light or baseballs should behave at such speeds. The only thing actually violated by the example of the relativistic flashlight is our untutored expectation that nature should be the same at high velocities as it is at low ones. But this is only an assumption and, like other assumptions, it must be tested against experiment before we can accept it.
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