Knocking on Heaven's Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World - Lisa Randall (2011)
Part V. SCALING THE UNIVERSE
Chapter 19. INSIDE OUT
Back when I was in elementary school, I woke up one morning to read the bewildering news that the universe (at least in our understanding) had suddenly aged by a factor of two. I was astonished by this revision. How could something as important as the universe’s age be at liberty to change so radically without destroying everything else about it that we knew?
Today my surprise works in the opposite direction. I am stunned by how much we can precisely measure now about the universe and its history. Not only do we know the universe’s age much more accurately than ever before, but we know how the universe grew with time, how nuclei were formed, and how galaxies and clusters of galaxies began their evolution. Before, we had a qualitative picture of what had happened. Now we have an accurate scientific picture.
Cosmology has recently entered a remarkable era in which revolutionary advances, both experimental and theoretical, have precipitated a more extensive and detailed description than anyone would have believed possible even 20 years ago. By combining improved experimental methods with calculations rooted in general relativity and particle physics, physicists have established a detailed picture of what the universe looked like in its earlier stages and how it evolved into its form today.
So far, this book has focused primarily on smaller scales at which we examine the inner nature of matter. Having reached the current limit of our inward journey, let’s now complete the tour over distance scales we began in Chapter 5 and turn our attention outward to consider the sizes of objects in the outer universe.
We need to be wary of one big difference in this journey to cosmic scales since we can’t neatly characterize all aspects of the universe according to size alone. Observations don’t just record the universe today. Because of the finite speed of light, they also look back in time. Structures we observe today can be early universe occupants whose light reached our telescopes only billions of years after being emitted. The size of the current greatly expanded universe we now see encompasses many times the size of the universe earlier on.
Size nevertheless plays a critical role in characterizing our observations—both of the current universe and its history over time, and this chapter explores both. In the second half, we’ll consider the evolution of the universe as a whole, from its tiny initial size to the vast structure we now observe. But first we’ll look out at the universe as it appears today in order to familiarize ourselves with some of the lengths that characterize what surrounds us. We’ll work our way up in scales to consider larger sizes and more distant objects—on Earth and in the cosmos—to get a feeling for the bigger types of structures that are out there to explore. This tour of large scales will be briefer than our earlier tour of matter’s interior. Despite the richness of structure in the universe, most of what we see can be explained with known physical laws—not fundamental, new ones. Star and galaxy formation rely on known laws of chemistry and electromagnetism—science rooted in the small scales we have already discussed. Gravity, however, now plays a critical role as well, and the best description will depend on the speed and density of the objects it is acting on, leading to varying theoretical descriptions in this case too.
TOUR OF THE UNIVERSE
The book and film Powers of Ten,67 one of the iconic tours of distance scales, starts and ends with a couple sitting in Grant Park in Chicago—as good a place to begin our journey as any. Let’s momentarily pause on (what we now know to be largely empty) solid ground to view the familiar lengths and sizes around us. After momentarily reflecting on their human scale of about a couple of meters’ height, let’s take leave of this comfortable resting place and ascend to greater heights and sizes. (Refer to Figure 70 for a sampling of the scales this chapter explores.)
[ FIGURE 70 ] A tour of large scales, and the length units that are used to describe them.
One of the more spectacular demonstrations of human response to height that I’ve seen occurred during a performance of Elizabeth Streb’s dance company. Her dancers (or “action engineers”) fall onto their stomachs from a rail raised higher and higher until the final dancer falls a full 30 feet. That is definitely beyond our comfort zone as the many gasps in the audience make abundantly clear. People shouldn’t fall from that height—certainly not onto their faces.
Though maybe not so dramatic, most tall buildings inspire strong reactions too, ranging from awe to alienation. One of the challenges architects face is to humanize structures that are so much bigger than we are. Buildings and structures vary in size and shape, but our response to them inevitably reflects our psychological and physiological attitudes toward size.
The world’s tallest man-made structure is Burj Khalifa in Dubai, United Arab Emirates, which stands 828 meters (2,717 ft.) tall. That is dauntingly high, but it’s largely empty and the movie Mission Impossible 4 probably won’t confer on it the same cultural status that King Kong gave to the Empire State Building. New York’s iconic 381-meter building stands at less than half the height of Burj Khalifa. However, to its credit, it has a much higher occupancy rate.
We live in a world surrounded by much larger natural entities, many of which inspire awe. In the vertical direction, Mt. Everest, at 8.8 kilometers, is the highest peak on Earth. Mt. Blanc, the tallest mountain in Europe (at least if you’re not from the country of Georgia), is only about half as high—but I was still pretty happy years ago when I made it to the summit—though my friend and I look pretty miserable in the photo we took at the top. At 11 kilometers deep, the Mariana Trench is the deepest known place in the ocean, and the lowest elevation of the Earth’s surface crust. This otherworldly trench was the director James Cameron’s destination once he had successfully conquered three-dimensional imagery with his successful movie Avatar.
Natural bodies spread on the Earth’s surface over far more extended regions. The Pacific Ocean, for example, is about 20 million meters wide, while Russia—at nearly eight million meters across—is almost half the extent of that. The nearly spherical Earth itself is some 12 million meters in diameter, with a circumference about three times as big. The United States, at 4.2 million meters across, is about a tenth this wide, but is still bigger than the diameter of the Moon, which measures about 3.6 million meters.
Objects in outer space have a large range of sizes as well. Asteroids, for example, vary quite a bit—tiny ones can be as small as pebbles, while bigger ones are far greater than any feature on Earth. At approximately a billion meters across, the Sun is about 100 times the size of the Earth. And the solar system, which I’ll take to be roughly the distance from the Sun to Pluto (which is in the solar system whether or not it merits planet status) is about 7,000 times the radius of the Sun.
The distance from the Earth to the Sun is considerably smaller—a mere 100 billion meters—a hundredth of a thousandth of a light-year. A light-year is the distance light can travel in a year—the product of 300 million meters/second (the speed of light) and 30 million seconds (the number of seconds in a year). Because of this finite speed of light, the illumination we see from the Sun is already about eight minutes old.
Many visible structures, of varying shapes and sizes, exist within our vast universe. Astronomers have organized most astral bodies according to type. To set some scales, galaxies are typically about 30,000 light-years or 3 × 1020meters across. That includes our galaxy—the Milky Way—which is about three times that size. Galaxy clusters, which contain from tens to thousands of galaxies, are about 1023 meters in size, or 10 million light-years big. Light takes about 10 million years to traverse from one end of a galaxy cluster to the other.
Yet despite the huge range of sizes, most of these bodies act in accordance with Newton’s laws. The orbit of the Moon, like the orbit of Pluto, or the orbit of the Earth itself, can be explained in terms of Newtonian gravity. Based on the planet’s distances from the Sun, its orbit can be predicted with Newton’s gravitational force law. That’s the same law that caused Newton’s apple to fall to Earth.
Nonetheless, more precise measurements of planetary orbits revealed that Newton’s laws were not the final word. General relativity was needed to explain the precession of the perihelion of Mercury, which is the observed change in its orbit around the Sun over time. General relativity is a more comprehensive theory that includes Newton’s laws when densities are low and speeds are small, but also works outside these restrictions.
General relativity isn’t needed to describe most objects however. But its effects can accumulate over time, and are prominent when objects are sufficiently dense, as with black holes. The black hole at the center of our galaxy is about 10 trillion (1013) meters in radius. The enclosed mass is very large—about 4 million times the mass of the Sun—and, as with all other black holes, requires general relativity to describe its gravitational properties.
The entire visible universe is currently 100 billion light-years across—1027 meters, a million times the size of our galaxy. That is enormous and superficially surprising since it is bigger than the distance we can actually observe, 13.75 billion years since the time of the Big Bang. Nothing is supposed to travel faster than light speed so with the universe only 13.75 billion years old, this size might seem impossible.
However, no such contradiction exists. The reason the universe as a whole is bigger than the distance a signal could have traveled given its age is that space itself has expanded. General relativity plays a big role in understanding this phenomenon. Its equations tell us that the very fabric of space has expanded. We can observe places in the universe that are that far apart, even though they cannot see each other.
Given the finite speed of light and the finite age of the universe, this section has now taken us to the limit of observable sizes. The visible universe is all our telescopes can access. Nonetheless, the size of the universe is almost certainly not limited to what we can see. As with small scales, where we can make conjectures that extend beyond current experimental constraints, we can also consider what exists beyond the observable universe. The only limit to the largest sizes we can think about is our imagination, and our patience for contemplating structure that we can’t hope to observe.
We really don’t know what exists beyond the horizon—the boundary of the observable universe. The limits to our observations allow for the possibility of new and exotic phenomena beyond. Different structures, different dimensions, and even different laws of physics can in principle apply so long as they don’t contradict anything that has been observed. That doesn’t mean every possibility is realized in nature, as my astrophysics colleague Max Tegmark sometimes asserts. However, it does mean there are many possibilities for what can be out there.
We don’t yet know if other dimensions or other universes exist. Really, we can’t even say with certainty whether the universe as a whole is finite or infinite, though most of us think it’s likely to be the latter. No measurement shows any sign of its ending, but measurements only reach so far. In principle, the universe could end, or even have the shape of a ball or balloon. But no theoretical or experimental clue leads us in that direction at present.
Most physicists prefer not to think too much about the regime beyond the visible universe, since we are unlikely to ever know what is there. However, any theory of gravity or quantum gravity gives us the mathematical tools to contemplate the geometry of what might exist. Based on theoretical methods and ideas about extra dimensions of space, physicists sometimes consider exotic other universes, which are not in contact with us over the lifetime of our universe or are only in contact via gravity. As discussed in Chapter 18, string theorists and others contemplate the existence of a multiverse that contains many disconnected independent universes that are consistent with string theory’s equations, sometimes combining these ideas with the anthropic principle that exploits the possible riches of universes that might exist. Some even try to find observable signatures of such multiverses for the future. As we saw in Chapter 17, in one distinct scenario, a two-brane “multiverse” might even help us understand questions in particle physics and in that case have testable consequences. But most additional universes, though conceivable and maybe even likely, will probably remain beyond the realm of experimental testability for the foreseeable future. They will then remain theoretical abstract possibilities.
THE BIG BANG: FROM SMALL TO LARGE THROUGH TIME
Now that we’ve ventured out to the largest sizes we can observe or discuss in the context of the observable universe, and reached the outer limits as to what we can see (and contemplate with our imagination), let’s explore how the universe we do live in and observe evolved over time to create the enormous structures we see today. The Big Bang theory tells us how the universe grew during its 13.75-billion-year life span from its small initial size to the current extent, 100 billion light-years across. Fred Hoyle facetiously (and skeptically) named the theory after the initial explosion when a hot dense fireball began to expand into the massive extent of stars and structures we now observe: growing, diluting matter, and cooling as it evolved.
However, the one thing we certainly don’t know is what banged in the beginning and how it appened—or even the precise size it had been when it did. Despite our understanding of the universe’s late evolution, its beginnings remain shrouded in mystery. Nonetheless, although the Big Bang theory does not tell us anything about the universe’s initial moment, it is a very successful theory that tells us much about its subsequent history. Current observations combined with the Big Bang theory teach us quite a lot about how the universe has evolved.
No one knew the universe was expanding when the twentieth century began. At the time that Edwin Hubble first peered into the sky, very little was known. Harlow Shapley had measured the size of the Milky Way to be 300,000 light-years across, but he was convinced that the Milky Way was all that the universe contained. In the 1920s, Hubble realized that some of the nebula that Shapley had thought were clouds of dust—which did indeed merit this uninspiring name—were in fact galaxies, millions of light-years away.
Once he identified galaxies, Hubble made his second stunning discovery—the universe’s expansion. In 1929, he observed that galaxies red-shifted, which is to say there was a Doppler effect in which light waves shifted to longer wavelengths for more distant objects. This red shift demonstrated that galaxies were receding, much as the high-pitched wail of a siren decreases in frequency as an ambulance speeds away. (See Figure 71.) The galaxies he had identified were not stationary with respect to our location, but were all expanding away from us. This was evidence that we live in an expanding universe, in which galaxies are growing farther apart.
[ FIGURE 71 ] The light from an object moving away from us is shifted to lower frequencies—or shifted toward the red end of the spectrum—whereas light from objects moving away is shifted to higher frequencies, or blue shifted. This is analogous to the noise from a siren that is lower pitched when an ambulance moves away and higher pitched when it approaches.
The universe’s expansion is different from the pictures we might first imagine since the universe doesn’t expand into some preexisting space. The universe is all there is. Nothing is present for it to expand into. The universe, as well as space itself, expands. Any two points within it grow farther apart as time progresses. Other galaxies move farther away from us, but our location is not special—they move farther from each other as well.
One way to picture this is to imagine the universe as the surface of a balloon. Suppose you had marked two points on the balloon’s surface. As the balloon blows up, the surface becomes stretched and those two points grow farther apart. (See Figure 72.) This is in fact what happens to any two points in the universe as it expands. The distance between any two points—or any two galaxies—increases.
[ FIGURE 72 ] The “ballooniverse” illustrates how all points move away from one another as the balloon (universe) expands.
Notice in our analogy that the points themselves don’t necessarily expand—just the space between them. This is in fact what happens in the expanding universe as well. Atoms, for example, are tightly bound together via electromagnetic forces. They don’t get any bigger. Neither do relatively dense strongly bound structures such as galaxies. The force driving the expansion acts on them too, but because other force contributions are at work, the galaxies don’t themselves grow with the overall expansion of the universe. They feel such strong attractive forces that they remain the same size while their relative distance from each other gets bigger.
Of course, this balloon analogy is not perfect. The universe has three spatial dimensions, not two. Furthermore, the universe is large and probably infinite in size, and not small and curved like the balloon’s surface. On top of that, the balloon exists in our universe and expands into existing space, unlike the universe, which permeates space and doesn’t expand into something else. But even with these caveats, the surface of a balloon illustrates quite nicely what it means for space to expand. Every point moves away from every other point at the same time.
A balloon analogy—this time referring to the interior—is also helpful for understanding how the universe cooled from its initial hot dense fireball existence. Imagine an extremely hot balloon that you allow to expand to a very big size. Though it might have been too hot to handle at first, the expanded balloon will contain much cooler air that would no longer be alien to human contact. The Big Bang theory predicts that the initial hot dense universe expanded, all the while cooling as it did so.
Einstein had actually derived an expanding universe from his equations of general relativity. At that time, however, no one had yet measured the universe’s expansion, so he didn’t trust his prediction. Einstein introduced a new source of energy in an attempt to reconcile his theory with a static universe. After Hubble’s measurements, Einstein dispensed with the fudge he had made, calling it “his biggest blunder.” This modification was not entirely erroneous, however. We will soon see that more recent measurements show that the cosmological constant term he added is actually necessary to account for recent observations—although the measured magnitude, which accounts for the recently established acceleration of its expansion, is about an order of magnitude bigger than the one Einstein proposed to merely stall it.
The expansion of the universe was a nice example of a convergence of top-down and bottom-up physics. Einstein’s theory of gravity implies that the universe expands, yet only with the discovery of the expansion did physicists feel confident they were on the right track.
Today, we refer to the number that determines the rate at which the universe expands at present as the Hubble constant. It is a constant in the sense that the fractional expansion everywhere in space is the same. However, the Hubble parameter is not constant over time. At an earlier time, when the universe was hotter and denser and gravitational effects were stronger, it expanded at a far more rapid rate.
Measuring the Hubble constant precisely is difficult, since we face exactly the problem we raised earlier of disentangling the past from the present. We need to know how far away the red-shifting galaxies are, since the red shift depends both on the Hubble parameter and distance. This imprecise measurement was the source of the factor-of-two uncertainty in the age of the universe that I mentioned at the beginning of this chapter. If the Hubble parameter measurements were uncertain by a factor of two, so too would be the universe’s age.
That controversy is now pretty much resolved. The Hubble parameter has been measured by Wendy Freedman of the Smithsonian Astronomical Observatories and her collaborators and others, and the expansion rate is about 22 kilometers per second for a galaxy a million light-years away. Based on this value, we now know the universe is about 13.75 billion years old. This might under- or overestimate the age by 200 million years, but not by a factor of two. Although this might still sound like a good deal of uncertainty, the range is too small to make any great difference in our understanding today.
Two other key observations that agreed nicely with predictions further confirmed the Big Bang theory. One class of measurement that relied on both particle physics and general relativity predictions and therefore confirmed both was the density of various elements in the cosmos, such as helium and lithium. The amount of these elements that the Big Bang theory predicts agrees with measurements. This is in some respects indirect proof, and detailed calculations based on nuclear physics and cosmology are required to compute these values. Even so, this agreement of many different element abundances with predictions would be an unlikely coincidence unless physicists and astronomers were on the right track.
When the American Robert Wilson and the German-born Arno Penzias accidentally discovered the 2.7-degree microwave background in 1964, it was further confirmation of the Big Bang theory. To put this temperature in perspective, nothing is colder than absolute zero, which is zero degrees kelvin. The universe’s radiation is less than three degrees warmer than this absolute limit to how cold anything can be.
The collaboration and adventure of Robert Wilson and Arno Penzias (for which they won the 1978 Nobel Prize) was a superb example of how science and technology sometimes work in concert to achieve results beyond what anyone had imagined. Back when AT&T was a phone monopoly, it did something rather wonderful, which was to create Bell Laboratories, a spectacular research environment where pure and applied research proceeded side by side.
Robert Wilson, who was a detail-oriented gadget technology geek, and Arno Penzias, who was more of a big picture scientist, both worked there, and together used and developed radio telescopes. Wilson and Penzias were interested in science and technology, while AT&T was understandably interested in communications, so radio waves in the sky were important to everyone involved.
While pursuing a specific radio astronomy goal, Wilson and Penzias found what they initially considered a mysterious nuisance that they simply couldn’t explain. It seemed to be uniform background noise—essentially static. It wasn’t coming from the Sun, and it wasn’t related to a nuclear test from the previous year. They tried every explanation they could think of, most famously pigeon droppings, in their nine-month attempt to figure out what was going on. After considering all imaginable possibilities, cleaning out the pigeon droppings (or “white dielectric material” as Penzias called it), and even shooting the pigeons, the noise still didn’t go away.
Wilson told me how lucky they were in the timing of their discovery. They didn’t know about the Big Bang, but Robert Dicke and Jim Peebles at Prince ton University did. The physicists there had just realized that one implication of the theory would be a relic microwave radiation. They were in the process of designing an experiment to measure this radiation when they discovered they had been scooped—by the Bell Lab scientists who hadn’t yet realized what they had discovered. Luckily for Penzias and Wilson, the MIT astronomer Bernie Burke, who Robert Wilson described to me as the early version of the Internet, knew about the Princeton research and also the Penzias and Wilson discovery. He put two and two together and brought the connection to fruition by bringing the relevant players into contact.
This was a lovely example of science in action. The research was done for a specific scientific purpose that could also have ancillary technological and scientific benefits. The astronomers weren’t looking for what they found, but they were extremely technologically and scientifically skilled. When they discovered something, they knew not to dismiss it. Their research—while looking for relatively small phenomena—resulted in a discovery with tremendously deep implications, which they found because they and others were thinking about the big picture at the same time. The discovery by the Bell Lab scientists was accidental, but it forever changed the science of cosmology.
The cosmic radiation has proved to be a tremendous tool—not just for confirming the Big Bang but for turning cosmology into a detailed science. The cosmic microwave background (CMB) radiation gives us a very different way of observing the past than traditional astronomy measurements.
In the past, astronomers would observe objects in the sky, try to determine their age, and attempt to deduce the evolutionary history that produced them. With the CMB, scientists can now also look directly back in time before structure such as stars and galaxies were even formed. The light they observe was emitted long ago—very early in the universe’s evolution. When the microwave background we now observe was emitted, the universe was only about one-thousandth its current size.
Although the universe was originally filled with all types of particles—both charged and uncharged—once it cooled sufficiently, 400,000 years into its evolution, charged particles combined together into neutral atoms. Once this happened, light no longer scattered. Observed CMB radiation therefore arrives directly from about four hundred thousand years into the universe’s evolution—unhindered and uninterrupted—to telescopes on Earth and on satellites. The background radiation Penzias and Wilson discovered was the same radiation present in the earlier stages of the universe’s history, but it has been diluted and cooled through its expansion. The radiation traveled directly to the telescopes that detected it with no hindrances from scattering off any intervening charged particles en route. This light gives us a direct and precise window into the past.
The Cosmic Microwave Background Explorer (COBE), a four-yearlong satellite mission launched in 1989, measured this background radiation extremely accurately, and the mission scientists found that their measurements agreed with predictions to better than one part in 1,000. But COBE measured something new as well. By far, the most interesting thing that COBE measured was a tiny bit of nonuniformity in temperature across the sky. Although the universe is extremely smooth, tiny in-homogeneities at the level of less than one in 10,000 in the early universe grew bigger and were essential to the development of structure. The in-homogeneities originated on minuscule length scales, but were stretched to sizes relevant to astrophysical measurements and structure. Gravity caused the denser regions where the perturbations were especially large to become more concentrated and form the massive objects we currently observe. The stars, galaxies, and clusters of galaxies that we discussed earlier are all the result of these initial tiny quantum mechanical fluctuations and their evolution through the gravitational force.
The microwave background measurement continues to be critical to our understanding of the universe’s evolution. It’s role as a direct window into the early universe cannot be underestimated. More recently, along with more traditional methods, CMB measurements have provided experimental insights into several other more mysterious phenomena—cosmological inflation, dark matter, and dark energy—subjects that we turn to next.