The Fabric of the Cosmos: Space, Time, and the Texture of Reality - Brian Greene (2004)
Part III. SPACETIME AND COSMOLOGY
Chapter 9. Vaporizing the Vacuum
HEAT NOTHINGNESS AND UNIFICATION
For as much as 95 percent of the universe’s history, a cosmic corre-spondent concerned with the broad-brush, overall form of the universe would have reported more or less the same story: Universe continues to expand. Matter continues to spread due to expansion. Density of universe continues to diminish. Temperature continues to drop. On largest of scales, universe maintains symmetric, homogeneous appearance. But it wouldn’t always have been so easy to cover the cosmos. The earliest stages would have required furiously hectic reporting, because in those initial moments the universe underwent rapid change. And we now know that what happened way back then has played a dominant role in what we experience today.
In this chapter, we will focus on critical moments in the first fraction of a second after the big bang, when the amount of symmetry embodied by the universe is believed to have changed abruptly, with each change launching a profoundly different epoch in cosmic history. While the correspondent can now leisurely fax in the same few lines every few billion years, in those early moments of briskly changing symmetry the job would have been considerably more challenging, because the basic structure of matter and the forces responsible for its behavior would have been completely unfamiliar. The reason is tied up with an interplay between heat and symmetry, and requires a complete rethinking of what we mean by the notions of empty space and of nothingness. As we will see, such rethinking not only enriches substantially our understanding of the universe’s first moments, but also takes us a step closer to realizing a dream that harks back to Newton, Maxwell, and, in particular, Einstein—the dream of unification. Of equal importance, these developments set the stage for the most modern cosmological framework, inflationary cosmology, an approach that announces answers to some of the most pressing questions and thorniest puzzles on which the standard big bang model is mute.
Heat and Symmetry
When things get very hot or very cold, they sometimes change. And sometimes the change is so pronounced that you can’t even recognize the things with which you began. Because of the torrid conditions just after the bang, and the subsequent rapid drop in temperature as space expanded and cooled, understanding the effects of temperature change is crucial in grappling with the early history of the universe. But let’s start simpler. Let’s start with ice.
If you heat a very cold piece of ice, at first not much happens. Although its temperature rises, its appearance remains pretty much unchanged. But if you raise its temperature all the way to 0 degrees Celsius and you keep the heat on, suddenly something dramatic does happen. The solid ice starts to melt and turns into liquid water. Don’t let the familiarity of this transformation dull the spectacle. Without previous experiences involving ice and water, it would be a challenge to realize the intimate connection between them. One is a rock-hard solid while the other is a viscous liquid. Simple observation reveals no direct evidence that their molecular makeup, H2O, is identical. If you’d never before seen ice or water and were presented with a vat of each, at first you would likely think they were unrelated. And yet, as either crosses through 0 degrees Celsius, you’d witness a wondrous alchemy as each transmutes into the other.
If you continue to heat liquid water, you again find that for a while not much happens beyond a steady rise in temperature. But then, when you reach 100 degrees Celsius, there is another sharp change: the liquid water starts to boil and transmute into steam, a hot gas that again is not obviously connected to liquid water or to solid ice. Yet, of course, all three share the same molecular composition. The changes from solid to liquid and liquid to gas are known as phase transitions. Most substances go through a similar sequence of changes if their temperatures are varied through a wide enough range.1
Symmetry plays a central role in phase transitions. In almost all cases, if we compare a suitable measure of something’s symmetry before and after it goes through a phase transition, we find a significant change. On a molecular scale, for instance, ice has a crystalline form with H2O molecules arranged in an ordered, hexagonal lattice. Like the symmetries of the box in Figure 8.1, the overall pattern of the ice molecules is left unchanged only by certain special manipulations, such as rotations in units of 60 degrees about particular axes of the hexagonal arrangement. By contrast, when we heat ice, the crystalline arrangement melts into a jumbled, uniform clump of molecules—liquid water—that remains unchanged under rotations by any angle, about any axis. So, by heating ice and causing it to go through a solid-to-liquid phase transition, we have made it more symmetric. (Remember, although you might intuitively think that something more ordered, like ice, is more symmetric, quite the opposite is true; something is more symmetric if it can be subjected to more transformations, such as rotations, while its appearance remains unchanged.)
Similarly, if we heat liquid water and it turns into gaseous steam, the phase transition also results in an increase of symmetry. In a clump of water, the individual H2O molecules are, on average, packed together with the hydrogen side of one molecule next to the oxygen side of its neighbor. If you were to rotate one or another molecule in a clump it would noticeably disrupt the molecular pattern. But when the water boils and turns into steam, the molecules flit here and there freely; there is no longer any pattern to the orientations of the H2O molecules and hence, were you to rotate a molecule or group of molecules, the gas would look the same. Thus, just as the ice-to-water transition results in an increase in symmetry, the water-to-steam transition does so as well. Most (but not all2) substances behave in a similar way, experiencing an increase of symmetry when they undergo solid-to-liquid and liquid-to-gas phase transitions.
The story is much the same when you cool water or almost any other substance; it just takes place in reverse. For example, when you cool gaseous steam, at first not much happens, but as its temperature drops to 100 degrees Celsius, it suddenly starts to condense into liquid water; when you cool liquid water, not much happens until you reach 0 degrees Celsius, at which point it suddenly starts to freeze into solid ice. And, following the same reasoning regarding symmetries—but in reverse—we conclude that both of these phase transitions are accompanied by a decrease in symmetry.23
So much for ice, water, steam, and their symmetries. What does all this have to do with cosmology? Well, in the 1970s, physicists realized that not only can objects in the universe undergo phase transitions, but the cosmosas a whole can do so as well. Over the last 14 billion years, the universe has steadily expanded and decompressed. And just as a decompressing bicycle tire cools off, the temperature of the expanding universe has steadily dropped. During much of this decrease in temperature, not much happened. But there is reason to believe that when the universe passed through particular critical temperatures—the analogs of 100 degrees Celsius for steam and 0 degrees Celsius for water—it underwent radical change and experienced a drastic reduction in symmetry. Many physicists believe that we are now living in a “condensed” or “frozen” phase of the universe, one that is very different from earlier epochs. The cosmological phase transitions did not literally involve a gas condensing into a liquid, or a liquid freezing into a solid, although there are many qualitative similarities with these more familiar examples. Rather, the “substance” that condensed or froze when the universe cooled through particular temperatures is a field—more precisely, a Higgs field. Let’s see what this means.
Force, Matter, and Higgs Fields
Fields provide the framework for much of modern physics. The electromagnetic field, discussed in Chapter 3, is perhaps the simplest and most widely appreciated of nature’s fields. Living among radio and television broadcasts, cell phone communications, the sun’s heat and light, we are all constantly awash in a sea of electromagnetic fields. Photons are the elementary constituents of electromagnetic fields and can be thought of as the microscopic transmitters of the electromagnetic force. When you see something, you can think of it in terms of a waving electromagnetic field entering your eye and stimulating your retina, or in terms of photon particles entering your eye and doing the same thing. For this reason, the photon is sometimes described as the messenger particle of the electromagnetic force.
The gravitational field is also familiar since it constantly and consistently anchors us, and everything around us, to the earth’s surface. As with electromagnetic fields, we are all immersed in a sea of gravitational fields; the earth’s is dominant, but we also feel the gravitational fields of the sun, the moon, and the other planets. Just as photons are particles that constitute an electromagnetic field, physicists believe that gravitons are particles that constitute a gravitational field. Graviton particles have yet to be discovered experimentally, but that’s not surprising. Gravity is by far the weakest of all forces (for example, an ordinary refrigerator magnet can pick up a paper clip, thereby overcoming the pull of the entire earth’s gravity) and so it’s understandable that experimenters have yet to detect the smallest constituents of the feeblest force. Even without experimental confirmation, though, most physicists believe that just as photons transmit the electromagnetic force (they are the electromagnetic force’s messenger particles), gravitons transmit the gravitational force (they are the gravitational force’s messenger particles). When you drop a glass, you can think of the event in terms of the earth’s gravitational field pulling on the glass, or, using Einstein’s more refined geometrical description, you can think of it in terms of the glass’s sliding along an indentation in the spacetime fabric caused by the earth’s presence, or—if gravitons do indeed exist—you can also think of it in terms of graviton particles firing back and forth between the earth and the glass, communicating a gravitational “message” that “tells” the glass to fall toward the earth.
Beyond these well-known force fields, there are two other forces of nature, the strong nuclear force and the weak nuclear force, and they also exert their influence via fields. The nuclear forces are less familiar than electromagnetism and gravity because they operate only on atomic and subatomic scales. Even so, their impact on daily life, through nuclear fusion that causes the sun to shine, nuclear fission at work in atomic reactors, and radioactive decay of elements like uranium and plutonium, is no less significant. The strong and weak nuclear force fields are called Yang-Mills fields after C. N. Yang and Robert Mills, who worked out their theoretical underpinnings in the 1950s. And just as electromagnetic fields are composed of photons, and gravitational fields are believed to be composed of gravitons, the strong and weak fields also have particulate constituents. The particles of the strong force are called gluons and those of the weak force are called W and Z particles. The existence of these force particles was confirmed by accelerator experiments carried out in Germany and Switzerland in the late 1970s and early 1980s.
The field framework also applies to matter. Roughly speaking, the probability waves of quantum mechanics may themselves be thought of as space-filling fields that provide the probability that some or other particle of matter is at some or other location. An electron, for instance, can be thought of as a particle—one that can leave a dot on a phosphor screen, as in Figure 4.4—but it can (and must) also be thought of in terms of a waving field, one that can contribute to an interference pattern on a phosphor screen as in Figure 4.3b.3 In fact, although I won’t go into it in greater detail here,4 an electron’s probability wave is closely associated with something called an electron field—a field that in many ways is similar to an electromagnetic field but in which the electron plays a role analogous to the photon’s, being the electron field’s smallest constituent. The same kind of field description holds true for all other species of matter particles as well.
Having discussed both matter fields and force fields, you might think we’ve covered everything. But there is general agreement that the story told thus far is not quite complete. Many physicists strongly believe that there is yet a third kind of field, one that has never been experimentally detected but that over the last couple of decades has played a pivotal role both in modern cosmological thought and in elementary particle physics. It is called a Higgs field, after the Scottish physicist Peter Higgs.5 And if the ideas in the next section are right, the entire universe is permeated by an ocean of Higgs field—a cold relic of the big bang—that is responsible for many of the properties of the particles that make up you and me and everything else we’ve ever encountered.
Fields in a Cooling Universe
Fields respond to temperature much as ordinary matter does. The higher the temperature, the more ferociously the value of a field will—like the surface of a rapidly boiling pot of water—undulate up and down. At the chilling temperature characteristic of deep space today (2.7 degrees above absolute zero, or 2.7 Kelvin, as it is usually denoted), or even at the warmer temperatures here on earth, field undulations are minuscule. But the temperature just after the big bang was so enormous—at 10−43 seconds after the bang, the temperature is believed to have been about 1032 Kelvin—that all fields violently heaved to and fro.
As the universe expanded and cooled, the initially huge density of matter and radiation steadily dropped, the vast expanse of the universe became ever emptier, and field undulations became ever more subdued. For most fields this meant that their values, on average, got closer to zero. At some moment, the value of a particular field might jitter slightly above zero (a peak) and a moment later it might dip slightly below zero (a trough), but on average the value of most fields closed in on zero—the value we intuitively associate with absence or emptiness.
Here’s where the Higgs field comes in. It’s a variety of field, researchers have come to realize, that had properties similar to other fields’ at the scorchingly high temperatures just after the big bang: it fluctuated wildly up and down. But researchers believe that (just as steam condenses into liquid water when its temperature drops sufficiently) when the temperature of the universe dropped sufficiently, the Higgs field condensed into a particular nonzerovalue throughout all of space. Physicists refer to this as the formation of a nonzero Higgs field vacuum expectation value—but to ease the technical jargon, I’ll refer to this as the formation of a Higgs ocean.
It’s kind of like what would happen if you were to drop a frog into a hot metal bowl, as in Figure 9.1a, with a pile of worms lying in the center. At first, the frog would jump this way and that—high up, low down, left, right—in a desperate attempt to avoid burning its legs, and on average would stay so far from the worms that it wouldn’t even know they were there. But as the bowl cooled, the frog would calm itself, would hardly jump at all, and, instead, would gently slide down to the most restful spot at the bowl’s bottom. There, having closed in on the bowl’s center, it would finally rendezvous with its dinner, as in Figure 9.1b.
But if the bowl were shaped differently, as in Figure 9.1c, things would turn out differently. Imagine again that the bowl starts out very hot and that the worm pile still lies at the bowl’s center, now high up on the central bump. Were you to drop the frog in, it would again wildly jump this way and that, remaining oblivious to the prize perched on the central plateau. Then, as the bowl cooled, the frog would again settle itself, reduce its jumping, and slide down the bowl’s smooth sides. But because of the new shape, the frog would never make it to the bowl’s center. Instead, it would slide down into the bowl’s valley and remain at a distance from the worm pile, as in Figure 9.1d.
Figure 9.1 (a) A frog dropped into a hot metal bowl incessantly jumps around. (b) When the bowl cools, the frog calms down, jumps much less, and slides down to the bowl’s middle.
If we imagine that the distance between the frog and the worm pile represents the value of a field—the farther the frog is from the worms, the larger the value of the field—and the height of the frog represents the energy contained in that field value—the higher up on the bowl the frog happens to be, the more energy the field contains—then these examples convey well the behavior of fields as the universe cools. When the universe is hot, fields jump wildly from value to value, much as the frog jumps from place to place in the bowl. As the universe cools, fields “calm down,” they jump less often and less frantically, and their values slide downward to lower energy.
Figure 9.1 (c) As in (a), but with a hot bowl of a different shape. (d) As in (b), but now when the bowl cools, the frog slides down to the valley, which is some distance from the bowl’s center (where the worms are located).
But here’s the thing. As with the frog example, there’s a possibility of two qualitatively different outcomes. If the shape of the field’s energy bowl—its so-called potential energy—is similar to that in Figure 9.1a, the field’s value throughout space will slide all the way down to zero, the bowl’s center, just as the frog slides all the way down to the worm pile. However, if the field’s potential energy looks like that in Figure 9.1c, the field’s value will not make it all the way to zero, to the energy bowl’s center. Instead, just as the frog will slide down to the valley, which is a nonzero distance from the worm pile, the field’s value will also slide down to the valley—a nonzero distance from the bowl’s center—and that means the field will have a nonzero value.6 The latter behavior is characteristic of Higgs fields. As the universe cools, a Higgs field’s value gets caught in the valley and never makes it to zero. And since what we’re describing would happen uniformly throughout space, the universe would be permeated by a uniform and nonzero Higgs field—a Higgs ocean.
The reason this happens sheds light on the fundamental peculiarity of Higgs fields. As a region of space becomes ever cooler and emptier—as matter and radiation get ever more sparse—the energy in the region gets ever lower. Taking this to the limit, you know you’ve reached the emptiest a region of space can be when you’ve lowered its energy as far as possible. For ordinary fields suffusing a region of space, their energy contribution is lowest when their value has slid all the way down to the center of the bowl as in Figure 9.1b; they have zero energy when their value is zero. That makes good, intuitive sense since we associate emptying a region of space with setting everything, including field values, to zero.
But for a Higgs field, things work differently. Just as a frog can reach the central plateau in Figure 9.1c and be zero distance from the worm pile only if it has enough energy to jump up from the surrounding valley, a Higgs field can reach the bowl’s center, and have value zero, only if it too embodies enough energy to surmount the bowl’s central bump. If, to the contrary, the frog has little or no energy, it will slide to the valley in Figure 9.1d—a nonzerodistance from the worm pile. Similarly, a Higgs field with little or no energy will also slide to the bowl’s valley—a nonzero distance from the bowl’s center—and hence it will have a nonzero value.
To force a Higgs field to have a value of zero—the value that would seem to be the closest you can come to completely removing the field from the region, the value that would seem to be the closest you can come to a state of nothingness—you would have to raise its energy and, energetically speaking, the region of space would not be as empty as it possibly could. Even though it sounds contradictory, removing the Higgs field— reducing its value to zero, that is—is tantamount to adding energy to the region. As a rough analogy, think of one of those fancy noise reduction headphones that produce sound waves to cancel those coming from the environment that would otherwise impinge on your eardrums. If the headphones work perfectly, you hear silence when they produce their sounds, but you hear the ambient noise if you shut them off. Researchers have come to believe that just as you hear less when the headphones are suffused with the sounds they are programmed to produce, so cold, empty space harbors as little energy as it possibly can—it is as empty as it can be—when it is suffused with an ocean of Higgs field. Researchers refer to the emptiest space can be as the vacuum, and so we learn that the vacuum may actually be permeated by a uniform Higgs field.
The process of a Higgs field’s assuming a nonzero value throughout space—forming a Higgs ocean—is called spontaneous symmetry breaking24 and is one of the most important ideas to emerge in the later decades of twentieth-century theoretical physics. Let’s see why.
The Higgs Ocean and the Origin of Mass
If a Higgs field has a nonzero value—if we are all immersed in an ocean of Higgs field—then shouldn’t we feel it or see it or otherwise be aware of it in some way? Absolutely. And modern theory claims we do. Take your arm and swing it back and forth. You can feel your muscles at work driving the mass of your arm left and right and back again. If you take hold of a bowling ball, your muscles will have to work harder, since the greater the mass to be moved the greater the force they must exert. In this sense, the mass of an object represents the resistance it has to being moved; more precisely, the mass represents the resistance an object has to changes in its motion—to accelerations—such as first going left and then right and then left again. But where does this resistance to being accelerated come from? Or, in physics-speak, what gives an object its inertia?
In Chapters 2 and 3 we encountered various proposals Newton, Mach, and Einstein advanced as partial answers to this question. These scientists sought to specify a standard of rest with respect to which accelerations, such as those arising in the spinning-bucket experiment, could be defined. For Newton, the standard was absolute space; for Mach, it was the distant stars; and for Einstein, it was initially absolute spacetime (in special relativity) and then the gravitational field (in general relativity). But once delineating a standard of rest, and, in particular, specifying a benchmark for defining accelerations, none of these scientists took the next step to explain why objects resist accelerations. That is, none of them specified a mechanism whereby an object acquires its mass—its inertia— the attribute that fights accelerations. With the Higgs field, physicists have now suggested an answer.
The atoms that make up your arm, and the bowling ball you may have picked up, are all made of protons, neutrons, and electrons. The protons and neutrons, experimenters revealed in the late 1960s, are each composed of three smaller particles known as quarks. So, when you swing your arm back and forth, you are actually swinging all the constituent quarks and electrons back and forth, which brings us to the point. The Higgs ocean in which modern theory claims we are all immersed interactswith quarks and electrons: it resists their accelerations much as a vat of molasses resists the motion of a Ping-Pong ball that’s been submerged. And this resistance, this drag on particulate constituents, contributes to what you perceive as the mass of your arm and the bowling ball you are swinging, or as the mass of an object you’re throwing, or as the mass of your entire body as you accelerate toward the finish line in a 100-meter race. And so we do feel the Higgs ocean. The forces we all exert thousands of times a day in order to change the velocity of one object or another—to impart an acceleration—are forces that fight against the drag of the Higgs ocean.8
The molasses metaphor captures well some aspects of the Higgs ocean. To accelerate a Ping-Pong ball submerged in molasses, you’d have to push it much harder than when playing with it on your basement table—it will resist your attempts to change its velocity more strongly than it does when not in molasses, and so it behaves as if being submerged in molasses has increased its mass. Similarly, as a result of their interactions with the ubiquitous Higgs ocean, elementary particles resist attempts to change their velocities—they acquire mass. However, the molasses metaphor has three misleading features that you should be aware of.
First, you can always reach into the molasses, pull out the Ping-Pong ball, and see how its resistance to acceleration diminishes. This isn’t true for particles. We believe that, today, the Higgs ocean fills all of space, so there is no way to remove particles from its influence; all particles have the masses they do regardless of where they are. Second, molasses resists all motion, whereas the Higgs field resists only accelerated motion. Unlike a Ping-Pong ball moving through molasses, a particle moving through outer space at constant speed would not be slowed down by “friction” with the Higgs ocean. Instead, its motion would continue unchanged. Only when we try to speed the particle up or slow it down does the ocean of Higgs field make its presence known by the force we have to exert. Third, when it comes to familiar matter composed of conglomerates of fundamental particles, there is another important source of mass. The quarks constituting protons and neutrons are held together by the strong nuclear force: gluon particles (the messenger particles of the strong force) stream between quarks, “gluing” them together. Experiments have shown that these gluons are highly energetic, and since Einstein’s E=mc2 tells us that energy (E) can manifest itself as mass (m), we learn that the gluons inside protons and neutrons contribute a significant fraction of these particles’ total mass. Thus, a more precise picture is to think of the molasseslike drag force of the Higgs ocean as giving mass to fundamental particles such as electrons and quarks, but when these particles combine into composite particles like protons, neutrons, and atoms, other (well understood) sources of mass also come into play.
Physicists assume that the degree to which the Higgs ocean resists a particle’s acceleration varies with the particular species of particle. This is essential, because the known species of fundamental particles all have different masses. For example, while protons and neutrons are composed of two species of quarks (called up-quarks and down-quarks: a proton is made from two ups and a down; a neutron, from two downs and an up), over the years experimenters using atom smashers have discovered four other species of quark particles, whose masses span a wide range, from .0047 to 189 times the mass of a proton. Physicists believe the explanation for the variety of masses is that different kinds of particles interact more or less strongly with the Higgs ocean. If a particle moves smoothly through the Higgs ocean with little or no interaction, there will be little or no drag and the particle will have little or no mass. The photon is a good example. Photons pass completely unhindered through the Higgs ocean and so have no mass at all. If, to the contrary, a particle interacts significantly with the Higgs ocean, it will have a higher mass. The heaviest quark (it’s called the top-quark), with a mass that’s about 350,000 times an electron’s, interacts 350,000 times more strongly with the Higgs ocean than does an electron; it has greater difficulty accelerating through the Higgs ocean, and that’s why it has a greater mass. If we liken a particle’s mass to a person’s fame, then the Higgs ocean is like the paparazzi: those who are unknown pass through the swarming photographers with ease, but famous politicians and movie stars have to push much harder to reach their destination.9
This gives a nice framework for thinking about why one particle has a different mass from another, but, as of today, there is no fundamental explanation for the precise manner in which each of the known particle species interacts with the Higgs ocean. As a result, there is no fundamental explanation for why the known particles have the particular masses that have been revealed experimentally. However, most physicists do believe that were it not for the Higgs ocean, all fundamental particles would be like the photon and have no mass whatsoever. In fact, as we will now see, this may have been what things were like in the earliest moments of the universe.
Unification in a Cooling Universe
Whereas gaseous steam condenses into liquid water at 100 degrees Celsius, and liquid water freezes into solid ice at 0 degrees Celsius, theoretical studies have shown that the Higgs field condenses into a nonzero value at a million billion (1015) degrees. That’s almost 100 million times the temperature at the core of the sun, and it is the temperature to which the universe is believed to have dropped by about a hundredth of a billionth (10−11) of a second after the big bang (ATB). Prior to 10 −11 seconds ATB, the Higgs field fluctuated up and down but had an average value of zero; as with water above 100 degrees Celsius, at such temperatures a Higgs ocean couldn’t form because it was too hot. The ocean would have evaporated immediately. And without a Higgs ocean there was no resistance to particles undergoing accelerated motion (the paparazzi vanished), which implies that all the known particles (electrons, up-quarks, down-quarks, and the rest) had the same mass: zero.
This observation partly explains why the formation of the Higgs ocean is described as a cosmological phase transition. In the phase transitions from steam to water and from water to ice, two essential things happen. There is a significant qualitative change in appearance, and the phase transition is accompanied by a reduction in symmetry. We see the same two features in the formation of the Higgs ocean. First, there was a significant qualitative change: particle species that had been massless suddenly acquired nonzero masses—the masses that those particle species are now found to have. Second, this change was accompanied by a decrease in symmetry: before the formation of the Higgs ocean, all particles had the same mass—zero—a highly symmetric state of affairs. If you were to exchange one particle species’ mass with another, no one would know, because the masses were all the same. But after the Higgs field condensed, the particle masses transmuted into nonzero—and nonequal— values, and so the symmetry between the masses was lost.
In fact, the reduction in symmetry arising from the formation of the Higgs ocean is more extensive still. Above 1015 degrees, when the Higgs field had yet to condense, not only were all species of fundamental matter particles massless, but also, without the resistive drag from a Higgs ocean, all species of force particles were massless as well. (Today, the W and Z messenger particles of the weak nuclear force have masses that are about 86 and 97 times the mass of the proton.) And, as originally discovered in the 1960s by Sheldon Glashow, Steven Weinberg, and Abdus Salam, the masslessness of all the force particles was accompanied by another, fantastically beautiful symmetry.
In the late 1800s Maxwell realized that electricity and magnetism, although once thought to be two completely separate forces, are actually different facets of the same force—the electromagnetic force (see Chapter 3). His work showed that electricity and magnetism complete each other; they are the yin and yang of a more symmetric, unified whole. Glashow, Salam, and Weinberg discovered the next chapter in this story of unification. They realized that before the Higgs ocean formed, not only did all the force particles have identical masses—zero—but the photons and W and Z particles were identical in essentially every other way as well.10 Just as a snowflake is unaffected by the particular rotations that interchange the locations of its tips, physical processes in the absence of the Higgs ocean would have been unaffected by particular interchanges of electromagnetic and weak-nuclear-force particles—by particular interchanges of photons and W and Z particles. And just as the insensitivity of a snowflake to being rotated reflects a symmetry (rotational symmetry), the insensitivity to interchange of these force particles also reflects a symmetry, one that for technical reasons is called a gauge symmetry. It has a profound implication. Since these particles convey their respective forces—they are their force’s messenger particles—the symmetry between them means there was symmetry between the forces. At high enough temperatures, therefore, temperatures that would vaporize today’s Higgs-filled vacuum, there is no distinction between the weak nuclear force and the electromagnetic force. At high enough temperatures, that is, the Higgs ocean evaporates; as it does, the distinction between the weak and electromagnetic forces evaporates, too.
Glashow, Weinberg, and Salam had extended Maxwell’s century-old discovery by showing that the electromagnetic and weak nuclear forces are actually part of one and the same force. They had unified the description of these two forces in what is now called the electroweak force.
The symmetry between the electromagnetic and weak forces is not apparent today because as the universe cooled, the Higgs ocean formed, and—this is vital—photons and W and Z particles interact with the condensed Higgs field differently. Photons zip through the Higgs ocean as easily as B-movie has-beens slip through the paparazzi, and therefore remain massless. W and Z particles, though, like Bill Clinton and Madonna, have to slog their way through, acquiring masses that are 86 and 97 times that of a proton, respectively. (Note: this metaphor is not to scale.) That’s why the electromagnetic and weak nuclear forces appear so different in the world around us. The underlying symmetry between them is “broken,” or obscured, by the Higgs ocean.
This is a truly breathtaking result. Two forces that look very different at today’s temperatures—the electromagnetic force responsible for light, electricity, and magnetic attraction, and the weak nuclear force responsible for radioactive decay—are fundamentally part of the same force, and appear to be different only because the nonzero Higgs field obscures the symmetry between them. Thus, what we normally think of as empty space—the vacuum, nothingness—plays a central role in making things in the world appear as they do. Only by vaporizing the vacuum, by raising the temperature high enough so that the Higgs field evaporated—that is, acquired an average value of zero throughout space—would the full symmetry underlying nature’s laws be made apparent.
When Glashow, Weinberg, and Salam were developing these ideas, the W and Z particles had yet to be discovered experimentally. It was the strong faith these physicists had in the power of theory and the beauty of symmetry that gave them the confidence to go forward. Their boldness proved well founded. In due course, the W and Z particles were discovered and the electroweak theory was confirmed experimentally. Glashow, Weinberg, and Salam had looked beyond superficial appearances—they had peered through the obscuring fog of nothingness—to reveal a deep and subtle symmetry entwining two of nature’s four forces. They were awarded the 1979 Nobel Prize for the successful unification of the weak nuclear force and electromagnetism.
When I was a freshman in college, I’d drop in every now and then on my adviser, the physicist Howard Georgi. I never had much to say, but it hardly mattered. There was always something that Georgi was excited to share with interested students. On one occasion in particular, Georgi was especially worked up and he spoke rapid fire for over an hour, filling the chalkboard a number of times over with symbols and equations. Throughout, I nodded enthusiastically. But frankly, I hardly understood a word. Years later I realized that Georgi had been telling me about plans to test a discovery he had made called grand unification.
Grand unification addresses a question that naturally follows the success of the electroweak unification: If two forces of nature were part of a unified whole in the early universe, might it be the case that, at even higher temperatures, at even earlier times in the history of the universe, the distinctions among three or possibly all four forces might similarly evaporate, yielding even greater symmetry? This raises the intriguing possibility that there might actually be a single fundamental force of nature that, through a series of cosmological phase transitions, has crystallized into the four seemingly different forces of which we are currently aware. In 1974, Georgi and Glashow put forward the first theory to go partway toward this goal of total unity. Their grand unified theory, together with later insights of Georgi, Helen Quinn, and Weinberg, suggested that three of the four forces—the strong, weak, and electromagnetic forces— were all part of one unified force when the temperature was above 10 billion billion billion (1028) degrees—some thousand billion billion times the temperature at the center of the sun—extreme conditions that existed prior to 10−35 seconds after the bang. Above that temperature, these physicists suggested, photons, gluons of the strong force, as well as W and Z particles, could all be freely interchanged with one another—a more robust gauge symmetry than that of the electroweak theory—without any observable consequence. Georgi and Glashow thus suggested that at these high energies and temperatures there was complete symmetry among the three nongravitational-force particles, and hence complete symmetry among the three nongravitational forces.11
Glashow and Georgi’s grand unified theory went on to say that we do not see this symmetry in the world around us—the strong nuclear force that keeps protons and neutrons tightly glued together in atoms seems completely separate from the weak and electromagnetic forces—because as the temperature dropped below 1028 degrees, another species of Higgs field entered the story. This Higgs field is called the grand unified Higgs. (Whenever they might be confused, the Higgs field involved in electroweak unification is called the electroweak Higgs.) Similar to its electroweak cousin, the grand unified Higgs fluctuated wildly above 1028 degrees, but calculations suggested that it condensed into a nonzero value when the universe dropped below this temperature. And, as with the electroweak Higgs, when this grand unified Higgs ocean formed, the universe went through a phase transition with an accompanying reduction in symmetry. In this case, because the grand unified Higgs ocean has a different effect on gluons than it does on the other force particles, the strong force splintered off from the electroweak force, yielding two distinct nongravitational forces where previously there was one. A fraction of a second and a drop of billions and billions of degrees later, the electroweak Higgs condensed, causing the weak and electromagnetic forces to split apart as well.
While a beautiful idea, grand unification (unlike electroweak unification) has not been confirmed experimentally. To the contrary, Georgi’s and Glashow’s original proposal predicted a trace, residual implication of the universe’s early symmetry that should be apparent today, one that would allow protons to every so often transmute into other species of particles (such as anti-electrons and particles known as pions). But after years of painstaking search for such proton decay in elaborate underground experiments—the experiment Georgi had excitedly described to me in his office years ago—none were found; this ruled out Georgi and Glashow’s proposal. Since then, however, physicists have developed variations on that original model that are not ruled out by such experiments; however, so far none of these alternative theories have been confirmed.
The consensus among physicists is that grand unification is one of the great, as yet unrealized, ideas in particle physics. Since unification and cosmological phase transitions have proven so potent for electromagnetism and the weak nuclear force, many feel that it is only a matter of time before other forces are also gathered within a unified framework. As we shall see in Chapter 12, great strides in this direction have recently been made using a different approach—superstring theory—that has, for the first time, brought all forces, including gravity, into a unified theory, albeit one which is still, as of this writing, under vigorous development. But what is already clear, even in just considering the electroweak theory, is that the universe we currently see exhibits but a remnant of the early universe’s resplendent symmetry.
The Return of the Aether
The concept of symmetry’s breaking, and its realization through the electroweak Higgs field, clearly plays a central role in particle physics and cosmology. But the discussion may have left you wondering about the following: If a Higgs ocean is an invisible something that fills what we ordinarily think of as empty space, isn’t it just another incarnation of the long discredited notion of the aether? The answer: yes and no. The explanation: yes, indeed, in some ways a Higgs ocean does smack of the aether. Like the aether, a condensed Higgs field permeates space, surrounds us all, seeps right through everything material, and, as a nonremovable feature of empty space (unless we reheat the universe above 1015 degrees, which we can’t actually do), it redefines our conception of nothingness. But unlike the original aether, which was introduced as an invisible medium to carry light waves in much the same way that air carries sound waves, a Higgs ocean has nothing to do with the motion of light; it does not affect light’s speed in any way, and so experiments from the turn of the twentieth century that ruled out the aether by studying light’s motion have no bearing on the Higgs ocean.
Moreover, since the Higgs ocean has no effect on anything moving with constant velocity, it does not pick out one observational vantage point as somehow being special, as the aether did. Instead, even with a Higgs ocean, all constant velocity observers remain on a completely equal footing, and hence a Higgs ocean does not conflict with special relativity. Of course, these observations do not prove that Higgs fields exist; instead, they show that despite certain similarities to the aether, Higgs fields are not in conflict with any theory or experiment.
If there is an ocean of Higgs field, though, it should yield other consequences that will be experimentally testable within the next few years. As a primary example, just as electromagnetic fields are composed of photons, Higgs fields are composed of particles that, not surprisingly, are called Higgs particles. Theoretical calculations have shown that if there is a Higgs ocean permeating space, Higgs particles should be among the debris from the high-energy collisions that will take place at the Large Hadron Collider, a giant atom smasher now under construction at Centre Européène pour la Recherche Nuclaire (CERN) in Geneva, Switzerland, and slated to come online in 2007. Roughly speaking, enormously energetic head-on collisions between protons should be able to knock a Higgs particle out of the Higgs ocean somewhat as energetic underwater collisions can knock H2O molecules out of the Atlantic. In due course, these experiments should allow us to determine whether this modern form of the aether exists or whether it will go the way of its earlier incarnation. This is a critical question to settle because, as we have seen, condensing Higgs fields play a deep and pivotal role in our current formulation of fundamental physics.
If the Higgs ocean is not found, it will require major rethinking of a theoretical framework that has been in place for more than thirty years. But if it is found, the event will be a triumph for theoretical physics: it will confirm the power of symmetry to correctly shape our mathematical reasoning as we venture forth into the unknown. Beyond this, confirmation of the Higgs ocean’s existence would also do two more things. First, it would provide direct evidence of an ancient era when various aspects of today’s universe that appear distinct were part of a symmetric whole. Second, it would establish that our intuitive notion of empty space—the end result of removing everything we can from a region so that its energy and temperature drop as low as possible—has, for a long time, been naïve. The emptiest empty space need not involve a state of absolute nothingness. Without invoking the spiritual, therefore, we may well closely brush up against the thinking of Henry More (Chapter 2) in our scientific quest to understand space and time. To More, the usual concept of empty space was meaningless because space is always filled with divine spirit. To us, the usual concept of empty space may be similarly elusive, since the empty space we’re privy to may always be filled with an ocean of Higgs field.
Figure 9.2 A time line schematically illustrating the standard big bang model of cosmology.
Entropy and Time
The time line in Figure 9.2 places the phase transitions we’ve discussed in historical context and hence gives us a firmer grasp of the sequence of events the universe has gone through from the big bang to the egg on your kitchen counter. But crucial information is still hidden within the fuzzy patch. Remember, knowing how things begin—the order of the stack of pages of War and Peace, the pressurized carbon dioxide molecules in your bottle of Coke, the state of the universe at the big bang—is essential to understanding how they evolve. Entropy can increase only if it is given room to increase. Entropy can increase only if it starts out low. If the pages of War and Peace begin thoroughly jumbled, further tosses will merely leave them jumbled; if the universe started out in a thoroughly disordered, high-entropy state, further cosmic evolution would merely maintain the disorder.
The history illustrated in Figure 9.2 is manifestly not a chronicle of eternal, unchanging disorder. Even though particular symmetries have been lost through cosmic phase transitions, the overall entropy of the universe has steadily increased. In the beginning, therefore, the universe must have been highly ordered. This fact allows us to associate “forward” in time with the direction of increasing entropy, but we still need to figure out an explanation for the incredibly low entropy—the incredibly high state of uniformity—of the newly born universe. This requires that we go even farther back than we have so far and try to understand more of what went on at the beginning—during the fuzzy patch in Figure 9.2—a task to which we now turn.