The Fabric of the Cosmos: Space, Time, and the Texture of Reality (33 page)

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 10
³²
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
nonzero
value 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
nonzero
distance 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 breaking
²⁴
and is one of the most important ideas to emerge in the later decades of twentieth-century theoretical physics. Let's see why.

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
interacts
with 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=mc
²
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.