The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

Instead, the uniformity of the radiation’s temperature attests to the young universe being homogeneous; and, as we saw in Chapter 6, when gravity matters— as it did in the dense early universe—homogeneity implies low entropy. That’s a good thing, because our discussion of time’s arrow relied heavily on the universe’s starting out with low entropy.

One of our goals in this part of the book is to go as far as we can toward explaining this observation—we want to understand how the homogeneous, low-entropy, highly unlikely environment of the early universe came to be. This would take us a big step closer to grasping the origin of time’s arrow.

The uniformity of the radiation is thus a fossilized testament to the uniformity of both the laws of physics and the details of the environment across the cosmos.

The homogeneity of space thus provides a universal synchrony.

This tangible image captures well our belief—supported by increasingly precise astronomical surveys—that an observer in any one of the universe’s more than 100 billion galaxies, gazing across his or her night sky with a powerful telescope, would, on average, see an image similar to the one we see: surrounding galaxies rushing away in all directions.

The farther away two galaxies are, the more space there is between them, so the faster they’re pushed away from one another as space swells.

There is essentially universal agreement that the fabric of the space is stretching.

Time in an Expanding Universe

Cosmology, Symmetry, and the Shape of Space

Cosmology and Symmetry

9

Vaporizing the Vacuum

HEAT NOTHINGNESS AND U...

Heat and Symmetry

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.

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.

Rather, the “substance” that condensed or froze when the universe cooled through particular temperatures is a field—more precisely, a Higgs field.

Force, Matter, and Higgs Fields

Photons are the elementary constituents of electromagnetic fields and can be thought of as the microscopic transmitters of the electromagnetic force.

For this reason, the photon is sometimes described as the messenger particle of the electromagnetic force.

Just as photons are particles that constitute an electromagnetic field, physicists believe that gravitons are particles that constitute a gravitational field.

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 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.

The particles of the strong force are called gluons and those of the weak force are called W and Z particles.

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.

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.

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.

When the universe is hot, fields jump wildly from value to value,

As the universe cools, fields “calm down,” they jump less often and less frantically, and their values slide downward to lower energy.

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.

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.

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.

Even though it sounds contradictory, removing the Higgs field— reducing its value to zero, that is—is tantamount to adding energy to the region.

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

The Higgs Ocean and the Origin of Mass

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 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.

Physicists assume that the degree to which the Higgs ocean resists a particle’s acceleration varies with the particular species of particle.

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.

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.

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.

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.

But after the Higgs field condensed, the particle masses transmuted into nonzero—and nonequal— values, and so the symmetry between the masses was lost.

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.

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.

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.