Hyperspace (36 page)

Now replace the bed sheet with ten-dimensional space-time, the space-time of ultimate symmetry. At the beginning of time, the universe was perfectly symmetrical. If anyone was around at that time, he could freely pass through any of the ten dimensions without problem. At that time, gravity and the weak, the strong, and the electromagnetic forces were all unified by the superstring. All matter and forces were part of the same string multiplet. However, this symmetry couldn’t last. The ten-dimensional universe, although perfectly symmetrical, was unstable, just like the bed sheet, and in a false vacuum. Thus tunneling to a lower-energy state was inevitable. When tunneling finally occurred, a phase transition took place, and symmetry was lost.

Because the universe began to split up into a four- and a six-dimensional universe, the universe was no longer symmetrical. Six dimensions have curled up, in the same way that the bed sheet curls up when one elastic pops off a corner of a mattress. But notice that there are four ways in which the bed sheet can curl up, depending on which corner pops off first. For the ten-dimensional universe, however, there are apparently millions of ways in which to curl up. To calculate which state the ten-dimensional universe prefers, we need to solve the field theory of strings using the theory of phase transitions, the most difficult problem in quantum theory.

Phase transitions are nothing new. Think of our own lives. In her book
Passages
, Gail Sheehy stresses that life is not a continuous stream of experiences, as it often appears, but actually passes through several stages, characterized by specific conflicts that must be resolved and goals that must be achieved.

The psychologist Erik Erikson even proposed a theory of the psychological stages of development. A fundamental conflict characterizes each phase. When this conflict is correctly resolved, we move on to the next
phase. If this conflict is not resolved, it may fester and even cause regression to an earlier period. Similarly, the psychologist Jean Piaget showed that early childhood mental development is also not a smooth process of learning, but is actually typified by abrupt stages in a child’s ability to conceptualize. One month, a child may give up looking for a ball once it has rolled out of view, not understanding that an object exists even if you can no longer see it. The next month, this is obvious to the child.

This is the essence of dialectics. According to this philosophy, all objects (people, gases, the universe itself) go through a series of stages. Each stage is characterized by a conflict between two opposing forces. The nature of this conflict, in fact, determines the nature of the stage. When the conflict is resolved, the object goes to a higher stage, called the synthesis, where a new contradiction begins, and the process starts over again at a higher level.

Philosophers call this the transition from “quantity” to “quality.” Small quantitative changes eventually build up until there is a qualitative rupture with the past. This theory applies to societies as well. Tensions in a society can rise dramatically, as they did in France in the late eighteenth century. The peasants faced starvation, spontaneous food riots took place, and the aristocracy retreated behind its fortresses. When the tensions reached the breaking point, a phase transition occurred from the quantitative to the qualitative: The peasants took up arms, seized Paris, and stormed the Bastille.

Phase transitions can also be quite explosive affairs. For example, think of a river that has been dammed up. A reservoir quickly fills up behind the dam with water under enormous pressure. Because it is unstable, the reservoir is in the false vacuum. The water would prefer to be in its true vacuum, meaning it would prefer to burst the dam and wash downstream, to a state of lower energy. Thus a phase transition would involve a dam burst, which could have disastrous consequences.

An even more explosive example is an atomic bomb. The false vacuum corresponds to stable uranium nuclei. Although the uranium nucleus appears stable, there are enormous, explosive energies trapped within the uranium nucleus that are a million times more powerful, pound for pound, than a chemical explosive. Once in a while, the nucleus tunnels to a lower state, which means that the nucleus spontaneously splits apart all by itself. This is called radioactive decay. However, it is possible, by shooting neutrons at the uranium nucleus, to release this pent-up energy all at once. This, of course, is an atomic explosion.

The new feature discovered by scientists about phase transitions is that they are usually accompanied by a symmetry breaking. Nobel laureate
Abdus Salam likes the following illustration: Consider a circular banquet table, where all the guests are seated with a champagne glass on either side. There is a symmetry here. Looking at the banquet table through a mirror, we see the same thing: each guest seated around the table, with champagne glasses on either side. Similarly, we can rotate the circular banquet table, and the arrangement is still the same.

Now break the symmetry. Assume that the first diner picks up the glass on his or her right. By custom, all the other guests pick up the champagne glass to their right. Notice that the image of the banquet table as seen in the mirror produces the opposite situation. Every diner has picked up the glass to his or her left. Thus left-right symmetry has been broken.

Another example of symmetry breaking comes from an ancient fairy tale. This fable concerns a princess who is trapped on top of a polished crystal sphere. Although there are no iron bars confining her to the sphere, she is a prisoner because if she makes the slightest move, she will slip off the sphere and kill herself. Numerous princes have tried to rescue the princess, but each has failed to scale the sphere because it is too smooth and slippery. This is an example of symmetry breaking. While the princess is atop the sphere, she is in a perfectly symmetrical state. There is no preferred direction for the sphere. We can rotate the sphere at any angle, and the situation remains the same. Any false move off the center, however, will cause the princess to fall, thereby breaking the symmetry. If she falls to the west, for example, the symmetry of rotation is broken. The westerly direction is now singled out.

Thus the state of maximum symmetry is often also an unstable state, and hence corresponds to a false vacuum. The true vacuum state corresponds to the princess falling off the sphere. So a phase transition (falling off the sphere) corresponds to symmetry breaking (selecting the westerly direction).

Regarding superstring theory, physicists assume (but cannot yet prove) that the original ten-dimensional universe was unstable and tunneled its way to a four- and a six-dimensional universe. Thus the original universe was in the state of the false vacuum, the state of maximum symmetry, while today we are in the broken state of the true vacuum.

This raises a disturbing question: What would happen if our universe were actually not the true vacuum? What would happen if the superstring only temporarily chose our universe, but the true vacuum lay among the millions of possible orbifolds? This would have disastrous consequences. In many other orbifolds, we find that the Standard Model is not present. Thus if the true vacuum were actually a state where the
Standard Model was not present, then all the laws of chemistry and physics, as we know them, would come tumbling down.

If this occurred, a tiny bubble might suddenly appear in our universe. Within this bubble, the Standard Model would no longer hold, so a different set of chemical and physical laws would apply. Matter inside the bubble would disintegrate and perhaps re-form in different ways. This bubble would then expand at the speed of light, swallowing up entire star systems, galaxies, and galactic clusters, until it gobbled up the entire universe.

We would never see it coming. Traveling at the speed of light, it could never be observed beforehand. We would never know what hit us.

Consider an ordinary ice cube sitting in a pressure cooker in our kitchen. We all know what happens if we turn on the stove. But what happens to an ice cube if we heat it up to
trillions upon trillions
of degrees?

If we heat the ice cube on the stove, first it melts and turns into water; that is, it undergoes a phase transition. Now let us heat the water until it boils. It then undergoes another phase transition and turns into steam. Now continue to heat the steam to enormous temperatures. Eventually, the water molecules break up. The energy of the molecules exceeds the binding energy of the molecules, which are ripped apart into elemental hydrogen and oxygen gas.

Now we continue to heat it past 3,000°K, until the atoms of hydrogen and oxygen are ripped apart. The electrons are pulled from the nucleus, and we now have a plasma (an ionized gas), often called the fourth state of matter (after gases, liquids, and solids). Although a plasma is not part of common experience, we can see it every time we look at the sun. In fact, plasma is the most common state of matter in the universe.

Now continue to heat the plasma on the stove to 1 billion°K, until the nuclei of hydrogen and oxygen are ripped apart, and we have a “gas” of individual neutrons and protons, similar to the interior of a neutron star.

If we heat the “gas” of nucleons even further to 10 trillion°K, these subatomic particles will turn into disassociated quarks. We will now have a gas of quarks and leptons (the electrons and neutrinos).

If we heat this gas to 1 quadrillion°K, the electromagnetic force and the weak force will become united. The symmetry SU(2) × U(l) will emerge at this temperature. At 10
²⁸
°K, the electroweak and strong forces
become united, and the GUT symmetries [SU(5), 0(10), or E(6)] appear.

Finally, at a fabulous 10
³²
°K, gravity unites with the GUT force, and all the symmetries of the ten-dimensional superstring appear. We now have a gas of superstrings. At that point, so much energy will have gone into the pressure cooker that the geometry of space-time may very well begin to distort, and the dimensionality of space-time may change. The space around our kitchen may very well become unstable, a rip may form in the fabric of space, and a wormhole may appear in the kitchen. At this point, it may be advisable to leave the kitchen.

Thus by heating an ordinary ice cube to fantastic temperatures, we can retrieve the superstring. The lesson here is that matter goes through definite stages of development as we heat it up. Eventually, more and more symmetry becomes restored as we increase the energy.

By reversing this process, we can appreciate how the Big Bang occurred as a sequence of different stages. Instead of heating an ice cube, we now cool the superhot matter in the universe through different stages. Beginning with the instant of Creation, we have the following stages in the evolution of our universe.

10
⁻⁴³
seconds
The ten-dimensional universe breaks down to a four-and a six-dimensional universe. The six-dimensional universe collapses down to 10
⁻³²
centimeter in size. The four-dimensional universe inflates rapidly. The temperature is 10
³²
°K.

10
⁻³⁵
seconds
The GUT force breaks; the strong force is no longer united with the electroweak interactions. SU(3) breaks off from the GUT symmetry. A small speck in the larger universe becomes inflated by a factor of 10
⁵⁰
, eventually becoming our visible universe.

10
⁻⁹
seconds
The temperature is now 10
¹⁵
°K, and the electroweak symmetry breaks into SU(2) and U(l).

10
⁻³
seconds
Quarks begin to condense into neutrons and protons. The temperature is roughly 10
¹⁴
°K.

3 minutes
The protons and neutrons are now condensing into stable nuclei. The energy of random collisions is no longer powerful enough to break up the nucleus of the emerging nuclei. Space is still opaque to light because ions do not transmit light well.

300,000 years
Electrons begin to condense around nuclei. Atoms
begin to form. Because light is no longer scattered or absorbed as much, the universe becomes transparent to light. Outer space becomes black.

3 billion years
The first quasars appear.

5
billion years
The first galaxies appear.

10 to 15 billion years
The solar system is born. A few billion years after that, the first forms of life appear on earth.

It seems almost incomprehensible that we, as intelligent apes on the third planet of a minor star in a minor galaxy, would be able to reconstruct the history of our universe going back almost to the instant of its birth, where temperatures and pressures exceeded anything ever found in our solar system. Yet the quantum theory of the weak, electromagnetic, and strong interactions reveals this picture to us.

As startling as this picture of Creation is, perhaps stranger still is the possibility that wormholes can act as gateways to another universe and perhaps even as time machines into the past and future. Armed with a quantum theory of gravity, physicists may be able to answer the intriguing questions: Are there parallel universes? Can the past be changed?

Listen, there’s a hell of a universe next door: let’s go!

e. e. cummings

BLACK holes have recently seized the public’s imagination. Books and documentaries have been devoted to exploring this strange prediction of Einstein’s equations, the final stage in the death of a collapsed star. Ironically, the public remains largely unaware of perhaps the most peculiar feature of black holes, that they may be
gateways to an alternative universe
. Furthermore, there is also intense speculation in the scientific community that a black hole may open up a tunnel in time.