A Brief History Of Time

In this chapter, Hawking presents his conception of and theories about time. Most of the laws of physics work equally well if time goes forward or backward, yet a broken teacup never repairs itself. The law of entropy requires that things become more disordered over time; this is called the “thermodynamic arrow of time” (149). Related to it is the psychological arrow of time, referring to the human perception of events moving forward in time, and by which people remember the past but not the future. A third arrow of time is the cosmological, which points forward as the universe expands but reverses as it contracts.

There is only one state in which a jigsaw puzzle makes a complete picture, but many states in which it’s a jumble of puzzle pieces. Any orderly object exists in a specific state, but, over time, the laws of physics will cause it to change, and, because there are vastly more states of disorder than order, the originally well-ordered object will tend to become a jumble. If the universe started out randomly but became more orderly, it might seem that people would remember the future but not the past. Similarly, if, after expanding, the universe then contracts, maybe during the contraction the thermodynamic and psychological arrows of time reverse direction, and people remember the future and things get more orderly.

Hawking’s no-boundary proposal states that, after the early moments of cosmic inflation, the universe is only mildly disordered, and it thereafter expands for a very long time, until all matter decays into energy and the universe achieves a nearly perfect state of disorder. Then, it will begin to collapse, but during this time no life can exist, since life needs to process energy to survive, and that process requires at least some form of orderliness that life can break down for its own use.

In this way, the thermodynamic, psychological, and cosmological arrows of time always point in the same direction because humans can only exist in a universe that’s expanding and increasing in entropy.

Faster-than-light travel, as in science fiction, isn’t possible using ships powered with engines that push them through space. As a ship approaches lightspeed, the mass of the ship increases toward infinity. A way to break the speed of light maybe be possible by creating a “wormhole” through space that connects two faraway places.

The only way to create a wormhole is through the use of “negative” energy. Such energy exists in very particular places. An example is the space between metal plates held very close together: Their proximity limits the possible wavelengths of virtual particles (which appear and disappear in accordance with the uncertainty principle) between the plates, so that fewer can exist between the plates than outside them. This causes more pressure from virtual particles outside the plates than between them. Since the total field energy from virtual particles out in the universe is zero, the energy of virtual particles between the plates is negative. This means negative energy exists and might possibly be harvested to create a wormhole.

Wormholes would create weird time effects: A person could go to Alpha Centauri, four light-years away, and return home before they left. This also means it would be possible to go back in time and change events so that one never went through the wormhole in the first place. The only way to prevent these contradictions is if the time travel happened before you left through the wormhole. In this way, the universe would protect itself from the chaos of time travel.

On the microscopic scale, time travel actually happens. A particle moving forward in time is the same as an anti-particle moving backward in time. When virtual particles form at the edges of black holes, and one of them, the anti-particle, falls into the hole, the escaping particle can be conceived of as traveling backward in time out of the hole.

The theories of gravity, electromagnetics, and the strong and weak forces are “partial theories” that don’t fully fit together and that contain arbitrary values that the theories don’t predict. Gravity in particular is understood as a classical theory—it’s not a quantum-based concept—while the other three depend on quantum mechanics to be understood. Hawking notes that to develop a unified theory, the “necessary first step […] is to combine general relativity with the uncertainty principle” (172-73). This is harder than it might seem. To fit gravity into a quantum theory, theorists must account for all the mass contained in virtual particles, which should be so great that the universe curls up into a tiny point. Workarounds exist that “renormalize” these problems, and they work, but they often depend on estimates or arbitrary values. A successful Grand Unified Theory of Everything would be more accurate.

One solution, presented in 1976, was “supergravity,” which combined the graviton with several particles of various spin values, into aspects of a single “superparticle.” The calculations, though, would take four years to complete. In 1984 a new idea called “string theory” proposed that particles weren’t dimensionless points but strings that extend through several dimensions, some hanging open and some closed in a loop.

Figures 11.1 and 11.2 illustrate strings and their travel through time. In Figure 11.1 is an open string—it looks like an ordinary piece of string—and its travel upward through time looks like a strip of paper that’s as wide as the string; this is called the string’s “world-sheet.” Figure 11.2 shows a closed string—it’s a loop, like a string whose ends have joined—and its travel upward through time generates a “world-sheet” that looks like a cylinder.

Theoretically, strings can join up when one particle absorbs another. Their world sheets, as shown in Figures 11.3 and 11.4, might then merge to form a single, larger string. Two open strings, in Figure 11.3, merge together as they move upward in time; they form a single, larger string. Similarly, Figure 11.4 shows two closed-loop strings whose cylindrical world-sheets travel upward in time until they join to form a single, larger cylinder. The shape is somewhat like a pair of pants, with the single closed-loop strings as the legs, while the torso above them is the larger cylindrical world-sheet of the larger, combined string.

Strings can also separate, and one string can leave another and join a third. Figure 11.5 shows the old diagram of two point-like particles, one in the sun and one in the Earth, traveling upward in parallel timelines, and, midway up, a wavy line representing a graviton travels across the gap between the two vertical timelines, like the crossbar on the letter “H.” Figure 11.6 shows a new string-theory diagram of the same event: This time, the two-particle timelines are replaced by world-sheets, and the graviton is a third world-sheet that travels across the gap between them. This diagram also looks like the letter “H” except much thicker.

The math for string theory requires a universe with at least 10 dimensions, most of which function at a scale too small to be observable or noticed. If some of the extra dimensions were uncurled, the universe would behave differently—gravity, for example, would be weaker, and electrons would act oddly—and human life might not be possible. The anthropic principle thus limits human life to universes with only three unfurled physical dimensions.

Figure 11.8 shows a sketch of a dog who exists in a flat, two-dimensional world. Its digestive tract runs across the dog and divides it into two parts. Such a creature would be unable to survive. This is an example of how worlds other than those with three physical dimensions likely are inhospitable to life.

String theory has evolved, and though it’s compatible with an endless number of possible configurations of spatial dimensions, many of them lead to the four known dimensions of space-time. Particle theory deals with zero-dimensional sub-atomic units, while string theory deals with particles in one dimension, and a new idea, p-brane theory, posits particles with two to nine dimensions. Each theory has its advantages and drawbacks; this is somewhat like needing multiple maps of the Earth to describe it completely.

It’s possible that the closest thing to a unified theory is what scientists have developed already: a collection of theories that are used individually, depending on circumstances. It’s also possible that there’s no ultimate theory of everything, but instead an infinite number of ever-more-accurate theories. It might also be that there’s no viable theory at all.

Hawking reiterates that scientific theories will never be able to predict the course of the universe completely because of the limits on knowledge set by the uncertainty principle and because the calculations for the interactions of three or more objects quickly become infinitely complex. Still, continued experimentation and theorizing helps humanity to understand the universe more and more fully.

Hawking returns to early philosophical and religious beliefs. Ancient theories held that the world was controlled by spirits who lived inside of rivers and mountains and the sun and Moon. Early people made offerings to these gods to win their favor and receive blessings like good harvests. Over time, careful record-keeping showed that celestial bodies moved very precisely and predictably; offerings made no difference. More recently, science discovered laws that explain the motions of the universe and its contents. Personification was no longer necessary to explain the functions of the cosmos, but the creation of the cosmos remained mysterious. The Marquis de Laplace, who theorized the deterministic universe, proposed that while the laws of physics could be discovered, their origin belonged solely to a divine creator. Yet scientific discoveries—and especially the uncertainty principle—maintain a degree of unpredictability to the universe. Both the position and velocity of a given particle can never be known exactly. Instead, quantum mechanics sees particles as a set of waves that propagate over time. That history, which includes all possible future states of the particle, can be described. Like spirits and mythologies, Hawking posits that maybe position and velocity are simply old biases that science can someday abandon.

The theory of gravity, combined with quantum mechanics, predicts a universe that got started with a bang and has since spread out very evenly. Hawking notes that this does not explain why the universe necessarily exists at all, however, and that cosmology began as a way to understand the nature or existence of the divine and determine why anything exists at all. Though modern investigations of the origins of the universe tend toward the technical, rather than the philosophical, Hawking expresses hope that popular understanding and discussion of theoretical physics will encourage new advances in “human reasoning.”