From Eternity to Here (17 page)

Even in Newtonian gravity, there’s nothing to stop us from contemplating an object so massive and dense that the escape velocity is greater than the speed of light, rendering the body “black.” Indeed, the idea was occasionally contemplated, including by British geologist John Michell in 1783 and by Pierre-Simon Laplace in 1796.
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At the time, it wasn’t clear whether the idea quite made sense, as nobody knew whether light was even affected by gravity, and the speed of light didn’t have the fundamental importance it attains in relativity. More important, though, there is a very big distinction hidden in the seemingly minor difference between “an escape velocity greater than light” and “light cannot escape.” Escape velocity is the speed at which we would have to start an object moving upward in order for it to escape the gravitational field of a body
without any further acceleration
. If I throw a baseball up in the air in the hopes that it escapes into outer space, I have to throw it faster than escape velocity. But there is absolutely no reason why I couldn’t put the same baseball on a rocket and gradually accelerate it into space without ever reaching escape velocity. In other words, it’s not necessary to reach escape velocity in order to actually escape; given enough fuel, you can go as slowly as you like.

But a real black hole, as predicted by general relativity, is a lot more dramatic than that. It is a true region of no return—once you enter, there is no possibility of leaving, no matter what technological marvels you have at your disposal. That’s because general relativity, unlike Newtonian gravity or special relativity, allows spacetime to curve. At every event in spacetime we find light cones that divide space into the past, future, and places we can’t reach. But unlike in special relativity, the light cones are not fixed in a rigid alignment; they can tilt and stretch as spacetime curves under the influence of matter and energy. In the vicinity of a massive object, light cones tilt toward the object, in accordance with the tendency of things to be pulled in by the gravitational field. A black hole is a region of spacetime where the light cones have tilted so much that you would have to move faster than the speed of light to escape. Despite the similarity of language, that’s an enormously stronger statement than “the escape velocity is larger than the speed of light.” The boundary defining the black hole, separating places where you still have a chance to escape from places where you are doomed to plunge ever inward, is the
event horizon
.

Figure 19:
Light cones tilt in the vicinity of a black hole. The event horizon, demarcating the edge of the black hole, is the place where they tip over so far that nothing can escape without moving faster than light.

There may be any number of ways that black holes could form in the real world, but the standard scenario is the collapse of a sufficiently massive star. In the late 1960s, Roger Penrose and Stephen Hawking proved a remarkable feature of general relativity: If the gravitational field becomes sufficiently strong, a singularity
must
be formed.
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You might think that’s only sensible, since gravity becomes stronger and stronger and pulls matter into a single point. But in Newtonian gravity, for example, it’s not true. You can get a singularity if you try hard enough, but the generic result of squeezing matter together is that it will reach some point of maximum density. But in general relativity, the density and spacetime curvature increase without limit, until they form a singularity of infinite curvature. Such a singularity lies inside every black hole.

It would be wrong to think of the singularity as residing at the “center” of the black hole. If we look carefully at the representation of spacetime near a black hole shown in Figure 19, we see that the future light cones inside the event horizon keep tipping toward the singularity. But that light cone
defines
what the observer at that event would call “the future.” Like the Big Bang singularity in the past, the black hole singularity in the future is a moment of time, not a place in space. Once you are inside the event horizon, you have absolutely no choice but to continue on to the grim destiny of the singularity, because it lies ahead of you in time, not in some direction in space. You can no more avoid hitting the singularity than you can avoid hitting tomorrow.

When you actually do fall through the event horizon, you might not even notice. There is no barrier there, no sheet of energy that you pass through to indicate that you’ve entered a black hole. There is simply a diminution of your possible future life choices; the option of “returning to the outside universe” is no longer available, and “crashing into the singularity” is your only remaining prospect. In fact, if you knew how massive the black hole was, you could calculate precisely how long it will take (according to a clock carried along with you) before you reach the singularity and cease to exist; for a black hole with the mass of the Sun, it would be about one-millionth of a second. You might try to delay this nasty fate, for example, by firing rockets to keep yourself away from the singularity, but it would only be counterproductive. According to relativity, unaccelerated motion
maximizes
the time between two events. By struggling, you only hasten your doom.
⁷⁵

There is a definite moment on your infalling path when you cross the event horizon. If we imagine that you had been sending a constant stream of radio updates to your friends outside, they will never be able to receive anything sent after that time. They do not, however, see you wink out of existence; instead, they receive your signals at longer and longer intervals, increasingly redshifted to longer and longer wavelengths. Your final moment before crossing the horizon is (in principle) frozen in time from the point of view of an external observer, although it becomes increasingly dimmer and redder as time passes.

Figure 20:
As an object approaches an event horizon, to a distant observer it appears to slow down and become increasingly redshifted. The moment on the object’s world line when it crosses the horizon is the last moment it can be seen from the outside.

WHITE HOLES: BLACK HOLES RUN BACKWARD

If you think a bit about this black-hole story, you’ll notice something intriguing: time asymmetry. We have been casually tossing around terminology that assumes a directionality to time; we say “once you pass the event horizon you can never leave,” but not “once you leave the event horizon you can never return.” That’s not because we have been carelessly slipping into temporally asymmetric language; it’s because the notion of a black hole is intrinsically time-asymmetric. The singularity is unambiguously in your future, not in your past.

The time asymmetry here isn’t part of the underlying physical theory. General relativity is perfectly time-symmetric; for every specific spacetime that solves Einstein’s equation, there is another solution that is identical except that the direction of time is reversed. A black hole is a particular solution to Einstein’s equation, but there are equivalent solutions that run the other way:
white holes
.

The description of a white hole is precisely the same as that of a black hole, if we simply reverse the tenses of all words that refer to time. There is a singularity in the past, from which light cones emerge. The event horizon lies to the future of the singularity, and the external world lies to the future of that. The horizon represents a place past which, once you exit, you can never return to the white-hole region.

Figure 21:
The spacetime of a white hole is a time-reversed version of a black hole.

So why do we hear about black holes in the universe all the time, and hardly ever hear about white holes? For one thing, notice that we can’t “make” a white hole. Since we are in the external world, the singularity and event horizon associated with a white hole are necessarily in our
past
. So it’s not a matter of wondering what we would do to create a white hole; if we’re going to find one, it will already have been out there in the universe from the beginning.

But in fact, thinking slightly more carefully, we should be suspicious of that word
make
. Why, in a world governed by reversible laws of physics, do we think of ourselves as “making” things that persist into the future, but not things that extend into the past? It’s the same reason why we believe in free will: A low-entropy boundary condition in the past dramatically fixes what possibly could have happened, while the absence of any corresponding future boundary condition leaves what can yet happen relatively open.

So when we ask, “Why does it seem relatively straightforward to make a black hole, while white holes are something that we would have to find already existing in the universe?” the answer should immediately suggest itself: because a black hole tends to have more entropy than the things from which you would make it. Actually calculating what the entropy is turns out to be a tricky business involving Hawking radiation, as we’ll see in Chapter Twelve. But the key point is that black holes have a lot of entropy. Black holes turn out to provide the strongest connection we have between gravitation and entropy—the two crucial ingredients in an ultimate explanation of the arrow of time.

6

LOOPING THROUGH TIME

You see, my son, here time changes into space.

—Richard Wagner, Parsifal

Everyone knows what a time machine looks like: something like a steampunk sled with a red velvet chair, flashing lights, and a giant spinning wheel on the back. For those of a younger generation, a souped-up stainless-steel sports car is an acceptable substitute; our British readers might think of a 1950s-style London police box.
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Details of operation vary from model to model, but when one actually travels in time, the machine ostentatiously dematerializes, presumably to be re-formed many millennia in the past or future.

That’s not how it would really work. And not because time travel is impossible and the whole thing is just silly; whether or not time travel is possible is more of an open question than you might suspect. I’ve emphasized that time is kind of like space. It follows that, if you did stumble across a working time machine in the laboratory of some mad inventor, it would simply look like a “space machine”—an ordinary vehicle of some sort, designed to move you from one place to another. If you want to visualize a time machine, think of launching a rocket ship, not disappearing in a puff of smoke.

So what is actually entailed in traveling through time? There are two cases of possible interest: traveling to the future and traveling to the past. To the future is easy: Just keep sitting in your chair. Every hour, you will move one hour into the future. “But,” you say, “that’s boring. I want to move far into the future, really quickly, a lot faster than one hour per hour. I want to visit the twenty-fourth century before lunchtime.” But we know it’s impossible to move faster than one hour per hour, relative to a clock that travels along with you. You might be able to trick yourself, by going to sleep or entering suspended animation, but time will still be passing.