In that case, our simple picture in which the state of our perceptions becomes entangled with the state of Miss Kitty’s location is an oversimplification. A crucial part of the story is played by the entanglement of us with the external world. Let’s imagine that Miss Kitty starts out in a true quantum superposition, un-entangled with the rest of the world; but we, complicated creatures that we are, are deeply entangled with the outside world in ways we can’t possibly specify. The wave function of the universe assigns distinct amplitudes to all the alternative configurations of the combined system of Miss Kitty, us, and the outside world. After we observe Miss Kitty’s location, the wave function evolves into something of the form
(sofa, you see her on the sofa, world1) + (table, you see her under the table, world2),
where the last piece describes the (unknown) configuration of the external world, which will be different in the two cases.
Because we don’t know anything about that state, we simply ignore the entanglement with the outside world, and keep the knowledge of Miss Kitty’s location and our own mental perceptions. Those are clearly correlated: If she is on the sofa, we believe we have seen her on the sofa, and so forth. But after throwing away the configuration of the outside world, we’re no longer in a real quantum superposition. Rather, there are two alternatives that seem for all intents and purposes classical: Miss Kitty is on the sofa and we saw her on the sofa, or she’s under the table and we saw her under the table.
That’s what we mean when we talk about the branching of the wave function into different “worlds.” Some small system in a true quantum superposition is observed by a macroscopic measuring apparatus, but the apparatus is entangled with the outside world; we ignore the state of the outside world and are left with two classical alternative worlds. From the point of view of either classical alternative, the wave function has “collapsed,” but from a hypothetical larger point of view where we kept all of the information in the wave function of the universe, there were no sudden changes in the state, just a smooth evolution according to the Schrödinger equation.
This business about throwing away information may make you a little uneasy, but it should also sound somewhat familiar. All we’re really doing is coarse-graining, just as we did in (classical) statistical mechanics to define macrostates corresponding to various microstates. The information about our entanglement with the messy external environment is analogous to the information about the position and momentum of every molecule in a box of gas—we don’t need it, and in practice can’t keep track of it, so we create a phenomenological description based solely on macroscopic variables.
In that sense, the irreversibility that crops up when wave functions collapse appears to be directly analogous to the irreversibility of ordinary thermodynamics. The underlying laws are perfectly reversible, but in the messy real world we throw away a lot of information, and as a result we find apparently irreversible behavior on macroscopic scales. When we observe our cat’s location, and our own state becomes entangled with hers, in order to reverse the process we would need to know the precise state of the outside world with which we are also entangled, but we’ve thrown that information away. It’s exactly analogous to what happens when a spoonful of milk mixes into a cup of coffee; in principle we could reverse the process if we had kept track of the position and momentum of every single molecule in the mixture, but in practice we keep track of only the macroscopic variables, so reversibility is lost.
In this discussion of decoherence, a crucial role was played by our ability to take the system to be observed (Miss Kitty, or some elementary particle) and isolate it from the rest of the world in a true quantum superposition. But that’s clearly a very special kind of state, much like the low-entropy states we start with by hypothesis when discussing the origin of the Second Law of Thermodynamics. A completely generic state would feature all kinds of entanglements between our small system and the external environment, right from the start.
None of which is intended to give the impression that the application of decoherence to the many-worlds interpretation manages to swiftly solve all of the interpretive problems of quantum mechanics. But it seems like a step in the right direction, and highlights an important relationship between the macroscopic arrow of time familiar from statistical mechanics and the macroscopic arrow of time exhibited when wave functions collapse. Perhaps best of all, it helps remove i ll-defined notions such as “conscious observers” from the vocabulary with which we describe the natural world.
With that in mind, we’re going to go back to speaking as if the fundamental laws of physics are all completely reversible on microscopic scales. This isn’t an unassailable conclusion, but it has some good arguments behind it—we can keep an open mind while continuing to explore the consequences of this particular point of view. Which leaves us, of course, right where we started: with the task of explaining the apparent lack of reversibility on macroscopic scales in terms of special conditions near the Big Bang. To take that problem seriously, it’s time that we start thinking about gravity and the evolution of the universe.
PART FOUR
FROM THE KITCHEN TO THE MULTIVERSE
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BLACK HOLES: THE ENDS OF TIME
Time, old gal of mine, will soon dim out.
—Anne Sexton, “For Mr. Death Who Stands with His Door Open”
Stephen Hawking is one of the most willful people on Earth. In 1963, while working toward his doctorate at Cambridge University at the age of twenty-one, he was diagnosed with motor neurone disease. The prognosis was not good, and Hawking was told that he likely did not have long to live. After some soul-searching, he decided to move forward and redouble his commitment to research. We all know the outcome; now well into his seventh decade, Hawking has been the most influential scientist in the field of general relativity since Albert Einstein, and is instantly recognizable worldwide through his efforts to popularize physics.
Among other things, Hawking is a tireless traveler, and he spends some time in California every year. In 1998, I was a postdoctoral research fellow at the Institute for Theoretical Physics at the University of California, Santa Barbara, and Hawking came to visit on his annual sojourn. The institute administrator gave me a simple task: “Pick up Stephen at the airport.”
As you might guess, picking up Stephen Hawking at the airport is different than picking up anyone else. For one thing, you’re not really “picking him up”; he rents a van that is equipped to carry his wheelchair, for which a special license is required to drive it—a license I certainly didn’t have. The actual driving was left to his graduate assistant; my job was merely to meet them at the tiny Santa Barbara airport and show them to the van. By “them,” I mean Hawking’s entourage: a graduate assistant (usually a physics student who helps with logistics), other graduate students, family members, and a retinue of nurses. But it wasn’t a matter of pointing to the van and going on my way. Despite the fact that the graduate assistant was the only person allowed to drive the van, Hawking insisted that the van stay with him at all times, and also wanted to go to a restaurant for dinner before dropping off the assistant at his apartment. Which meant that I tagged along in my car while they all went to dinner, so I could shuttle the assistant back and forth. Hawking was the only one who knew where the restaurant was, but speaking through his voice synthesizer is a slow process; we spent several tense moments stopped in the middle of a busy road while Hawking explained that we had passed the restaurant and would have to turn around.
Figure 58: Stephen Hawking, who gave us the most important clue we have about the relationship between quantum mechanics, gravity, and entropy.
Stephen Hawking has been able to accomplish remarkable things while working under extraordinary handicaps, and the reason is basically straightforward: He refuses to compromise in any way. He’s not going to cut down his travel schedule, or eat at the wrong restaurant, or drink a lesser quality of tea, or curtail his wicked sense of humor, or think less a
mbitiously about the inner workings of the universe, merely because he is confined to a wheelchair. And that strength of character pushes him scientifically, as well as getting him through life.
In 1973, Hawking was annoyed. Jacob Bekenstein, a young graduate student at Princeton, had written a paper suggesting something crazy: that black holes carried huge amounts of entropy.206 By this time Hawking was the world’s expert on black holes, and (in his own words) he was irritated at Bekenstein, who he thought had misused some of his earlier results.207 So he set about showing exactly how crazy Bekenstein’s idea was—for one thing, if black holes had entropy, you could show that they would have to give off radiation, and everyone knows that black holes are black!
In the end, of course, Hawking ended up surprising everyone, including himself. Black holes do have entropy, and indeed they do give off radiation, once we take into account the subtle consequences of quantum mechanics. No matter how stubborn your personality may be, Nature’s rules will not bend to your will, and Hawking was smart enough to accept the radical implications of his discovery. He ended up providing physicists with their single most important clue about the interplay of quantum mechanics and gravity, and teaching us a deep lesson about the nature of entropy.
BLACK HOLES ARE FOR REAL
We have excellent reasons to believe that black holes exist in the real world. Of course we can’t see them directly—they’re still pretty dark, even if Hawking showed that they’re not completely black. But we can see what happens to things around them, and the environment near a black hole is sufficiently unique that we can often be confident that we’ve located one. Some black holes are formed from the collapse of very massive stars, and frequently these have companion stars orbiting them. Gas from the companion can fall toward the black hole, forming an accretion disk that heats to tremendous temperatures and emits X-ray radiation in copious amounts. Satellite observatories have found a number of X-ray sources that demonstrate all of the qualities you would expect in such an object: In particular, a large amount of high-intensity radiation coming from a very small region of space. Astrophysicists know of no good explanations for these observations other than black holes.
There is also good evidence for supermassive black holes at the centers of galaxies—black holes more than a million times the mass of the Sun. (Still a very tiny fraction of the total mass of a galaxy, which is typically a hundred billion times the mass of the Sun.) In the early stages of galaxy formation, these giant black holes sweep up matter around them in a violent maelstrom, visible to us as quasars. Once the galaxy has settled down a bit, things become calmer, and the quasars “turn off.” In our own Milky Way, we nevertheless are pretty sure that there lurks a black hole weighing in at about 4 million solar masses. Even without the blazing radiation of a quasar, observations of stars in the galactic center reveal that they are orbiting in tight ellipses around an invisible object. We can deduce that these stars must be caught in the gravitational field of something that is so dense and massive that it can’t be anything but a black hole, if general relativity has anything to say about the matter.208
BLACK HOLES HAVE NO HAIR
But as much fun as it is to search for real black holes in the universe, it is even more fun to sit and think about them.209 Black holes are the ultimate thought-experiment laboratory for anyone interested in gravity. And what makes black holes special is their purity.
While observations convince us that black holes exist, they don’t give us a lot of detailed information about their properties; we aren’t able to get up close to a black hole and poke at it. So when we make confident assertions about this or that feature of black holes, we’re always implicitly speaking within some theoretical framework. Unfortunately, scientists don’t yet fully understand quantum gravity, the presumed ultimate reconciliation of general relativity with the tenets of quantum mechanics. So we don’t have a single correct theory in which to answer our questions once and for all.
Instead, we often investigate questions within one of three different theoretical frameworks:
1. Classical general relativity, as written down by Einstein. This is the best full theory of gravity we currently possess, and it is completely consistent with all of known experimental data. We understand the theory perfectly, in the sense that any well-posed question has a definite answer (even if it might be beyond our calculational abilities to figure it out). Unfortunately it’s not right, as it’s completely classical rather than quantum mechanical.
2. Quantum mechanics in curved spacetime. This is a framework with a split personality. We treat spacetime, the background through which stuff in the universe moves, as classical, according to the rules of general relativity. But we treat the “stuff ” as quantum mechanical, described by wave functions. This is a useful compromise approach for trying to understand a number of real-world problems.
3. Quantum gravity. We don’t know the correct theory of quantum gravity, although approaches like string theory are very promising. We’re not completely clueless—we know something about how relativity works, and something about how quantum mechanics works. That’s often sufficient to make some reasonable guesses about how things should work in an ultimate version of quantum gravity, even if we don’t have the full-blown theory.
Classical general relativity is the best understood of these, while quantum gravity is the least well understood; but quantum gravity is the closest to the real world. Quantum mechanics in curved spacetime occupies a judicious middle ground and is the approach Hawking took to investigating black-hole radiation. But it behooves us to understand how black holes work in the relatively safe context of general relativity before moving on to more advanced but speculative ideas.
In classical general relativity, a black hole is just about the purest kind of gravitational field you can have. In the flexible world of thought experiments, we could imagine creating a black hole in any number of ways: from a ball of gas like an ordinary star, or out of a huge planet made of pure gold, or from an enormous sphere of ice cream. But once these things collapse to the point where their gravitational field is so strong that nothing can escape—once they are officially black holes—any indication of what kind of stuff they were made from completely disappears. A black hole made out of a ball of gas the mass of the Sun is indistinguishable from a black hole made from a ball of ice cream the mass of the Sun. The black hole isn’t, according to general relativity, just a densely packed version of whatever we started with. It’s pure gravitational field—the original “stuff ” has disappeared into the singularity, and we’re left with a region of strongly curved spacetime.
When we think of the gravitational field of the Earth, we might start by modeling our planet as a perfect sphere of a certain mass and size. But that’s clearly just an approximation. If we want to do a little bit better, we’ll take into account the fact that the Earth also spins, so it’s a little wider near the equator than near the poles. And if we want to be super-careful about it, the exact gravitational field of the Earth changes from point to point in complicated ways; changes in altitude of the surface, as well as changes in density between land and sea or between different kinds of rock, lead to small but measurable variations in the Earth’s gravity. All of the local features of the gravitational field of the Earth actually contain quite a bit of information.
Black holes are not like that. Once they form, any bumps and wiggles in the stuff they formed from are erased. There might be a short period right when the formation happens, when the black hole hasn’t quite settled down, but it quickly becomes smooth and featureless. Once it has settled, there are three things that we can measure about a black hole: its total mass, how fast it is spinning, and how much electric charge it has. (Real astrophysical black holes usually have close to zero net electric charge, but they are often spinning very rapidly.) And that’s it. Two collections of stuff with the same mass, charge, and spin, once they get turned into black holes, will become completely indistinguishable, as fa
r as classical general relativity is concerned. This interesting prediction of general relativity is summed up in a cute motto coined by John Wheeler, the same guy who gave black holes their name: “Black holes have no hair.”
This no-hair business should set off some alarm bells. Apparently, if everything we’ve just said is true, the process of forming a black hole has a dramatic consequence: Information is lost. We can take two very different kinds of initial conditions (one solar mass of hot gas, or one solar mass of ice cream), and they can evolve into precisely the same final condition (a one-solar-mass black hole). But up until now we’ve been saying that the microscopic laws of physics—of which Einstein’s equation of general relativity is presumably one—have the property that they conserve information. Put another way: Making a black hole seems to be an irreversible process, even though Einstein’s equation would appear to be perfectly reversible.
You are right to worry! This is a time puzzle. In classical general relativity, there is a way out: We can say that the information isn’t truly lost; it’s just lost to you, as it’s hidden behind the event horizon of a black hole. You can decide for yourself whether that seems satisfying or sounds like a cop-out. Either way, we can’t just stop there, as Hawking will eventually tell us that black holes evaporate once quantum mechanics is taken into account. Then we have a serious problem, one that has launched a thousand theoretical physics papers.210
From Eternity to Here: The Quest for the Ultimate Theory of Time Page 33