Trespassing on Einstein's Lawn (27 page)

Actually, it really is like a black hole. The boundary between the inaccessible region and the rest of the universe marks an event horizon. Known as a Rindler horizon, it has all the same features as a black hole's. It has all the weird quirks of relativity: wavelengths of light stretch to huge proportions, and time slows down and halts at its edge. It's got an entropy proportional to one-quarter of its area—the same
formula Hawking had discovered for black holes. With entropy comes temperature. With temperature comes heat. With heat comes particles.

These particles were variously described as “Rindler particles,” “Unruh radiation,” “Unruh-Davies radiation,” or “Hawking-Unruh radiation,” but they all amounted to the same thing: observer-dependent particles produced by an observer-dependent horizon. In fact, black hole horizons and Rindler horizons are totally identical at the level of equations. They might seem like very different physical situations, but as far as the math was concerned they were indistinguishable. And if you think about it, there's an obvious reason for this: the equivalence principle. Einstein said that gravity and acceleration are equivalent. Not just similar or analogous, but
equivalent.
Two ways of looking at the same thing. If gravity could create an event horizon, so could acceleration.

I imagined Safe and Screwed hanging out in ordinary flat space free from black holes. Safe was my accelerated observer, so as he accelerates through flat space, he carves out an event horizon. If he whips out a thermometer on the run, he'll measure a nonzero temperature all around him, courtesy of the Rindler-Unruh-Davies-Hawking particles. But ask Screwed to do the same and his thermometer won't register a thing. No matter how much I stewed over it, I couldn't get past how insane that was: two observers occupying the
same exact space
, and one is undeniably surrounded by particles while the other unequivocally sees empty space. And the only difference between them is that Screwed doesn't have an event horizon. Safe physically restructures the vacuum and creates actual measurable particles just by having a particular point of view. Particles that exist, objectively, for him alone.

For years I had suspected that the secret ingredient for turning my father's nothing—the infinite, boundless homogeneous state—into something was a boundary. And Fotini Markopoulou had me wondering if perhaps an observer's internal perspective, which was invariably bounded by his light cone, was somehow enough to do the trick. Still, I had been skeptical that a light cone was capable of physically transforming
nothing into anything. After all, a light cone is merely a reference frame; it's not a
thing
that exists out there in the universe. But maybe my skepticism had been shortsighted. Here I was learning about observer-dependent boundaries that create particles using nothing more “physical” than an observer's point of view. Granted, these horizons were a little different. Unlike light cones, they were time-dependent; they formed dynamically. But it was an intriguing prospect all the same, one that I wrote down, and then underlined, in my notebook:
Horizons show how an observer's point of view can physically restructure the universe. Or maybe the H-state.

The whole thing was downright freaky. And the key point was that neither Safe's nor Screwed's vacuum state is the “real” one. Relativity had shown that space and time were different for different observers. They weren't invariant. They weren't real. Now it was clear that vacuum states, and with them particles, were the next to go. Particles weren't real. Their existence was observer-dependent.

It all tied back in to that definition of particles: irreducible representations of the Poincaré symmetry group. Poincaré symmetry is a global symmetry of flat spacetime, but global symmetries are useless in the face of horizons. Horizons require us to define everything locally, to slice up the global view into individual observers' patches. The problem is that there's no unique, preferred way to slice it, and different slices give you different vacuums—just a series of incommensurable partial views, no one any truer than the next. Curved spacetime—the kind with gravity, with event horizons—isn't Poincaré symmetric. Take away the symmetry and you lose any clear definition of a “particle.” When you make the geometry of the spacetime observer-dependent—whether it's flat, as Screwed sees it, or curved, as it is for Safe—you bring the ambiguity to a whole new level. It no longer made sense to ask, “Is there a particle there?” Now we have to specify: “Is there a particle there
according to Safe
?” And as if that weren't enough to blow my mind, I discovered a third kind of event horizon, one that literally marked the edge of the universe.

* * *

If you have an accelerated observer in a flat space, you get a Rindler horizon. But I soon discovered that you could swap the situation around and have space itself accelerate while an observer like Screwed stays still in an inertial frame. With space expanding at an accelerated rate, light can only travel a finite distance even given infinite time—no matter how far the light gets, more distance just keeps opening up ahead of it, like a light beam on a treadmill. Some light beams will never be able to reach Screwed. Thus, for him, part of the universe is forever dark. The darkness is encircled by an event horizon—a de Sitter horizon.

Willem de Sitter was the first physicist to spot an accelerating universe buried in Einstein's equations—one totally devoid of matter, emptier than the emptiest stretches of cold interstellar space. Just a vast, barren, swelling nothing.

Only it wasn't quite nothing. Woven into the fabric of space was a strange form of energy that exerted a kind of antigravitational effect, a force that pushed outward, causing the space to inflate. Its source was a seemingly innocuous term in the equations of general relativity: the cosmological constant. Because it was a feature of space itself, and because it was constant, the strange antigravitational energy wasn't diluted by expansion: the more space, the more cosmological constant. This produced a runaway effect, accelerating the universe's expansion faster and faster the bigger it grew. It was the opposite of gravitational collapse—the formation of a black hole in reverse.

When de Sitter proposed his model in 1917, Einstein was convinced it had to be wrong. It flew in the face of two of Einstein's deeply held philosophical beliefs: first, that spacetime without matter was impossible, and second, that the universe was static. Eternal. In fact, looking at his equations, Einstein believed that it was the cosmological constant that would anchor the universe in place and keep it from expanding or collapsing.

Unfortunately for Einstein, philosophy wasn't strong enough to hold the universe steady. In 1929 the American boxer-turned-astronomer Edwin Hubble made a world-changing discovery: all the galaxies in the sky were moving away from us at a velocity proportional
to their distance. Exactly what you'd expect to see if you lived in an expanding universe.

I have no idea how he reacted to Hubble's news, but I'd be willing to bet that Einstein punched a wall. I'm sure it took not even a moment for him to realize that he had missed out on the chance to make what would have gone down in history as one of the greatest scientific predictions of all time. And from cosmic expansion the big bang would have been two thoughts away. It had all been right there in front of his nose, in the very equations that
he
discovered, but he hadn't wanted to see it. Okay, sure, he had won a Nobel Prize seven years earlier and it wasn't like people would be walking around saying, “Man, that Einstein was an
idiot.
” But still, he must have been pretty pissed.

There's a photograph of Einstein peering through Hubble's telescope atop Mount Wilson to see the expansion of the cosmos; every time I looked at it, it sent a shiver down my spine. The idea that what a man armed with nothing more than philosophical principles had worked out with pencil and paper was actually happening in this huge way, playing itself out in the enormous reality of the world, underlined the power of the mind and the exquisite potential of science. Einstein wrote,
“I take it to be true that pure thought can grasp the real, as the ancients had dreamed.” I couldn't help wondering how an antirealist could bear to look at that photo. Could such a person honestly pass it all off as pure coincidence? A cosmic miracle? Was the universe expanding because we all agreed it was? I could just imagine the girl in my class:
Expansion? Is there not a certain male organ that's known for that?

After Hubble's discovery of the expanding universe, Einstein was forced to acknowledge that there were legit nonstatic solutions to general relativity. Solutions like de Sitter's. But de Sitter's model remained a mere theoretical curiosity until 1998, when those teams of astronomers went supernova hunting and discovered that the expansion rate of the universe is accelerating. Later studies pinned down exactly when the acceleration began: 5 billion years ago the cosmic expansion stopped slowing down from its initial burst of inflation and suddenly started speeding up. It was as if some strange force had lain dormant, crouching on its haunches in the stillness of space, waiting for the
right moment to pounce and overtake gravity. If it wasn't Einstein's cosmological constant, it was a damn good impersonator. Physicists named it dark energy, just in case.

Today's accelerated expansion showed no signs of slowing down. As space continues to swell, it will dilute the density of matter, thinning out the universe, separating any two objects by ever-longer stretches of hopeless, starless space. As the distances between galaxies grow, the sky will darken. Eventually space will accelerate so quickly that light from distant stars will never again be able to reach us. Swept off by cosmic expansion, they will disappear, leaving only darkness, our Milky Way a dim beacon in an inky sea of empty, expanding nothing. A lonely island in the void, surrounded by an event horizon. It slowly dawned on me now: in a universe ruled by dark energy, we're all Screwed.

Living in a universe permeated by dark energy means that an event horizon awaits us. It means that
this
is a de Sitter universe. And it means that all the disconcerting effects that come with horizons aren't confined to the safety of distant black holes. It means that they are all around us.

So there I was, at a miniature desk in a miniature flat in a cul-de-sac in London in a vast and expanding de Sitter universe surrounded by an event horizon. Being surrounded by a de Sitter horizon is like being surrounded by a black hole—galaxies accelerate toward the horizon as if being pulled by gravity, then plunge straight out of the universe. This time, with space itself doing the accelerating, it's Screwed, the inertial observer, who sees the horizon. From Screwed's frame we see the galaxy's light stretched and slowed as extreme relativistic effects take hold near the horizon. By the time the galaxy has crossed into the dark region of no return, it doesn't matter whether you call it a black hole or a de Sitter horizon; either way, that galaxy is gone.

As galaxies disappear behind the horizon, the horizon grows in area and entropy. Just two years after his discovery of black hole radiation, Hawking and fellow Cambridge physicist Gary Gibbons proved that, just like black hole horizons, de Sitter horizons had an entropy proportional
to a quarter of their area. With entropy came temperature; with temperature, particles. Observers in de Sitter space find themselves surrounded by heat. I began wondering why, in a de Sitter universe, London always seemed so cold. It turned out the de Sitter temperature is next to nothing, just a whisper above absolute zero. Virtually undetectable. But someday in our cosmic future, the microwave background will redshift away, leaving the de Sitter radiation as the sole source of constant heat throughout the cosmos.

The implications of all this were beginning to sink in. Like black hole and Rindler horizons, de Sitter horizons were observer-dependent. The objective acceleration of space gave rise to a horizon by hiding a region of spacetime from a given observer. It's one horizon per observer, each at a slightly different spot. No two observers will agree on the location of the universe's edge. Sitting there in London, I was in an entirely different de Sitter universe than my father back in Philadelphia.
We each have our own universe.
Markopoulou had been talking about light cones—and the thing I had learned about light cones is that they grow with time. Wait long enough and you'll see more of the universe. Wait an infinite amount of time and you'll see the whole thing. Not so in a de Sitter spacetime. A de Sitter horizon guarantees that the longer you wait, the less you'll see. In a de Sitter universe, no observer can see the whole thing.
Ever.

Of course, if you start accelerating, like Safe, the horizon disappears. Now you're in the same reference frame as the expanding space. Nothing is hidden from you, so long as you continue to accelerate. From Screwed's perspective, you'll come to a grinding halt at the de Sitter horizon and burn to a crisp in the radiation. But as far as you're concerned, everything's just fine. There's no horizon. Just more universe.

Unfortunately, you can't accelerate forever—light's speed limit makes sure of that. Spacetime, however, can. Spacetime has no speed limit—it can expand faster than light, just as it did during inflation. If you're racing spacetime, spacetime will always win. Eventually you'll have to stop accelerating and resign yourself to life behind a horizon, stuck in a de Sitter universe. Forever.

I was realizing now that cosmology in a de Sitter universe was a
whole new ballgame. How do you begin to talk about
the
universe when all observers have their own? In my search for answers, I came across a talk that physicist Raphael Bousso, a former student of Hawking's, had given at a Cambridge symposium in honor of Hawking's sixtieth birthday. Bousso's name rang a bell: he had tied for first place with Markopoulou in the young researchers' competition at the Wheeler symposium back in Princeton. At the Hawking conference, Bousso gave a talk called “Adventures in de Sitter Space.” He explained how Hawking and Gibbons had discovered that de Sitter horizons had all the same quantum properties as black hole horizons, including entropy and temperature. Noting that de Sitter horizons are observer-dependent, Bousso said that Hawking and Gibbons had
“interpreted their results as an indication that quantum gravity may not admit a single, objective, and complete description of the universe. Rather, its laws may have to be formulated with reference to an observer—no more than one at a time.”