Trespassing on Einstein's Lawn (48 page)

As we watched Susskind head off down the street, I turned to my father. “What was going through your head when Lenny and I came back to the table with our drinks?” I asked him.

He laughed. “I was thinking, ‘Holy shit. Lenny Susskind is carrying my coffee.' ”

Everything I knew about road trips had come from Jack Kerouac.
All that road going. All the people dreaming in the immensity of it.
This trip was exactly like that, except instead of wise hitchhikers there were physicists, and instead of cheap motels there were Marriotts. Instead of diners and roadhouses there were Jamba Juices and sushi bars, and instead of speeding down the highway with Dean Moriarty in a Cadillac, I was being chauffeured by my parents in a rented Toyota. Then again, the goal was the same. Enlightenment. Or reality. Or whatever you want to call it.

We drove from San Francisco down to Santa Barbara, stopping in little coastal towns along the way. My mother sat up front with my dad, while I slouched comfortably in the backseat, watching the world go by. I watched the lush green hills and the mountains rising in the distance, the palm trees, the endless sky, the ocean stretching out toward the horizon. And I wanted to be amazed. I wanted to marvel, awestruck, at the beauty of nature and the majesty of the Earth. Isn't that what you're supposed to feel at the sight of these things? Awe? Only I didn't. I didn't find it marvelous or majestic, not compared to the ideas dancing around in my head. For years we had been trying to unravel the nature of the reality outside the window, when all I really wanted to unravel was the world inside my mind. Then again, was there a difference?
For all intents and purposes, there is no outside.

Maybe the problem was that I knew that the things outside my
window—the trees, the sky, the mountains, the ocean—were just the tip of the cosmic iceberg, negligible in the scheme of things. That none of them was ultimately real. Nabokov once wrote that “ ‘reality' [is] one of the few words that means nothing without quotes” around it, and I was beginning to understand exactly what he meant. I traced my finger across the glass window, drawing quotation marks around a mountain: “mountain.” But as I looked at it, all I saw were my own brown eyes staring back: “me.”

The golden age of cosmology had passed awfully quickly, and it still wasn't clear what was going to take its place. I understood the draw of Susskind's FRW/CFT, but the decay of de Sitter space that's required to get there is governed by eternal inflation. You can't talk about eternal inflation without describing the universe beyond our cosmic horizon as part and parcel of the same cohesive reality. With its inherent God's-eye view, it seemed to me that eternal inflation was unphysical and incoherent from the start—so why invoke it at all?

Of course, invoking it brought invariance back to the S-matrix and made string theory viable again. Or did it? A quick Internet search on my cell phone led me to a Bousso paper entitled “Cosmology and the S-Matrix.” Reading it in the backseat, I grew unconvinced that having observers like the Census Taker out at the infinite boundary of a flat universe was enough to give meaning (substance, reality) to the S-matrix in the first place. Because the point about the S-matrix wasn't simply that you have to stand at the farthest possible corner of the universe, looking back. It was that you have to stand
outside
the system.

As Hawking had said, the S-matrix works like a charm for describing laboratory experiments because, as observers, we can stand completely outside the system being observed. From behind Wheeler's plate-glass window, we can see what goes in and what comes out, our own existence entirely irrelevant. But when it comes to cosmology, there's no window. When the system is the universe, there's no outside.
“The difference between cosmology and the S-matrix,” Bousso said, “is that in the S-matrix you're outside looking in, and in cosmology we're inside looking out.” It was Russell's barber paradox meets horizon complementarity: when you try to take the view from outside the brackets
and include it in your description of the inside, things go horribly awry. You can't be inside and outside simultaneously. You can be inside the universe
or
you can have an S-matrix. Really, there's not much of a choice.

As for the Census Taker, I thought, you can push him out to arbitrarily large distances, but at any given time he's still inside the universe. And while he can access a near-infinite amount of information in his causal patch, he can't access all of it, thanks to the simple but unavoidable fact that he can't measure himself.

In the paper, Bousso pointed out that the impossibility of self-measurement was not only a poignant problem for de Sitter space but one that would ultimately plague
any
space, including FRW.

“This is just a particularly bad version of a more general problem that arises whenever one part of a closed system measures another part,” he wrote. “This includes any measurement of the global state of the universe, independently of causal restrictions. Obviously the apparatus must have at least as many degrees of freedom as the system whose quantum state it attempts to establish (in practice it usually has orders of magnitude more).” He concluded, “No realistic cosmology permits the global observations associated with an S-matrix.”

Even the Census Taker will hit an impassable limit. His light cone might grow big enough to engulf the whole universe, but it will never engulf him, too. He can never be both subject and object in a single frame. As long as he attempts to describe the physics of a universe that contains him, his description will be thwarted by pathological self-reference, the kind of Gödelian uncertainty that Wheeler saw as containing the key to ultimate reality.
Always have this uncertainty … can't decide true or false values from the inside.

If self-reference undermined invariance even in an FRW universe, I thought, there didn't seem to be much hope for reality anywhere at all. The confusing coauthorship structure would be equally confusing in any universe. Even if my father and I waited for billions of years, surviving the apocalyptic decay of our vacuum into a lower-energy universe, which in turn would plummet after billions of years more, and still we waited, big bang after big bang, until finally we hit upon solid
ground where our light cones would come their very closest to consensus, even then Brockman and Matson would have every right to reject our proposal. Coauthorship was as much an illusion as everything else.

At least it was a good illusion, I thought as we cruised down the highway, chatting excitedly about physics and the encounters we'd just shared. When we weren't discussing the nature of ultimate reality my dad would blast music—Radiohead, Beck, Bob Dylan, the Roots—and my mother would dance in her seat, snapping her fingers, bobbing her shoulders, and making up her own inexplicable lyrics as she sang along. I supposed that someone outside the car looking in might have found it an odd family vacation: the three of us driving down the California coast, debating the status of string theory or the meaning of the holographic principle and meeting with various physicists along the way. But for me, on the inside, it was just family.

At the Kavli Institute in Santa Barbara, Joe Polchinski's office was small compared to David Gross's captain's quarters, but it was still pretty sweet.

“Not a bad view,” my father joked, pointing to the Pacific Ocean directly outside the window.

Polchinski laughed. “Sometimes when I'm working I see dolphins swim by.”

“I knew it!” I muttered.

He turned to me. “Have you been here before?”

I nodded. “A few years ago I arranged a debate between David Gross and Lenny Susskind.”

Polchinski's face lit up. “That was you? I heard about that!”

He took a seat in his desk chair while my father and I settled into the couch that faced a blackboard covered in equations. Polchinski seemed reserved, but thoughtful and kind.

Bousso had said that in certain settings, you could think of D-branes as the fundamental ingredients of ultimate reality, and Polchinski was the one who had discovered D-branes in the first place. If we wanted to know more about them, we had come to the right ocean-front office.

“Can you tell us what D-branes are?” I asked.

To understand D-branes, Polchinski said, you have to start with strings. By the 1990s, physicists had discovered not one but five consistent string theories in ten dimensions, whimsically named Type I, Type IIA, Type IIB, SO(32), and E
₈
×E
₈
. When it comes to theories of everything, no one wants five. After all, if there's just one right answer and you've found it, you're done. If there are five possible answers, you've still got a lot of work left to do in order to figure out which one is right.

Strings, Polchinski reminded us, can be open, like tiny shoelaces, or closed, like little rubber bands. Of those five string theories, some had only closed loops; others had both open and closed. In fact, if a theory has open strings in it, it
must
have closed strings, too, since two open strings can always join together to form a loop, even though the reverse doesn't hold true. It's a good rule, considering that gravitons are closed strings. If you had a theory with only open strings, you wouldn't have gravity—which, of course, was the whole point of the thing.

“In the early days, most of the focus was on closed strings,” Polchinski said, “because they seemed to give a complete description of what you need in a unified theory.” And one of the most remarkable things to come out of closed strings, he explained, was T-duality.

With Joe Polchinski at the Kavli Institute for Theoretical Physics
W. Gefter

The idea behind T-duality was this. Closed strings get their energy in two ways: from their vibrations and from their winding
number. The winding number comes into play because the strings can wind themselves around a tiny, curled-up, compact dimension of space, their energy growing as they stretch with every loop around the circle. The winding number is a kind of potential energy, the taut spring of a rat trap waiting to snap. Vibrational energy is kinetic.

As you vary the size of the compact dimension, there's a trade-off between the string's vibrational energy and its winding energy. The larger the radius of the dimension, the more stretched the string and the greater its winding energy; the smaller the dimension, the more localized the string's position, which, by quantum uncertainty, means the more erratic its momentum and the greater its vibrational energy. Physics, however, doesn't care about the difference between the two forms of energy—the only observable value is the total energy of the string. There's no experiment, even in principle, that could tell the difference between a string with high vibrational energy and low winding energy and a string with low vibrational energy and high winding energy so long as they sum to the same amount. That means that there's no experiment, even in principle, that could tell the difference between a space of radius R and a space of radius 1/R. Which, when you think about it, is fucking crazy.

Size is not invariant!
I wrote in my notebook.
What's big from one perspective looks small from another.

It was a pretty mind-blowing idea. Given the radical differences between the physics of big things, like planets, and small things, like subatomic particles, you'd think—with apologies to the girl from my philosophy class—that size matters. Turns out it doesn't.

Think of what that means for the big bang
, I scrawled.
Shrink the radius of the universe small enough and eventually it starts to look bigger again. Bounce, not bang.

“Strings have a natural vibrational size, and you can imagine taking some space and you start making it smaller and smaller,” Polchinski said. “The question is, what happens when the space gets smaller than a string? T-duality shows that if you put a string in a box and you make the box smaller and smaller, what you find rather remarkably is that when the box gets smaller than the string, there's kind of another way to look at the system in which the box is getting larger again. A new
spacetime emerges. That's a slogan we have: emergent spacetime. Spacetime is not fundamental. The spacetime in the final picture is not the one you began with—it somehow emerges from the stringiness of space. But it's indistinguishable from the original, so neither one is more fundamental than the other. They are both emergent.”

“So instead of thinking of them as two different spacetimes, you can think of them as one spacetime looked at in two different ways?” I asked.

“Exactly.” He nodded. “Two ways of looking at it. It's a duality.”

It's also a fundamental difference between a world built of point particles and a world built of strings. Particles don't have winding energy, because dimensionless points have nothing to wind. According to particles, big is big and small is small. Strings, however, see geometry differently. The idea that point particles are really one-dimensional strings doesn't just change the nature of matter—it changes the nature of spacetime, too.