Trespassing on Einstein's Lawn (31 page)

Like, why was string theory so useless in the face of cosmology? Why, as Gross said, was it incapable of describing a single universe that made sense? Perhaps because the theory doesn't exist, I thought. What did they mean by that? And how dangerous were those rampant infinities? Susskind had said that they were eternal inflation's Achilles' heel, preventing physicists from calculating probabilities, undermining the entire appeal of the landscape in the first place. Gross had said that a fundamental principle was missing from string theory, from cosmology. But what kind? If the anthropic argument thrived on ignorance, what brand of wisdom was going to take it down?

As I flew back to the East Coast, I felt overwhelmed by how much more I needed to learn, but certain that I had found the right leads to follow. I needed to delve deeper into string theory, even if it didn't exist. I was itching to get back to the issues of horizons, invariance, de Sitter
space, and observer-dependence. And I couldn't wait to figure out what Susskind's horizon complementarity was all about.

I was also struck by a sudden, disturbing thought. If we really did live in an infinite multiverse, then the number of computer-simulated universes would skyrocket exponentially, and with it, the odds of our being real—whatever that meant—became infinitely negligible. In the face of a multiverse, Bostrom's little comedy routine was even more terrifying. Then again, I still wasn't convinced that there was any fundamental difference between simulation and reality, since the only view of reality that would reveal it to be a simulation would be a God's-eye view from outside reality, and reality, whatever it is, does not have an outside. Besides, the multiverse hypothesis arose as a direct consequence of the laws of physics—of eternal inflation and the string landscape—which themselves were designed to explain the universe we see around us. If the universe we see around us is a fake, then the laws of physics don't tell us anything about the “real” world beyond our simulation, the world in which the hardware lives, which might easily not include a multiverse at all, driving down our odds of being in a simulation in the first place.

My brain was starting to hurt. Were these thoughts getting me closer to ultimate reality or was I spinning in circles? And if the multiverse did exist, were there infinite copies of me thinking the same infinitely circular thoughts an infinite number of times?

Jesus, that was depressing. It was too much pressure. I couldn't stand the idea that every trivial thing that came out of my mouth was being broadcast over and over, echoing stupidly in the vast and repetitive multiverse. I suddenly understood Borges's fear of mirrors,
“that horror of the spectral duplication or multiplication of reality.” The multiverse rendered me even less authentic than did the Bostrom nightmare, because at least there I could imagine myself to be a unique, one-of-a-kind simulation, a simulation of myself. In the multiverse, I couldn't even take credit for a single word I said or wrote. It wasn't as though I would be the one true, original version of me, and the rest just carbon copies. If the multiverse was real, then I was a carbon copy, too, my thoughts mere facsimiles, my words as empty as their echoes. In an
infinite multiverse, everything I did or thought or said would bear infinite weight and at the same time mean nothing at all. “I” would be “we,” and “we” would be a dime a dozen.

I was back in the
New Scientist
office browsing the latest physics preprints on the arXiv when I spotted it, that one thing that can make any girl giggle and blush with delight: a new paper by Stephen Hawking. Written with Thomas Hertog, a young physicist at CERN, the paper promised to introduce a new approach to cosmology
“in which the histories of the universe depend on the precise question asked.”

Intrigued, I dove in. String theory, Hawking began, offers a vast landscape of universes, “but it has remained unclear what is the correct framework for cosmology in the string landscape.”
We don't have one universe that makes sense!
The problem, Hawking explained, is that string theory grew out of the S-matrix, out of the need to make sense of those weird hadron collisions. When physicists model particle collisions, they do so from the perspective of an observer standing outside the accelerator, sending two particles racing toward each other, and recording what comes out while happily ignoring all the convoluted crap in the middle. It was a bottom-up approach, one in which you know the exact initial state of the system (step one) and from that you can evolve it forward in time to predict the outcome (step three). That works great for laboratory experiments, Hawking said,
“but cosmology poses questions of a very different character.… Clearly it is not an S-matrix that is the relevant observable for these predictions, since we live in the middle of this particular experiment.” In other words, when it comes to cosmology, we
are
the convoluted crap in the middle.

From here inside step two, how are we supposed to get a handle on step one? How do we find the initial state of the universe? According to Hawking, we don't. The newborn universe's near-infinite energies and densities are fundamentally quantum mechanical. The early universe, according to Hawking, was a quantum superposition of all possible states, with no reality to call its own. So not only do we not know the exact initial state,
there is no initial state to know.

These two facts—that we are stuck in the middle of the experiment and that the universe had a quantum origin—render the S-matrix and its bottom-up philosophy useless for cosmology.

It was time to rethink the universe, Hawking said—and that meant working from the top down. It meant starting with the observer and working
backward
toward the origin of time. The top-down approach, Hawking wrote, “leads to a profoundly different view of cosmology, and the relation between cause and effect.” In this approach, “histories of the universe … depend on what is being observed, contrary to the usual idea that the universe has a unique, observer independent history.” My mind flashed back to the Davis conference, when Hawking had rained on the inflation parade, and to the clue I had scribbled in my notebook:
No observer-independent history.

I needed to find out more. I called a features editor in the London office, who, of course, had already heard the buzz about the paper. He agreed that we ought to run a big story, and, to my relief, told me to get to work.

I knew it wouldn't be easy, or even possible, to get an interview with Hawking, so I figured I'd start by calling Hertog.

“The top-down approach is a mixture of theory and our position within the universe,” Hertog told me over the phone. “It is very much a framework for cosmology from the perspective of an observer inside the universe. It is, in contrast with the bottom-up approach, most certainly not a framework from a God's-eye view.”

I asked him to take me through the details. He explained that their theory combined two key ingredients: Feynman's sum-over-histories approach to quantum mechanics and the Hartle-Hawking no-boundary proposal.

Feynman's sum-over-histories approach explained, in quantum mechanical terms, how a particle gets from here to there. That bat-shit double-slit experiment had already revealed that, when no one's looking, a photon travels multiple, mutually exclusive paths simultaneously. If I turn on a lamp, a photon travels from the bulb to my eye. Common sense tells me that it travels in a straight line, but, as usual
in physics, common sense is wrong. If I were to run the lamp-to-eye experiment many times, somehow recording the interference pattern that results on my retina, I could reconstruct the photon's travels and, according to Feynman, I would find that en route to my eye the photon had simultaneously navigated infinite paths throughout the entire universe, no matter how unlikely those paths may seem. In one it bounces off the Moon, circles the tower of London, and skims John Brockman's hat before hitting my retina. In another, it flies by the Great Pyramid, hitches a ride on an elephant, and skirts the horizon of a black hole. In still others, it laps the universe. Once. Twice. It ricochets off every mirror. It does the hokey pokey. It turns itself around.

The probability for each path takes the form of a wavefunction, and the waves' phases interfere constructively in some places and destructively in others. The most absurd routes are easily canceled out by equally absurd but oppositely aligned routes. When all interference is accounted for, the last wave standing gives a high probability for the most reasonable path: the straight line, lamp to eye.

There's just one weird mathematical trick you have to employ to get Feynman's procedure to work: you have to add the waves in imaginary time. Imaginary time isn't “pretend time”—it's a time coordinate written with an imaginary number; that is, a number multiplied by i, where i
²
= -1. And the point is, it works. Using imaginary time instead of real time yields the right probabilities for the outcomes of experiments.

In the early 1980s, Hawking and physicist Jim Hartle decided to apply Feynman's sum-over-histories approach to the universe as a whole. It was Wheeler who had first emphasized the need to treat the universe as quantum mechanical, and Hawking was one of the brave few who followed in his footsteps. Instead of adding wavefunctions that represent the paths of particles
through
the universe, Hawking and Hartle needed to add wavefunctions that represent
the universe itself
, entire cosmic histories encoded in spacetime geometry.

Here, too, the procedure required the use of imaginary time—but now it had some rather profound consequences. When it comes to cosmic time, there are usually only two options: either the universe has always existed, and so time stretches back into the eternal past, or the
universe has a beginning, and time begins at a singularity. As far as Hawking was concerned, they were both terrible options. If time is eternal, you're just stuck with it, with no hope of explaining where it came from, since it never
came
from anywhere—it just was. If it begins in a singularity, however, you're still just stuck with it, since the laws of physics break down there and lose their explanatory power.

In imaginary time, those two terrible options remain—imaginary time can extend into the eternal past or it can begin in a singularity—but there's also a third option. Imaginary time is indistinguishable from space, so it's possible that as you look back toward the universe's origin to just a Planck second after the big bang, what would have been the time dimension transforms into a spatial dimension, leaving the universe with four dimensions of space and no time at all. Where time was presumed to have begun at the singularity, a new dimension of space appears instead, and the singularity vanishes. Spacetime has no edge; it's more like the surface of a sphere: finite but unbounded. Hence the name “no-boundary.”

Hawking and Hartle realized that no-boundary cosmology was our only hope of explaining the origin of the universe
from the inside.
In a no-boundary universe, Hawking wrote,
“the universe would be completely self-contained and not affected by anything outside of itself.” No blank spots on the map, no breakdown of physics, no rift in spacetime through which something else—something external—could reach in. Just a one-sided coin, all inside, no outside.

Of course if you viewed the universe in ordinary time, the singularity would still be there, that blank spot on the map, that quantum dragon. But switch over to imaginary time and the singularity disappears, the rift heals, the world is whole again.

“This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations,” Hawking wrote in
A Brief History of Time.
“In real time, the universe has a beginning and an end at singularities that form a boundary to spacetime and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the
universe is like. But … it is meaningless to ask: which is real, ‘real' or ‘imaginary' time? It is simply a matter of which is the more useful description.”

Here's the reality test. If you can find one frame of reference in which the thing disappears, then it's not invariant. It's not real.
Imaginary time was the reference frame in which the singularity disappears. Did that mean the singularity was never real to begin with? That it's merely an artifact of perspective?

Hawking and Hartle proposed that because the universe has no outside, and therefore must be causally closed, only histories that make use of imaginary time's third option—the one in which the singularity disappears—should be included in the quantum sum. But their no-boundary proposal was still a bottom-up approach: it collected every possible history that begins in a no-boundary state and summed them to find the most probable universe.

Now Hawking and Hertog were advocating a top-down twist. Rather than starting from step one, they started from step two. They started from
today.
They started with
us.

To define step two, Hertog explained, you choose some measurements as your input—say, the universe is nearly flat, is expanding, and has a small cosmological constant. Then you work backward and consider every possible history of the universe—every history without a past boundary, that is—that could have led to our current observations. “The universe doesn't have a single history, but every possible history, each with its own probability,” Hertog said. Sum those together, letting their probability waves interfere until only one wave remains, and you've determined the history of the universe.

As Hertog talked, it began to sink in just how strange this idea was. It wasn't like they were reverse-engineering the universe to uncover its actual history. No. They were saying that the universe
had
no history—history is created the minute we make a measurement. In the present. Now. “As observers, we play an active role,” Hertog said. By making a measurement, we select out a subset of all possible histories, and from those histories a single past unfurls.