Trespassing on Einstein's Lawn (8 page)

I arrived with plenty of time to spare and snagged a table in the corner. It was too early for drinks or dinner, so the room was practically empty, only a few people scattered throughout the large space, chatting, reading magazines, and sipping icy beverages, having ducked into the darkened lounge to escape the relentless heat.

Markopoulou sauntered into the room in a long, flowing skirt and sandals. She was prettier than I had remembered from the Wheeler conference, with striking Greek features and long, shiny black hair. She seemed younger, too. She had a decade on me, but I'm not sure anyone would know it, and in her early thirties she was practically a newborn in her field. All said, she was not how you might imagine a physicist. When I told people I was into physics, they always seemed a little too surprised, and I imagined that Markopoulou knew what that was like. I smiled to myself, knowing that anyone glancing over at the two of us would assume that we were talking about boys or fashion, not the microscopic structure of spacetime. Not that I didn't enjoy talking about boys and fashion. But today it was loop quantum gravity.

I stood up to greet Markopoulou, shook her hand, and told her how great it was to finally meet in person. If she was thrown by my age, she didn't show it. She slid into the banquette alongside me and we ordered some cold drinks. After some obligatory small talk, I launched into a barrage of questions. I was sure that she would be able to tell what a rookie I was, but I didn't care. I was too excited by the prospect of learning physics straight from the mouth of a physicist. Who knew if I'd ever get the chance again?

Markopoulou explained to me the notorious obstacles involved in uniting general relativity with quantum mechanics. It was Wheeler who first took seriously the need for such unification and made the bold leap of applying quantum theory to the universe as a whole. You would think there would be no need for such a feat, since quantum theory is about tiny things, not about universes. But, as even Bohr himself acknowledged, there's no clear boundary separating the quantum world from the classical world, no state line marked by a billboard
that reads “Welcome to the non-quantum realm.” Yes, quantum mechanics requires a separation between the quantum system and its environment, observed and observer, inside and out. But the theory never tells us where to place the dividing line. The line is a moving target; it can be drawn anywhere and shifted to ever-bigger scales. If reality is quantum, then reality is quantum. It doesn't reach some scale and stop—it's quantum mechanics all the way up.

Of course, in ordinary quantum mechanics you could at least
pretend
to draw a distinction between observer and observed, arbitrarily slicing the universe in two, calling one side the classical measuring device and the other the quantum system. But when it came to the universe as a whole, you couldn't even fake the procedure. The universe, by definition, is the whole of spacetime, the complete set of everything that exists. It has no outside. No outside, no observers.

Quantum cosmology was born when Wheeler had to kill some time between flights. It was 1965 and he had a layover in North Carolina. He asked his friend and fellow physicist Bryce DeWitt, who happened to live nearby, to keep him company for a few hours at the airport. It was there that they wrote down an equation, which Wheeler called the Einstein-Schrödinger equation, everyone else came to call the Wheeler-DeWitt equation, and DeWitt himself eventually called “that damned equation.”

That damned equation was meant to solve a problem that had plagued earlier attempts to quantize general relativity. In quantum mechanics, time is always external to the system; clocks live in that murky classical realm—the “environment”—where observers reside. Wavefunctions describe the physical system at an instant of time; the wavefunction then evolves
in
time according to the Schrödinger equation. When it comes to spacetime, though, there's no such thing as spacetime
at an instant
, because spacetime contains
all
instants. And you can't have spacetime evolve
in
time, because it
is
time. The only way forward seemed to be this: break four-dimensional spacetime into three dimensions of space and one of time, then describe the spatial portion as a wavefunction that can evolve relative to the dimension you called “time.”

In this procedure, however, something crucial gets lost. The key
feature of general relativity, known as general covariance, is that there's no preferred way to slice up spacetime. All reference frames are relative to other reference frames, none more fundamental than the next. Different observers can slice up spacetime in different ways. So when we decide to quantize only the three dimensions of space, we have to choose certain coordinates to call “space” and others to call “time.” But whose space? Whose time? Making any kind of choice would suggest that one observer had a truer view of reality than all others. But that can't be so. That was Einstein's whole point:
the laws of physics must be the same for everyone.

Wheeler and DeWitt saw a way out. As long as the quantum space evolved according to their damned equation—a kind of Schrödinger equation for spacetime—general covariance would be restored, all observers would be created equal, the laws of physics would be the same for everyone, and all would be right in the quantum universe. But there was a snag in the plan. The equation required that the total energy of the universe be precisely zero.

In itself, that wasn't so strange—if the universe really came from nothing, it would have to have a total energy of zero. But quantum mechanics is never so certain. Just as position and momentum are bound together by uncertainty—the more precisely you know one, the less you know the other—so, too, are time and energy. As soon as you've specified a quantum universe's energy with exact precision, you'd better say goodbye to time.

Wheeler and DeWitt had successfully rescued the attempts to quantize spacetime, but at a cost: they ended up with a quantum universe that was frozen in time, stuck in a single, eternal instant. It was a universe in limbo—no giant clock hovering on the outskirts of reality, ticking away each second after absolute second so that we might live in a world in which time actually means something, in which anything ever changes at all.

When you think about it, it ought to have been obvious from the start that there's no possible way to have both general covariance and a universe that evolves in time—the two ideas are mutually exclusive, because for the universe as a whole to evolve in time, it must be evolving relative to a frame of reference that is outside the universe. That
frame is now a preferred frame, and you've violated general relativity. It's one or the other—you can't have an evolving universe and eat it, too.

As Markopoulou talked, it occurred to me that the very notion of “the universe as a whole” might be similarly doomed. Could you talk about “the universe as a whole” without talking about it from an impossible reference frame outside the universe?

The problem of Wheeler and DeWitt's frozen universe is intimately tied to the measurement problem in quantum mechanics. Quantum systems seem to hover in a ghostly state of almost-existence until an observer or measuring apparatus makes a measurement, thereby collapsing the wavefunction of possibilities into a single actuality. But if the quantum system is the universe itself, who can collapse the wavefunction? Again the problem comes down to the fact that no one can step outside the bounds of the universe, turn around, and look back. “That's a whole sticky thing,” Markopoulou said. “Who looks at the universe?” The cosmos is a half-dead, half-alive cat. An almost, but never an is.

Markopoulou explained that she had set out to address the problem of quantum cosmology without falling into the trap set by that damned equation, heeding Smolin's slogan that “the first principle of cosmology must be ‘There is nothing outside the universe.' ” No clocks, no observers. No God's-eye point of view. How strange, I thought, that the universe is the only object with an inside but no outside. It reminded me of a line from a Borges poem:
Obverse without a reverse
,
one-sided coin
,
the side of things …
The universe is a one-sided coin. Not quite an object, but an impossible object, like Escher's staircase or Penrose's triangle. Quantum cosmology is a science of impossible objects.

Still, Markopoulou believed there was a way forward, and it meant embracing a radically new view of things. “Any satisfactory theory of quantum cosmology has to refer to observations that can be made by observers inside the universe,” she said. “No Wheeler-DeWitt equation, no wavefunction of the universe.” By “observers,” she explained, she meant not humans or conscious creatures but simply reference frames, possible points of view. And a quantum cosmology that refers
only to the reference frames of internal observers requires us to change one thing that seems fundamentally unchangeable: logic.

You'd think logic is logic is logic, eternal and unbreakable. But if that was true, ordinary logic wouldn't need a name. It has one: Boolean. Codified in the countless “if P, then Q” statements that philosophy students around the world were memorizing as we spoke, Boolean logic is a binary logic, the logic of yes or no, 0 or 1, true or false, black or white.

But quantum cosmology needs shades of gray, Markopoulou explained, thanks to a simple yet profoundly important fact: the speed of light is finite. Whenever we observe something, light has to travel from the object to our eyes, and it doesn't happen instantaneously. It takes 186,000 miles per second. Sunlight takes eight minutes to reach the Earth—looking up at the Sun is like hopping into an eight-minute time machine. Look up at the stars and you're looking back thousands of years; grab a telescope and you can see billions of years into the past. But the point is this: there are stars whose light hasn't had enough time since the big bang to reach us yet. Wait long enough and some of it will. But with a finite speed of light, there will always be portions of the universe that we can't see.

Markopoulou explained that the slice of universe I
can
see is called my light cone—a sphere of space that grows with time, so that if you drew it in the spacetime coordinates on my father's yellow legal pad, you'd see nested spheres, swelling in diameter as they move upward along the time axis, tracing a cone. If an event is in my past light cone, I can see it; if it's not, I can't. I knew my light cone had to be pretty big, given the nearly 14 billion years of travel time that light has enjoyed since the beginning of the universe. But it still felt a little claustrophobic.

“Let's talk about an event, say a supernova explosion,” Markopoulou said. “It can have two possible values: yes or no. It happened or it didn't. That way of thinking about observables follows Boolean logic. But let's ask, is there a supernova explosion according to this particular observer? Now there are the following possibilities. If the supernova is in his past, we can say yes. Another possibility is that it's not in his past, but if he waits long enough he's going to see it. So it's ‘yes, but later.' Another possibility
is that the supernova is so far away from him that he'll never see it, so it's no. The fact that the supernova occurred doesn't matter, because the question was, did it occur
according to this observer
? So whereas before, in the old way of thinking, there were just two possible values, yes and no, now there's a whole range of possibilities.” This new kind of non-Boolean logic was called intuitionistic logic, she said—a name that made me chuckle to myself, given how counterintuitive it was. It had existed as its own kind of logic game among mathematicians, but Markopoulou was among the first to apply it to cosmology.

I started to understand the gist of what she had done that had so impressed the judges of the young researchers' competition at the Wheeler conference. She had attached tiny light cones to the atomic lattice of a quantum space, let the light cone structure determine how the network could evolve in time, applied the rules of intuitionistic logic in a mathematical form called a Heyting algebra, laid down some rules for transforming from one observer's perspective to another, and voilà—a theory of quantum cosmology that doesn't require observers or clocks to lurk beyond the bounds of space and time. It was a different kind of quantum cosmology, to be sure. It wasn't a quantum description of
the
universe; it was a quantum description of
each individual observer's
universe.

The conversation seemed to fly by, but when I checked my watch, several hours had passed. I felt guilty for taking up so much of her time, but it was my first one-on-one conversation with a physicist, and for all I knew my last, so I was hell-bent on learning everything I could. I was just glad she didn't attempt to quantum-tunnel her way out of there to escape my incessant questions. I wrapped up by asking her what she had thought of the Wheeler symposium.

“I've never been to such an open-minded meeting,” she said. “People just stood up and said what they really thought. That basically never happens. And it was all because of Johnny Wheeler. Not only did he stick to the big issues, the important problems, he also must have been very accepting of people. Oftentimes we're not so good at encouraging people to go out on a limb. The culture is to always say that something looks wrong. This is science—it's a bunch of immature boys who want to look smart.”

We laughed, then made our way out into the blazing sunlight, said goodbye, and walked off in opposite directions. I headed down into SoHo to catch the train back to Brooklyn. I couldn't wait to get in the tub and start writing.

As I walked toward the subway station, my brain was buzzing. I had already learned that both relativity and quantum mechanics were trying to tell us the same thing: we run into trouble when we try to describe physics from an impossible God's-eye view, a view from nowhere. We have to specify a reference frame, an observer. But now I finally understood the real tension between the two theories. The whole mess could be summed up with one question: where's the observer?