Trespassing on Einstein's Lawn (44 page)

Two years later, Wheeler wrote, “Hawking, Unruh says
observer
determines number of particles around a black hole,” but left it at that. A few months after that he scribbled, “Clear up: are Hawking particles a math[ematical] artifact?”

In a later journal, from 1990, I stumbled on an entry that read, “Think again about this horizon business. It seems to me I rang Bill Unruh already once about this question in the last 3 mos. If I remember his answer correctly, he feels much surer about the acceleration side of life than the horizon aspect. I remember—in perhaps important connection with this issue—Bill Unruh's Santa Fe talk re ‘there's no such thing as a particle' … Ring him now!”

Still, Wheeler never did go too far into the horizon business—maybe, I thought, because it only served to further fracture the world into a multiplicity of incommensurable viewpoints, while Wheeler was there trying his damnedest to bring it all together. “Not a word or a thought that we consider ‘ours' did not come from someone else or at someone's push,” he wrote. The universe—the
one
universe—is “an enormous construction we all have a part in.”

He never went for the string theory business, either. During a conference in Santa Fe in June 1989, Wheeler wrote, “Murray Gell-Mann … said, ‘You ought to learn string theory. It has everything you want.' I said, it's nothing but turtles; no place for observer-participancy. It real, ‘observer' a delusion? Just the other way around … All this talk about an external world—
that's
what's theory!”

That night, lying in bed in the bedroom where I had grown up, I thought more about the inside/outside problem, the problem of the second observer. The first principle of cosmology must be that there is nothing outside the universe, but a universe that contains its own observers on the inside is marred by pathological self-reference, since any observer who describes the universe has to include himself in the description, the kind of self-reference that Gödel had shown would lead to inherent uncertainty, the truth-values of propositions left hanging in the wind.

He wasn't the only one. In 1936, five years after Gödel had proven his incompleteness theorem and nine years after Heisenberg had discovered the uncertainty principle, Alfred Tarski, the Polish logician, had shown that any language capable of making self-referential statements couldn't assess the truth of its own sentences. That same year,
Alan Turing, the father of computer science, had shown that computer programs cannot determine whether they will run for a finite or infinite time—that is, computer programs, and presumably human minds, cannot calculate themselves. Amid a spate of such discoveries, scientists, philosophers, logicians, and mathematicians were confronted again and again with the same stark lesson: self-reference leads to limits that you can transcend only by stepping outside the system.

“Call observer, or data that can be got from the proposition, on one side; and ‘observed' on other side,” Wheeler wrote in his journal. “Can add more axioms or enlarge system, decide all in original, but then a new and larger region of undecidable, uncoordinatizable, outside the system. Always have this ‘uncertainty.' Always the same—can't decide true or false values from the inside.”

In this “uncertainty” Wheeler had glimpsed the essence of quantum mechanics, and it convinced him that Bohr's requirement that the observer be outside the system had to be obeyed at all costs. The problem was that Bohr's picture falls apart as soon as a second observer comes along and observes the first. When Wigner approaches, Bohr's external observer is suddenly internal to the very system he thought he was viewing from the outside. The observer becomes the observed. How can someone be simultaneously standing outside the system causing wavefunctions to collapse and internal to the system suspended in superposition? Both stories couldn't be true, and yet here we are, trapped inside the universe, where you can always find a second observer who sees us as part of the system inside. We are, as Wheeler's U-drawing showed, the universe looking at itself. It seems impossible, then, to apply quantum mechanics to the whole universe without spiraling into strange loops of self-reference and recursion.

I thought back to my teenage nights in this room, reading the existentialists in search of some justification for my angst. I remembered reading Sartre's
Being and Nothingness
, a book I had scored in the used-book store where I worked after school. Sartre had described the feeling you get the moment you realize that someone is watching you. What was it? Shame? Vertigo? Nausea? That sudden shift in reality as you are transformed from subject to object. Sartre would have been
really
nauseated if he had thought about quantum mechanics. Not only do you shift from subject to object, you also go from creating reality out of papier-mâché to hovering in some kind of feline purgatory.

It came down to the same inside/outside question I had confronted back at the Tribeca Grand, the problem of quantum gravity: where's the observer? Restated: quantum mechanics
forbids
us from being both subject and object, and being on the inside of a one-sided universe
requires
us to be both subject and object. And, really, aren't we? My father was a character in my story, and I was a character in his. Subject in one reference frame is object in another.

Then again, Susskind had taught me that physics only makes sense when you talk about one reference frame at a time—at least when event horizons are involved. Safe or Screwed. Accelerated or inertial. Did something similar apply here? Maybe quantum mechanics doesn't allow me to talk about my father's and my stories at the same time. Maybe neither of us could be subject and object simultaneously. Was that the solution to the problem of the second observer—to only talk about one observer at a time? But how then do you piece together our splintered stories into some single arena we call the universe? Moving from the single observer's reference frame to the global, God's-eye view seemed to lead inevitably to the overcounting of elephants, and to wavefunctions that both had and had not collapsed. “Properly to draw together the local and the large scale was one of the greatest of Einstein's tasks,” Wheeler wrote. “Here how do we draw together the ‘local' yes-no and the global ‘all there is'?”

And if there is no “global all there is”? If there is no universe? “The number one issue: Is everything nothingness?” Wheeler wrote. He had said he was prepared to question the very term
universe
, and I was feeling like I ought to prepare myself, too.

“Something of an information-theoretic character is at the bottom of physics, spacetime, existence itself,” Wheeler wrote on April 19, 1986. “This is a quick sentence, if anyone asks me for a last word before I leave this Earth.” He was en route to the hospital for heart surgery.

I couldn't help wondering what my quick sentence would be, should I need one.
What's real is what's invariant.
No, that was too simple.
Nothingness is a state of infinite, unbounded homogeneity.
I couldn't use that; it was my father's line.
The first principle of cosmology must be …
Jesus, I couldn't come up with one original thing to say for my last sentence on Earth?

Wheeler survived the surgery and continued on with his “lovely, lonely search,” but he was more poignantly aware than ever of those increasingly shorter days, torn between his need to solve the mystery of existence before it was too late and his fear that he was ruining his reputation in the process. “Darwin wouldn't, Bohr wouldn't, Newton wouldn't
expose
his half-baked ideas so widely as I do,” he wrote on March 6, 1987. “Yet I do it
anyway.
I see no way except
dialog
to get on with the job of clarification. And I don't have forever, nor do I see who will take up the work when I'm gone.”

Reading John Wheeler's journals at the American Philosophical Society library
A. Gefter

August 16, 1988: “I need to be tortured into ‘confessing' a really great and simple idea. Ha! Not
an
idea.
The
idea. And stop talking about how someone somehow sometime is
going
to find this idea. Keep quiet, talk quietly with those who can help, get busy and
find
this idea.”

“Life expectancy of the order of 3 to 5 years,” he noted later that month. “I consider my biggest commitment of all to be this greatest of all puzzles that we see around us every day, all that is, existence: how come? … I am not I unless I continue to hammer at that nut. Stop and I become a shrunken old man. Continue and I have a gleam in my eye.”

Days of reading and fourteen years later, Wheeler was still at it, still gleaming. In an entry dated March 8, 2002, he wrote, “Still agonizing over what shall I say at next week's Templeton Conference.”

“Oh my God, look!” I nudged my father, showing him the page. “It's the conference we crashed!”

“I'm still trying to develop the theme of it from bit,” Wheeler continued. “Nothing! How inject
us
into that nothingness? A question of philosophy? But maybe philosophy is too important to be left to the philosophers.”

I eagerly turned to the following entry, excited to read his postconference impressions and hoping, just a little, for some mention of an adorable young girl and her father and the penetrating questions they asked. He didn't. Strangely, he never wrote about the conference at all.

“I think I finally get it!” my father said excitedly when I walked into the kitchen. “The boundary of a boundary!”

My mother had gone to bed, so the two of us poured some coffee and set up shop at the kitchen table.

“Something to do with conservation of energy and momentum?” I asked. I had caught glimpses of it in the journals but was still struggling to understand.

“Exactly. Wheeler showed that the equations of general relativity
follow from the requirement that the boundary of a boundary is zero. The local curvature of spacetime cancels out the energy and momentum of the mass that's present there. That's why mass curves spacetime.”

“So it all adds up to zero?”

“In any local region. But the calculation only works out if the boundary of the region doesn't have any exposed edges. As long as the boundary of the boundary is closed, everything cancels out.”

He broke out a yellow legal pad and sketched the geometry, showing me how a four-dimensional region would be bounded by three-dimensional cubes whose own boundaries were two-dimensional faces, each sharing its edges with the adjacent faces to create a closed manifold. Adding up the currents of momentum-energy passing through the faces required counting each edge twice, once for each face of which it was a part, counting once as positive and once as negative and summing to a perfect zilch. Curvature manifested as distortions in the geometry of the faces, their opposite edges veering toward or away from one another, no longer parallel, tugged on by adjacent faces, the entire boundary warped and distorted by the presence of the mass. It was all rather technical, but the point was simple enough: most of the complicated structure of four-dimensional spacetime seemed ultimately to be rooted in nothing.

“In the journal he says that not only general relativity but all the quantum field theories are based on the boundary-of-a-boundary principle,” I said. “All the gauge theories.”

“Right. It's a universal thing. It's the basis for the way fields respond to masses or charges.”

That the boundary of a boundary is zero meant that everything you needed to know about what was going on in the interior of some region of spacetime could be read directly off its boundary without ever looking inside. “Outside reveals inside,” Wheeler had written. The conservation of momentum and energy could be read from the faces, the amount of mass inside deduced from their warped edges.

“That's what he meant when he compared it to elasticity,” my father said. “To calculate the elastic forces on some deformed body you only need to calculate what's going on at the surface. Everything inside cancels out.”

“He wrote something about that, hang on,” I said, sifting through my notes. “Here. In 1973 he wrote, ‘Elasticity is the lowest form of physics one can have without having no physics at all. Deals only with “the surface of things.” Want to argue that electromagnetism and gravitation are of the same breed of cats, except that they may not require any dimensionality at all.' ”

No dimensionality? The surface of things? Outside reveals inside? Was the boundary-of-a-boundary principle an early sign of the holographic principle at work?

My father knew exactly what I was thinking. “Sounds a bit holographic, huh?”

In one entry Wheeler had written, “One looks forward to the ‘dimensionality' of space (or better the ‘average effective dimensionality') as being determined out of basic theory in terms of a simpler basic substrate, pregeometry, which itself has no such property as dimensionality.” In another, “Ask if every law can be put in the ∂∂ ≡ 0 form. How come many dim[ensions] can be reduced to so few?”