Trespassing on Einstein's Lawn (42 page)

Below was the multiple-choice question Wheeler had written for the reluctant Gödel.

I laughed in admiration of Wheeler's chutzpah.
Persistence will be rewarded.

Within weeks he sent a second letter, this time to Paul Cohen, a
mathematician at Stanford who had won a Fields Medal for his work in logic. In analogy to Gödel, Cohen had proven that certain mathematical statements in set theory were similarly undecidable.

“I'm winding up twenty years' involvement with gravitation physics and relativity,” Wheeler wrote to Cohen, “with the conclusion that the mystery of things lies still deeper, in the quantum principle; that the quantum principle is connected in some deep sense with logic and the calculus of propositions; that the structure of the universe is connected with our own existence in some deep Leibnizian sense; and that only when we recognize how strange the universe is will we be able to understand how simple it is. I have no special axe to grind. I am simply in search of deeper understanding. I can't help feeling that the marvelous things you have done must have some much deeper connection with the issues that puzzle me than most physicists would recognize. There was a time when the parallel axiom of Euclid seemed to be ‘merely a matter of logic.' Then came Bolyai and Lobachevsky. Then came Riemann who opened the door to Einstein and general relativity, with the most direct possible tie to physics. Similarly today, so many people think the questions of undecidability are ‘merely matters of logic.' But the good Lord, I'm afraid, didn't have the benefits of the modern university business office, with precise allocations of so much to physics, so much to mathematics, and so much to philosophy. I'm afraid he got everything all mixed up together.”

Wheeler was clearly on a mission—but why? What was he trying to find? A few pages later, his agenda became clearer. Scrawled on TWA in-flight notepaper and glued into the journal was an entry entitled “Add ‘Participant' to ‘Undecidable Propositions' to Arrive at Physics.”

“We consider the quantum principle,” he said. “Of all the well-analyzed features of physics there is none more central, and none of an origin more mysterious. This note identifies its key idea as participation; and its point of origin as the ‘undecidable propositions' of mathematical logic. On this view physics is not machinery. Logic is not oil occasionally applied to that machinery. Instead everything, physics included, derives from two parents, and is nothing but cathode-tube image of the interplay between them. One is the ‘participant.' The
other is the complex of undecidable propositions of mathematical logic. The ‘participator' assigns true-false values to appropriate ones among these propositions at his own free will. As he does so, the corresponding world unrolls upon his screen. No participator, no world! … The propositions are not propositions about anything. They are the abstract building blocks, or ‘pregeometry,' out of which ‘reality' is conceived as being built.”

I was so engrossed in the journal that I nearly fell out of my seat when the sudden banging of some kind of drum shattered the silence, flooding the library with the sound of—“Yankee Doodle”? I looked over to see a marching band in full Revolutionary War–era garb drumming past the library window. Now that we had been jolted out of Wheeler's brain and into, apparently, 1776, I figured it was a good time to break for lunch.

“I just don't get this whole Gödel thing,” I said to my father as I spooned some lobster fried rice onto my plate. “He thinks that Gödel's undecidability makes room for quantum observer-participancy. Like you have some logical proposition, ‘The electron is spin up.' Is it true or false? You need an observer outside the calculus of propositions to decide. So Wheeler's idea is that every time an observer determines the truth or falsity of a proposition, he's registering a bit of information, or rather he's
introducing
a bit of information to the world, and bit by bit we build reality. He wrote, ‘Logic as building material.' ”

“So determining whether the proposition is true or false is like collapsing the wavefunction?” my father asked.

“I guess. Undecidability requires an external observer, the same way quantum mechanics does.”

“But when it comes to the universe, you can't be an external observer. Isn't that the basic problem in combining quantum mechanics with general relativity?”

I nodded. “Yup. I don't see how undecidability helps.”

“You think Wheeler knew how it helped?”

“Not so far. So far I think he just suspects that they're two expressions of the same thing. But two expressions of a problem don't add up
to a solution. Besides, I'm not convinced that Gödelian undecidability would apply to things like electron spin. Wouldn't it only apply to propositions that observers make about themselves?”

Back in the library, I immersed myself in Wheeler's world. Page after page he agonized over the same questions, circled the same ideas, desperate for some new connection to leap out from the words. He was convinced that there was more to the Gödel business, a kind of quantum logic embodied there. It was a logic that demanded external observers to decide the internally undecidable, to lift the equations from some lifeless heap so that they might “spread their wings and fly,” an “intervention … envisaged as the quantum principle showing up in its most primitive form.” Again and again he returned to the boundary of a boundary, a clue, he was certain, to how we might build physical structure from structurelessness, using the bootstraps of a self-referential loop—a self-excited circuit carved from “airy nothingness.” “Physics,” he wrote, is “machinery to make something out of nothing.” Bit by bit, measurement by measurement, proposition by proposition, he saw that airy nothingness solidifying, and he dreamed that together we would build the world from the primordial haze from which we ourselves arose.

I was confused. The self-referential loop invoked internal observers; it was the universe looking at itself, a windowless entirety, inside with no outside, a one-sided coin. As Thorne had said, “It's self-excited in the sense that the observation comes from within the universe, not from the outside.” But Wheeler's Gödelian vision required external observers who could make sense of things from some higher level. Which was it? Inside or out?

I wasn't the only one confused. In the journal, Wheeler noted a question that a student had asked during one of his lectures: “By slightly red-headed mathematically minded student, Isn't participator himself built from physics? And so don't you have a Gödel type of situation where the system makes metamathematical statements about the system.… I answered that I would think of the abstract element of participator as outside the system. This I said to him (or someone)
is trial approach. It is not mathematical logic. It is mathematical logic plus participator. The most important test is whether it gives anything like quantum mechanics. If it does, we have a go-ahead sign; if not, we have to revise our thinking.”

He seemed to be following in the footsteps of his mentor, Bohr, in drawing a stark line between observer and observed. But at the end of the day, Wheeler knew that such a line could never be maintained.
“Elementary phenomena are impossible without the distinction between observing equipment and observed system,” he wrote, “but the line of distinction can run like a maze, so convoluted that what appears from one standpoint to be on one side and to be identified as observing apparatus, from another point of view has to be looked at as observed system.”
We form what forms us.
“Aren't we mistaken in making this separation between ‘the universe' and ‘life and mind'?” he wrote. “Shouldn't we seek ways to think of them as one?”

I glanced over at my father, who was reading intently, and I smiled. Everything was back to the way it was supposed to be, back to the way it had been in the beginning. Back to Wheeler. Back to the two of us sitting side by side reading, quietly searching for the answers to the universe.

Several pages later I discovered a newspaper article from London's
Daily Telegraph
that Wheeler had glued into the journal: “Days Are Getting Shorter.”

The next morning we settled into our usual seats in the library and dove back into Wheeler's head. Once again I found him wrestling with the role of observers in the creation of reality. He needed to know what criteria were necessary to be an “observer” and what constituted an “observation” that would be capable of rendering some bit of the airy nothingness as real.

“What we have been accustomed to call ‘physical reality' turns out to be largely a papier-mâché construction of our imagination plastered in between the solid iron pillars of our observations,” Wheeler wrote in his journal. “Those observations constitute the true reality.” But there
were questions he couldn't seem to answer: Who was the observer? And, crucially, was there just one or were there many?

“On few issues in my life have I ever been more at sea than I am now on the relative weight of the individual and the collectivity in giving ‘meaning' to existence,” Wheeler wrote. “Last night before falling asleep I could not see how anyone could doubt it is the individual who gives meaning to existence—where else except in my mind is the world I seek to explain?” But soon after, on a train ride from Rhode Island to Boston, Wheeler scrawled, “How preposterous to think that each has to invent the universe afresh. Moreover, meaning comes from interaction with others, not from ‘one consciousness alone,' whatever that would mean.”

Why drag consciousness into it at all? I wondered. Wheeler knew it was a mystical morass, and that one gap in our understanding couldn't be plugged by another. Observers, sure—but why not stick with Einsteinian observers, just reference frames, coordinate systems, rods, and clocks? After all, in the first arc of the self-excited circuit, the universe gives rise to the observer. That meant that the observer, conscious or not, had to be built out of ordinary physics, not fairy dust.

But as I read further, Wheeler's reasons for turning to consciousness became clearer. As far as he could see, it was the only solution to the problem of the second observer.

“What happens when several observers are ‘working on' the same universe?” Wheeler asked in his journal. It wasn't a minor question. It was
the
fundamental obstacle to understanding the meaning of the quantum and, in turn, existence. Wheeler was sure that the self-excited circuit was the only viable explanatory structure for existence—no tower of turtles, no fundamental ingredient left unaccounted for—but he couldn't see how to squeeze more than one observer into the circuit. It was torturing him.

Wheeler wasn't the first to point out that quantum mechanics slips into paradox the minute you introduce a second observer. The Nobel Prize–winning physicist Eugene Wigner, for one, had emphasized it with a Schrödinger's-cat-style thought experiment that became known as “Wigner's friend.” It went something like this: Inside a lab, Wigner's
friend sets up an experiment in which an atom will randomly emit a photon, producing a flash of light that leaves a spot on a photographic plate. Before Wigner's friend checks the plate for signs of a flash, quantum mechanics shows that the atom is in a superposition of having emitted a photon and not having emitted a photon. Once the friend looks at the plate, however, he sees a single outcome—the atom flashed or it didn't. Somehow his looking collapses the atom's wavefunction, transforming two possibilities into a single reality.

Wigner, meanwhile, is standing outside the lab. From his point of view, quantum mechanics shows that until his friend tells
him
the outcome of the experiment, the atom remains in a superposition of having emitted a photon and not having emitted a photon. What's more, his friend is now in a superposition of having seen a spot of light on the plate and not having seen a spot of light on the plate. Only Wigner, quantum theory says, can collapse the wavefunction by asking his friend what happened in there.

The two stories are contradictory. According to Wigner's friend, the atom's wavefunction collapsed when he looked at the plate. According to Wigner, it didn't. Instead, his friend entered a superposition correlated with the superposition of the atom, and it wasn't until Wigner spoke to his friend that
both
superpositions collapsed. Which story is right? Who is the true creator of reality, Wigner or his friend?