Trespassing on Einstein's Lawn (57 page)

“I met him again later,” Rovelli continued. “He was extraordinarily warm and friendly with me, and I can't forget his eyes. We went for a long walk. He was talking a lot, but with a very soft voice, which I could barely hear. He was continuously stopping and looking at me. I felt a lot of affection from him. The first day I arrived in Princeton, he came early in the morning to pick me up at the bed-and-breakfast where I was staying—I was still sleeping when he rang me up from the reception—to have breakfast with me. He then took me for a walk toward the Institute. We started walking in silence and then he said to me, ‘Carlo, I did this another time.' I said, ‘What?' He said, ‘Coming to pick up somebody early for breakfast and walk him for the first time toward the Institute.' I looked at him, and he said, ‘It was Albert Einstein, when he escaped the Nazis and arrived here. I received him, like I receive you today.' He was like that, always emphatic, but always capable of touching you deeply. He showed me the rooms where he first discussed the atomic bomb and where he talked to Einstein about writing to Roosevelt.… Sorry for getting lost in these memories. John has always been my hero, and you can imagine how I felt, as a young man, when my hero wrote to me a letter full of compliments. I keep all his sweet cards. The last one of these is dated '95, which is when I
wrote the first relational paper. It says: ‘Dear Carlo, continuing pleasure that you exist in this puzzling world of ours. Warm good wishes, John.' ”

My eyes welled up as Rovelli recounted his times with Wheeler. I worried that if we talked much more about him I'd start sobbing into the phone like a weirdo, so I changed the topic.

“It seems like in relational quantum mechanics it must be impossible for observers to measure themselves,” I said.

“It's a fascinating point,” Rovelli replied. “It has enormously raised my curiosity, and I've spoken with philosophers who were interested in that. I've never come to total clarity about it. Indeed, the whole relational view is somehow related to the impossibility of total self-measurement. The entire structure of quantum mechanics tells us that our information is always limited. The quantum mechanical world is intrinsically probabilistic; we only have partial information about things. Formally, if an observer could measure himself completely he could violate quantum mechanics. But I can't articulate that. It's something I find fascinating, though.”

“There seem to be hints of a relationship to Gödel's incompleteness,” I suggested.

“Yes,” he said. “Absolutely. I just haven't been able to work it out.”

Wheeler hadn't been able to work it out, either, the whole Gödel business. He had sensed a profound connection between propositional logic, self-reference, and quantum mechanics. In his mind, determining the truth-value of a proposition, such as
Snow is white
or
My pants are on fire
, was akin to collapsing a quantum wavefunction. In his vision, if all observers—all who had ever lived, were living, would live—collectively assigned values to enough Boolean yes/no propositions, together we could build the universe. But the flaw in Wheeler's plan was becoming ever clearer: there is no collective universe. My pants may not be on fire relative to me, but they could well be on fire relative to some other point of view. As Rovelli had so elegantly demonstrated, wavefunction collapse, along with the truth-value of a proposition, was observer-dependent. Wheeler wanted co-authorship, but reality wasn't
having it. When he drew his U-diagram, Wheeler had assumed that the giant eye looking back at itself was a stand-in for a multitude of eyes, for countless observers all gazing at one and the same universe. A giant eye for a God's eye, one that encompassed every possible reference frame simultaneously. But if I had learned anything from black hole physics, horizon complementarity, top-down cosmology, the firewall paradox, and now relational quantum mechanics, it was this: there's just one eye. One eye per universe, with the cardinal rule that you can't talk about more than one at a time. Either you were in Safe's reference frame or you were in Screwed's. Mine or my father's. Observers could never see across more than one reference frame. If they could, physics would break down. Wheeler knew that this was a participatory universe—he just thought there could be more than one participant at a time. For a man who was on a mission to go everywhere, talk to everyone, and ask anything, nothing was worse than the specter of solipsism: one man (one worm, one rock), one universe.

“The Einstein-Rosen-Podolsky ‘experiment' is valuable among other reasons because it shows
two
observers participating in the making of reality,” Wheeler had written in one of his journals. “We are not concerned, as some are, with turning back from quantum mechanics, but with going on, to two or more observers, two and more ‘systems,' two and more observations, ultimately to see how the iron pillars and papier mâché are combined to make reality. What does the EPR experiment show?”

Rovelli had the answer: the EPR experiment showed that there's no single reality shared by all observers. Everyone's stuck having to papier-mâché a world for himself.

Wheeler knew that Gödel's incompleteness theorem was hiding something, some clue to understanding quantum mechanics and the universe, but he was looking in the wrong place: on the outside. Even Gödel himself had made the same mistake. He wasn't particularly distraught over incompleteness, because he was pretty sure that we could decide the undecidable from here, outside mathematics. Statements like “This statement can't be proven by this mathematical system” were undecidable from within the system, but looking down on it from the outside, we could still claim it to be true. Only that claim couldn't
be a mathematical claim—you can't be doing mathematics outside mathematics. It had to be something else. Something flimsier. Something like “intuition.” Intuition, Gödel said, was a valid enough decider of truth and falsity. Like Wheeler, he was hopeful that we could always impose truth-values from the outside; he believed in the power of the human mind to compensate for the deficits of our mathematical systems. Then again, he also starved himself to death because he was convinced his food was being poisoned, so he wasn't exactly the epitome of optimism.

Everything I had learned about physics led me to my own intuition: there is no outside. You can't step outside mathematics, the universe, or reality. They are one-sided coins.

Wheeler knew that the universe was a one-sided coin, but he wanted to flip it all the same. The tension he saw between the individual and the collective, the inside and the outside, the self-excited circuit and the Gödelian observer knocking at the door was
the
tension, the
ultimate
tension, which sat deep in reality's core, the buried heart of physics, a dense, gnarled pit that bore the universe's impossible form. Quantum mechanics needed external observers to collapse wavefunctions, but general relativity did away with external observers. Quantum gravity had to resolve that paradox while obeying Smolin's slogan:
The first principle of cosmology must be “There is nothing outside the universe.”

How else could an impossible object come to exist but from within its very own architecture? Where else but inside could the seed of creation lie for an object with no outside? The universe
had
to be a self-excited circuit, the spark of creation igniting in its belly, existence that hoists itself into being by its bootstraps. If observership was a prerequisite for existence, then the universe had no choice but to observe itself.

I thought back to what my father had said all those years ago:
There's something about reality you need to know. You think there's you, and then there's everything else outside you, but it's all just one thing.
We like to think of ourselves as standing apart from the world, from nature, interlopers who mysteriously awoke one day to find ourselves in a universe that is something other than us. But we are pieces of the universe,
fleeting patterns that the universe momentarily indulges, then dissipates. We are, as Wheeler envisioned, the universe looking at itself. How are we to hold a mirror to ourselves when we ourselves are the mirror?

We are stuck inside the universe—which means we can't give a consistent description of the universe without also describing ourselves. But Gödel's theorem showed that self-referential statements can't be proven from within the system that's stating them. What, then, of cosmology's self-referential statements? “Within” is all we have. They simply can't be proven. In physics, “proven” means “measured,” and measurements are about gathering information. The Gödelian incompleteness of the universe seemed to place fundamental limits on the amount of information we can access. If self-referential statements can't be proven by physical measurements, then observers can't measure themselves.

As Rovelli had confirmed for me, “the whole relational view [of quantum mechanics] is somehow related to the impossibility of total self-measurement. The entire structure of quantum mechanics tells us that our information is always limited.” He wasn't the only one. Bousso had said as much when describing the failure of the S-matrix to describe cosmology: he called it part and parcel of
“the more general problem that arises whenever one part of a closed system measures another part.… Obviously the apparatus must have at least as many degrees of freedom as the system whose quantum state it attempts to establish.” Indeed, the philosopher of science Thomas Breuer used a Gödelian argument to prove that
“no observer can obtain or store information sufficient to distinguish all states of a system in which he is contained.”

If an elephant could measure itself, collapsing its own wavefunction, then it needn't exist relative to anything outside itself—in other words, it would simply, inherently exist. It wouldn't be observer-dependent. It would just
be.
In an act of self-affirmation or quite possibly suicide, Schrödinger's cat would collapse its own wavefunction before anyone opened the box. But quantum mechanics—through the uncertainty relations, complementarity, EPR—has already proven that if we assume that elephants inherently exist in some objective, observer-independent way,
we get the wrong answers.

By relativizing everything, Rovelli had rejected any kind of ontological distinction between observer and observed, leveling the playing field to a quantum monism where every perspective is a possible reference frame, none of them any better than the next. That did away with the seeming paradox that an observer can't be a subject and object simultaneously, and yet somehow the observer is a subject and object simultaneously. I am the subject
relative to me.
I am an object
relative to my father.
There's no God's-eye view from which both would appear true at the same time. But again, that hinged on the impossibility of self-measurement. If I could measure myself, I'd be both subject and object and quantum physics would fall apart. The prohibition on self-measurement upheld Wittgenstein's intuition that “the subject does not belong to the world: rather, it is a limit of the world.”

Rovelli had shown that quantum mechanics seems bat-shit crazy as long as we assume the existence of a single reality shared by multiple observers. Give up that notion and all the quantum weirdness begins to make perfect, non-spooky sense. We can dissolve the problem of the second observer by embracing the cosmic solipsism that physics demands. It's not the brand of solipsism that Everett or Wigner momentarily considered, in which there is just one absolute observer. The solipsism that radical observer-dependence implies is itself observer-dependent—as Rovelli emphasized, observer in one frame is observed in another.

But that's only true if observers can't measure themselves. If they could, quantum states would be absolute, global logic would be Boolean, interference patterns would disappear, quantum monism would splinter into a dangerous dualism, Ladyman's realism would give way to Einstein's, the moon would hold steady in an invariant sky, and my father and I would hang our heads in defeat, because we would in fact be working on the same universe, one that is something, not nothing, something whose existence would forever go unexplained. Thank God for Gödel.

Everyone had always taken Gödel's theorem to be a deeply pessimistic statement about the limits of knowledge. But in a universe that
is
nothing, limits are exactly what we need.

I had already learned the implications of limited viewpoints when
it came to horizons—horizons mark the edges of an observer's reference frame, and the area of the horizon is a measure of how much information that observer can ever access. Now I saw that the self-referentiality inherent in a universe that contains its observers on the inside also limited an observer's information—it was a kind of logical horizon. Was our positive cosmological constant—our de Sitter horizon—some kind of physical manifestation of a Gödelian incompleteness?

How interesting, I thought, that the shift from invariance to observer-dependence always seemed to be sparked by the discovery that some feature of nature long thought to be infinite, or perhaps zero, was actually finite. In relativity, the finite speed of light, long believed to be infinite, rendered space and time observer-dependent. In quantum theory, Planck's finite constant was long held to be zero; it rendered all physical features connected by uncertainty relations observer-dependent. Most recently, the discovery that the entropy of a region of spacetime, which everyone had assumed to be infinite, was actually finite, made spacetime itself observer-dependent. The speed of light, Planck's constant, entropy—they all represented nature's most fundamental limits. The limits were the clues. If we could find the limits, we could find reality. Or the lack thereof.

Wheeler believed that information, binary bits related by the logical rules of the calculus of propositions, were the atoms that constituted reality. “Logic as building material,” he had scrawled. But logic had turned out to be observer-dependent—“yes” in one reference frame looked like “no” in another. Back in the lounge at the Tribeca Grand, Fotini Markopoulou had told me that we needed to use non-Boolean logic—observer-dependent logic—to account for the fact that each observer has only partial information. Boolean logic was just the ordinary logic we usually assume holds true, with its basic rules, like if
p
is true then not-
p
is false, or if
p
implies
q
and
p
is true then
q
is true. There was also the crucial law of the excluded middle: a proposition,
p
, is either true or false; there's no third option. Non-Boolean logic—
quantum
logic—openly defies the law of the excluded middle. A proposition
p
can be true
and
false, depending on who you ask.