Trespassing on Einstein's Lawn (58 page)

But I now saw that logic becomes non-Boolean only when you
compare
the perspectives of two or more observers. According to any one observer,
p
is either true or false. We only violate the law of the excluded middle when we try to view
p
from more than one reference frame at the same time. Classical logic tells us that the particle passed through one slit or the other. Non-Boolean logic offers a third option: it went through both. But the point is, there's no observer who can see it go through both. That would require an impossible God's-eye view, akin to seeing inside and outside a black hole's horizon.
No observer sees both elephants.
Look at the slits and you'll see that it only goes through one.
The phrase “both elephants” is totally misleading.
Statements such as “The photon travels two paths simultaneously” are wrong. They assume there's some singular reality, a way things “actually are.” There isn't. Nature has shown us otherwise. Here is what we know: when we compare two possible perspectives of the photon's path, mistakenly assuming a singular reality that both perspectives share, it
looks
as though the photon travels two paths simultaneously. It
looks
as though logic is non-Boolean.

We never see simultaneously-alive-and-dead cats because superpositions represent a multiplicity of points of view, and, by definition, a given observer has only one. Superpositions reek of a God's-eye view. We see
evidence
of superpositions in interference patterns, but interference patterns, as Rovelli said, are comparisons of multiple reference frames. And the key thing, I now realized, was that if reality weren't observer-dependent, we wouldn't see interference. Every perspective would be equivalent; you could map one onto the next, each proposition value lining up perfectly with the others, true on true, false on false, in the same way that perspectives line up in Susskind's FRW universe, straight line on straight line, an alignment that signals invariance and ultimate reality. If, however, reality is radically observer-dependent—if, that is, the universe
is
nothing, then we
need
interference to literally cancel out the disagreements between our perspectives. Interference—the physical manifestation of non-Boolean logic—exists because nothing is real. Or because reality is nothing. With this “many frames” interpretation of quantum mechanics, that bat-shit experiment was actually starting to make sense.

Logic had to be non-Boolean for the same reason that gravity exists.
It was like a logical gauge force. In general relativity, every observer's local patch of spacetime is flat, but when you try to stitch together many local patches, they don't always line up properly and you end up with a warped spacetime that gives rise to the force of gravity. Likewise, when it came to quantum measurements, each individual observer's local logic was Boolean—logic became non-Boolean only when you tried to piece one reference frame together with other points of view to form a single reality. The truth-values of propositions don't match up. Just as gravity exists to account for why an inertial observer appears to be accelerating from another point of view, quantum interference exists to account for why a true proposition appears false from another point of view. Stitched together, the local logics create a warped logical space. Non-Boolean logic is a fictitious logic.

Proposition:
Snow is white.
Truth-value according to me: yes. Truth-value according to some other guy:
no.
In the old-school Boolean view of the world, our mismatched information spelled catastrophe. But physics is now telling us that we can't talk about both truth assignments at once. They are noncommuting gauge copies, two quantum-mechanics-violating clones of the same elephant, two different its from the same bits. As Susskind had said, it all came down to the misuse of the word and. Not yes and no—yes
or
no.
“Quantum gravity may not admit a single, objective, and complete description of the universe,” Bousso had written. “Rather, its laws may have to be formulated with reference to an observer—no more than one at a time.” Pick a reference frame. Pick a local Boolean algebra. Pick an eye.

And really, wasn't that what quantum mechanics was trying to tell us all along? Like the uncertainty principle. We can't assign precise values to both position and momentum or to both time and energy simultaneously. And what did “simultaneously” mean?
Within a single reference frame.

Bohr and Heisenberg knew all that. They knew that the values of complementary features were relative to the measuring apparatus. Where they went wrong was in thinking that once a feature was measured and its wavefunction was collapsed, its value was then fixed for all observers everywhere. The only way to make that work would be to
consider the observer some special thing standing outside the laws of physics. That's exactly what Bohr did, and Wheeler tried to follow in his footsteps. But nagging in the back of his mind, Wheeler knew it wouldn't hold up:
Elementary phenomena are impossible without the distinction between observing equipment and observed system, but the line of distinction can run like a maze, so convoluted that what appears from one standpoint to be on one's side and to be identified as observing apparatus, from another point of view has to be looked at as observed system.
It was Rovelli who finally found the way through the maze. Indeed, all observers are, from some other reference frame, the observed. Reality is radically observer-dependent.

Einstein's spooky action-at-a-distance was spooky precisely because it was derived from a view from nowhere. And Einstein, of all people, should have known better. He thought that entanglement undermined locality, light's ultimate speed limit. But what
really
undermined locality was the reference frame he was using—one that simultaneously encompassed two light cones. Of course, it probably didn't occur to him to worry about describing physics across light cones because, even though he himself had discovered that space and time change from one frame to the next, he still believed that some basic features of reality were invariant. If he had been right—if an electron's spin was always up for all possible observers—then his God's-eye view wouldn't have caused any trouble. But it did cause trouble.
Spooky
trouble. The problem wasn't with locality. It was with reality. Despite Einstein's weirdly uncharacteristic commitment to old-school realism, the basic features of reality were
not
invariant. They were observer-dependent. If you tried to describe them from a God's-eye view, you'd get the wrong answer.

I knew that Einstein had talked a big realist game, but seriously? It hadn't occurred to him—to
Einstein
—that some seemingly invariant things might turn out to be relative?
Relativity?
Really? That hadn't rung a bell?

I needed to gather my thoughts, piece together these disparate strands, so I hopped on a train bound for Philadelphia.

When I rang the bell at my parents' house, I was greeted by a thick silence. No barking, no whimpering, no thump of a tail. At eleven years old, Cassidy had developed a tumor in her leg, which had swelled to the size of a grapefruit. Like a trouper she had held that leg in the air for nearly a year, until the pain became too much. The vet informed us that amputation would be difficult and wouldn't buy much time. My mother was the only observer in the room when the universe relative to Cassidy came to an end. My father placed her bowl and her chain on his desk. I cried into the phone when they told me the news. The knowledge that everything was an illusion was hardly a comfort. She was the sweetest illusion I had ever known.

Inside, I was eager to look back to the beginning, to the H-state, to try to make sense of things. “Didn't you keep some notebooks back when we first started working on this?” I asked my father.

“I think they're in one of the cabinets in the library,” my father said. “You're welcome to try to find them.”

In the library, countless stacks of books barricaded the cabinet doors. I rolled up my sleeves and began moving them, piling them on the couch and on rare patches of bookless floor. The stacks encoded a chronology of my father's intellectual interests, like rings in a tree. In front were more recent acquisitions: books on cosmology and quantum gravity. Behind them were relativity and quantum mechanics, followed by astrophysics and astronomy. When I finally reached the last stacks, the books were more diverse: a biography of Einstein, Schrödinger's
What Is Life?
, a compilation of Bob Dylan lyrics. There were a few books by the philosopher Alan Watts, including one entitled
The Way of Zen.

I flipped through the yellowed pages. My father had once told me that when he was a teenager on summer vacation, he was lying on a hammock in the backyard of his family home, not two miles from the home in which he and my mother would later raise me, reading
The Way of Zen.
“The book was talking about the illusion of the ego,” my father had told me, “and the duality of subject and object. I was totally blown away by this idea, which was so simple and yet so profound. It had such an effect on me that I became hyperaware of everything around me. I was so in the moment. And then a bee landed on the page
and pooped on it and then flew away. So I circled the stain on the page and wrote in the margin, ‘A bee pooped here.' ”

When he told me that story, I found myself wondering what I would have done if a bee had shat on my teenage reading, which was pretty much the opposite of everything Zen. Most likely I would have circled the stain in my Sartre and written, “Figures.” But the funny thing is, unbeknownst to my father, when I had snuck out of this house to get my first tattoo at the age of fourteen, I had, amidst my existentialism and angst, gotten a tattoo of the Chinese character for
Zen
, which looked like a little Hawaiian man carrying a tiki torch on my hip, because even though I was rebelling, I really just wanted to be like my father, to have the kind of subterranean wisdom I saw lurking behind his eyes, which were large and brown and sloped downward at the edges so that he appeared perpetually sleepy or stoned, eyes I had inherited from him and regarded not as mere genetic facsimile but as a secret handshake. It was his Zen-like thinking that led my father to his epiphany, the H-state, a way of thinking about nothing that made it the ontological equal of everything, and it was his H-state that led me to tell a little lie, and to dream up a life, and a book, and a universe.

I placed the book down gently, careful not to disturb any sentimental excrement. I moved some Buddhist texts, a philosophy of space and time, a collection of poems by William Carlos Williams. Williams, I remembered, was my father's favorite poet, maybe because of the surreal and Zen-like quality of his work—
So much depends on a piece of bee shit
—or maybe because he, too, had been a doctor at the University of Pennsylvania and because he, too, had gone home at night to live another life, one man writing poetry, the other tracking down the secret of the universe, which I suppose was really the same thing.

When I finally managed to open the cabinet doors, I spotted the stack of hardbound notebooks. I carried them into my old bedroom and sprawled out on the bed to read.

My father had filled perhaps a quarter of each of the notebooks, leaving the remainder blank and then inexplicably starting a new one. Every entry expounded on the meaning of the H-state and agonized over the same, infuriating question: why would it ever change?

“Everything and nothing are simply dualities which, in their extreme,
become one and the same.… Both everything and nothing are co-embedded in the H-state. So for everything to ‘appear' out of nothing is not a big conceptual leap. But how did it change from a featureless ‘void' to an inhomogeneous feature-full universe of ‘things'?

“Everything, including time, space, energy, and matter, is simply an expression of what appear to be changing faces of the H-state, but which ultimately never changes,” he wrote elsewhere. “How can it? It is by definition perfect homogeneity and thus without change.”

Eventually my father pieced together an answer. “We can turn to three different well-established laws of nature to explain this. In fact, it so well follows as a consequence of each of these laws that for the h-state not to have expressed itself in forms would have been a violation of our basic scientific principles.”

The first was the second law of thermodynamics. The H-state, he wrote, having only one unique configuration, has zero entropy, which, by the second law, is compelled to increase. At the same time, being maximally homogeneous, the H-state has infinite entropy. “The H-state is both ultimate order and disorder, and neither! It is a merging of the two. Thus ultimate order and disorder are the same! The universe must derive from the H-state and ultimately ‘return' to it.”

The second arbiter of change was symmetry breaking. “The H-state, in its perfect homogeneity, has by definition perfect symmetry. A perfectly symmetric state is perfectly unstable.… Physicists have come to understand that the features of our world are manifestations of broken symmetries. In fact, all of our conservation laws, such as the conservation of energy, angular rotation, etc., are themselves expressions of underlying symmetries. But if everything is derived from broken symmetry, all must originate from perfect symmetry: the H-state.”

The third piece of the puzzle was quantum mechanics, my father wrote. According to the laws of quantum mechanics, “nothing in the universe can have a perfectly defined energy level. So with the H-state. Uncertainty demands that the H-state give up its homogeneity.” Quantum fluctuations, he said, “create intrinsic oscillations that form the basis of ‘thingness,' like a wheel must rotate around a motionless hub.

“Since all is perfectly the same,” he noted, “one cannot specify a location or time within the H-state. There are no locations; all locations
are the same. There is no time; all instants are the same. Nothing changes, neither spatially nor temporally nor in any other dimension. But all of our fundamental laws of nature dictate that such a state cannot persist. It is unstable. The laws of thermodynamics, symmetry breaking, and quantum mechanics prescribe the transformation of the H-state, from nothing to something. Since there are no places or times within the H-state, the change will happen at all places and all times. You could say that the origin of the universe comes from a point, but it is infinite in size.… Homogeneity is ultimate reality. Patterns are conventional reality.… Nothingness cannot exist. It is unstable.”