Trespassing on Einstein's Lawn (38 page)

“So much for claims that string theory is untestable,” I said.

“Is that testing string theory?” Susskind asked. “I think so.”

It had to be a little vindicating for him, I thought, how it had all come full circle. After all, Susskind had originally invented string theory to describe hadrons, particles made of quarks and gluons. Later everyone realized the theory was actually describing things with much higher energies. But as it turned out, Susskind was right after all. String theory
does
describe hadrons—only in ten dimensions and a radically different spacetime geometry.

“And this duality between black holes and the quark-gluon plasma convinced physicists that information can't be lost?” I asked.

Yes, Susskind said. Everyone knew that information couldn't be lost in a hot gas of ordinary particles—that was just basic quantum mechanics. If a quark-gluon plasma was dual to a black hole—if they were two different descriptions of the very same thing—then a black hole couldn't lose information, either. Hawking admitted he had been wrong. Susskind won their thirty-year battle.

“But we don't live in an AdS universe,” I said to Susskind. “Our universe is de Sitter. AdS/CFT was enough to change Hawking's mind?”

“It was,” Susskind said. “The opposition, including Hawking, had to give up. It was so mathematically precise that for most practical purposes all theoretical physicists came to the conclusion that the holographic principle, complementarity, and the conservation of information would have to be true. It was the nail in the coffin of information loss.”

It was also the nail in the coffin of dimensionality's invariance. I could finally put my finger on what it was that had bugged me about the dimensional reduction of black hole entropy: it meant dimensionality wasn't ultimately real. The holographic principle, and specifically AdS/CFT, showed that two descriptions of the same exact physics could have different numbers of dimensions. The two descriptions were mathematically equivalent. As an ontic structural realist, I knew that neither description could be considered the “real” one; the only thing that was real was their mathematical relationship. Dimensionality wasn't invariant. It wasn't an ingredient of ultimate reality.

Neither were strings. AdS/CFT showed that strings were nothing
more than ordinary particles viewed in a higher-dimensional warped space. If the particles on the boundary and the strings in the bulk could be perfectly mapped to one another, there was no genuine difference between them. Particles, strings … they were just two ways of looking at the same thing.

Once the AdS/CFT duality had convinced physicists that information couldn't be lost in black holes, they all jumped on board Susskind's horizon complementarity train. As radical as it was, it was the only way to save information without violating quantum mechanics or general relativity in the process. But its implications were profound.
Really
profound. I realized just how freaking profound they were when I thought more about Safe watching an elephant fall toward a black hole.

It's a gruesome scene. As it nears the horizon, the elephant gets stretched from trunk to tail, twisted and deformed as it moves ever more slowly toward the looming abyss. Slower still, it approaches the point of no return, the space around it growing dangerously hotter. But before the elephant crosses the horizon, it's torched by the Hawking radiation, reduced to nothing but a sad mess of burning ash.

Screwed, true to form, is riding the elephant. From his point of view, he and the elephant sail smoothly into the black hole, encountering nothing remarkable at the point in space where Safe sees a horizon. No twisting, no burning. Just easy, empty space. If the black hole is big enough, Screwed and the elephant will happily live out the rest of their lives before hitting the singularity.

So the elephant is dead outside the black hole and alive and well on the inside. It was a pretty serious discrepancy. It was as if Schrödinger's cat was both dead and alive in a box and the box was both floating in empty space and bursting into flames a billion light-years away. There seemed to be two copies of a single elephant, but quantum mechanics forbids cloning and a single elephant can't be in two places at once. But Susskind's point was this:
no observer can see both elephants.

“Traditionally people thought there was stuff behind the horizon and stuff in front of the horizon and they were different things, different bits of information,” Susskind said. “You wouldn't confuse the two.
But what we've discovered is that you cannot speak of what is behind the horizon and what is in front of the horizon.”

The confusion, he explained, could be pegged to the misuse of the word
and.
“The operating word is
or
, not
and
,” he said. “Complementarity in quantum mechanics always involves replacing
and
with
or.
Light is waves
or
light is particles, depending on the experiment that you do. An electron has a position
or
it has a velocity, depending on what you measure. In each case there are complementary descriptions which are incompatible if you use them both at the same time. The same thing is happening with black holes. Either we describe the stuff that fell in in terms of things behind the horizon
or
we describe it in terms of the Hawking radiation that comes out. What's so surprising is that this kind of confusion or redundancy is occurring on such a huge scale. If we have a black hole that's a billion light-years in diameter, then we have a description of information a billion light-years deep into the black hole. People always thought quantum ambiguity was a small-scale phenomenon. We're learning that the more quantum gravity becomes important, the more large scales, even
huge
scales, come into play.”

The coolest part was that any experiment you could imagine to try to see both elephants would fail perfectly. For example, there seems to be a quick instant when both versions of the elephant are outside the horizon, accessible to the eyes of a single observer. That's because the elephant gets toasted by the Hawking radiation
before
it hits the horizon, say within a Planck's distance of it. At that exact moment, Safe sees the elephant reduced to ashes while Screwed sees it happily unharmed, both versions of the elephant still outside the black hole. You'd think that some third observer—Sucker—could try to catch a peek of both elephants. But, technically, catching a peek of something means bouncing light off it and hoping some of the rebounding photons hit your retina, and the light's wavelength has to be smaller than the object it's trying to resolve. The smaller the wavelength, the higher the energy. To glimpse the elephant at a Planck's distance from the horizon, Sucker would need to use photons with energies larger than the Planck energy—which is either downright impossible or would create another black hole on the spot, cloaking the elephant with another
horizon. Either way, Sucker's plan to see Safe's elephant and Screwed's elephant simultaneously will never work.

What if Safe watches the elephant burn and then jumps into the black hole to see its healthy doppelgänger? Again physics conspires against it. In order to measure even a single bit of information about the toasted elephant in the Hawking radiation, Safe has to wait until half of the black hole's mass has evaporated away. By that time, thanks to some simple geometric rules, it's guaranteed that Screwed and his elephant would be destroyed by the singularity. There was no way around it. No observer can see both elephants.

As I thought about it, it occurred to me that the phrase “both elephants” was totally misleading. There's only one elephant.
Or
, not and. There's Safe's elephant
or
there's Screwed's elephant. End of story. Any talk of two elephants automatically breaches the quantum no-cloning rule. It violates the laws of physics.

My mind was officially blown. Top-down cosmology had suggested that you violate the law of causality when you try to take a God's-eye view of the universe, leaving me to wonder if you would violate other laws, too.
Laws of physics intact only when viewed inside a single light cone?
Now, horizon complementarity answered with a resounding yes. All the laws of physics—both relativity and quantum mechanics—only hold true within a single light cone, finite and limited as it may be.

For years my father and I had talked about the impossibility of a God's-eye view. After all, that was Einstein's lesson: you can't talk about the universe without asking, from whose point of view? Reference frames make all the difference.
There is nothing outside the universe.
Thanks to the finite speed of light, any given observer can see only a piece of it. But we had been talking about it as a philosophical point: if no one can ever see the universe from a God's-eye view, it makes good pragmatic sense to avoid using that view in your description of the universe. Horizon complementarity was saying something way more powerful: it isn't just a matter of philosophy anymore; it's a matter of physics. Try to describe the universe from an impossible reference frame that can see across horizons, and
you'll get the wrong answers.
You'll count two elephants instead of one. The laws of quantum physics will break down.

Horizon complementarity's message was clear:
physics makes sense only within the reference frame of a single observer.

The idea was so radical it was hard to wrap my head around it. The situation with the elephant seemed so weird because intuition tells us that even if we can't be inside and outside the horizon simultaneously, there's still some ultimate answer to where the elephant
really
is. But “really” assumes a reality that can be described from a God's-eye view. There is no single “really.” There's Safe's “really” and Screwed's “really.” Nothing more.

“It's not only a new form of complementarity, it's also a new form of relativity,” Susskind told me. “Relativity told us that certain things are relative to the motion of an observer—for example, whether two events are simultaneous or not. But there were other things that remained invariant. A flash bulb goes off inside my house. That's an invariant statement. But now we're saying that's not true at the level of black holes. The location of the information, whether it's behind or in front of the black hole horizon, depends on the motion of the observer. Where a basic event takes place is subject to the observer in a way that was not true in standard relativity. The location of a bit becomes ambiguous and observer-dependent when gravity becomes important.”

Einstein had rendered three-dimensional space and one-dimensional time observer-dependent but left the unified four-dimensional spacetime invariant. Now, horizons made that observer-dependent, too. Spacetime was no longer invariant. It was no longer real.

“If horizon complementarity tells us that spacetime is observer-dependent, what's left invariant?” I asked Susskind.

“What's left invariant?” He paused. “That's a good question.”

“I'm starting to think we should focus our book on the search for invariants, how they seem undermined at every turn,” I said to my father. I had come to my parents' house in Philadelphia for a weekend, and my father and I were hanging out in our physics library, working on our book proposal. Thanks to AdS/CFT, the holographic principle, and horizon complementarity, we had now crossed dimensions, strings, and spacetime off our list. “Every time physicists think something is invariant
it turns out to be observer-dependent. An illusion. It's like that Lewis Carroll poem. What's it called?”

“
Alice in Wonderland
?”

“No, the poem,” I said. “The Snark?”

“I don't remember that one.”

“These characters are hunting for a Snark, but no one has ever seen one. Every time they think they've caught one, it turns out to be a Boojum and it disappears.”

I dug through the books in my old bedroom until I found my copy of
The Hunting of the Snark
, then read aloud to my father the story of the Bellman, the Banker, the Beaver, and their crew, who set sail in hopes of capturing a Snark.

“ ‘What's the good of Mercator's North Poles and Equators, / Tropics, Zones, and Meridian Lines?' / So the Bellman would cry: and the crew would reply / ‘They are merely conventional signs!' ”

“They're observer-dependent!” my father piped in.

“ ‘Other maps are such shapes, with their islands and capes! / But we've got our brave Captain to thank' / (So the crew would protest) ‘that he's brought us the best—/ A perfect and absolute blank!' ”

I looked up. My father was grinning.

I read on until the fateful end, when the Baker believes he's found the elusive creature: “ ‘ “It's a Snark!” was the sound that first came to their ears, / And seemed almost too good to be true. / Then followed a torrent of laughter and cheers: / Then the ominous words “It's a Boo—” ' ”

“I love it,” my father said.

“Oh my God, listen to this,” I said, reading from Martin Gardner's preface to the book.
“ ‘The Snark is a poem about being and nonbeing.… The Boojum is more than death. It is the end of all searching. It is final, absolute extinction, in Auden's phrase, “the dreadful Boojum of Nothingness.” In a literal sense, Carroll's Boojum means nothing at all. It is the void, the great blank emptiness out of which we miraculously emerged; by which we will ultimately be devoured; through which the absurd galaxies spiral and drift endlessly on their nonsense voyages from nowhere to nowhere.' ”

“Cheery,” my dad said.

“But appropriate! The Snark is invariance, ultimate reality. But
every time we think we've found a Snark, it turns out to be a Boojum. It disappears.”