Trespassing on Einstein's Lawn (55 page)

“The argument in the AMPS paper is that hypothetically we can
decode the radiation and then jump into the black hole,” Hayden said. “But in the spirit of complementarity we have to be as operational as possible.… Can you decode it on a quantum computer? And if so, on what time scale?”

Standing at the blackboard, Hayden took us through a number of calculations, showing what it would mean to put the Hawking radiation through a series of universal 2-qubit gates in a given amount of time. His conclusion? “Decoding the radiation would take exponential time.” That is, for every additional bit of information, the amount of time Screwed needs to decode the radiation increases exponentially. Given a black hole of any size, by the time Screwed and his quantum computer are finished decoding—by the time he can figure out that B is entangled with R—the black hole has long since evaporated and the threat of a firewall is long gone.

The next morning, before the meeting resumed, I spotted Hayden and Harlow sitting on a couch in front of an equation-clad chalkboard. I was eager to ask Hayden about his talk, which I hadn't been able to get out of my mind all night.

“Just because you can't decode the information, does that really mean it's not even there?” I asked. “I mean, just because we can't measure that B is entangled with R, does that automatically mean B isn't entangled with R?”

“Think about it like quantum complementarity,” Hayden said. “There you want to say, just because you can't measure position and momentum simultaneously doesn't mean the particle doesn't really have a position and momentum simultaneously. But that's exactly what it means. It could be the same kind of thing here.”

It was a good point, I thought as I headed back into the conference room. Still, one would be inclined to wonder why the hell what is operationally possible should have
any
connection to what is ontologically existent. It did—quantum mechanics made that perfectly clear. But why? If reality came in the Einsteinian brand—sitting out there, independent of observation—then the connection would be inexplicable.
There was only one way to explain why what we can
know
determines what can
exist:
reality is radically observer-dependent. And if reality is radically observer-dependent, I thought, then firewalls are going down.

Inside, Harlow took the floor and expressed his agreement with Hayden. “It seems there is a fairly robust conspiracy preventing [Screwed] from measuring R.… Even though they are in the same light cone, they are not computationally accessible to a single observer.”

Echoing Susskind's speculation that A equals R, Harlow wondered if we ought to adhere to “strong complementarity.” “Strong complementarity would say, the way to think about this is that [Safe] has some quantum mechanical theory and [Screwed] has some quantum mechanical theory and there's some criteria about how much they have to agree. But they only have to agree on things they can both measure.”

I was grinning in my uncomfortable chair.

Ordinary complementarity says that when there's an event horizon around, you have to restrict to a single observer's reference frame, rather than taking an unphysical God's-eye view. It was the bold claim that rendered spacetime observer-dependent.
Strong
complementarity took things to a whole new level. It says that you have to restrict to a single observer's reference frame
regardless of whether there's an event horizon.
After all, in the AMPS scenario, the discrepancy in Safe's and Screwed's descriptions occurs in a region where the two observers are not yet separated by a horizon. Strong complementarity doesn't just make spacetime observer-dependent—it makes
everything
observer-dependent.

On the other hand, Harlow said, his face darkening, “that doesn't seem to agree with AdS/CFT, because that suggests there should be one quantum mechanical description that you can put in one Hilbert space.”

But we don't live in AdS!
I silently protested. Banks was right: they were trying to make the fifth sequel to
Saw.
We live in de Sitter space, which, unlike AdS, has observer-dependent horizons. If we want to
understand cosmology, we have to stop tailoring everything to AdS and deal with
this
universe.

“Somehow these two things, [A and R], have to be the same operator,” Harlow said, “but I have a love/hate relationship with that idea.”

I could see Susskind nodding. “We all do.”

Something is happening?

What exactly does one do when one gets an email from one of the greatest living physicists reading only, “Something is happening”? Apparently one runs laps around one's living room, then jumps up and down in front of an annoyed cat, shouting, “Something is happening! Something is
happening
!”

“What do you think is happening?” my dad asked on the phone. Six weeks had passed since the Stanford meeting.

“What do I think? I think he resolved the firewall paradox, and I think he did it by making things even more observer-dependent. I think he gave in to A equals R and strong complementarity, and he knows he can do it because of Hayden and Harlow's claim about quantum computation.”

Come Monday, I was perched in front of my computer hitting the refresh button on my arXiv search, waiting for something new to pop up under Susskind's name. At 9:30
P.M.
it did: “Black Hole Complementarity and the Harlow-Hayden Conjecture.”

I read it as quickly as I could. I could barely see past my own smile.

“Bousso and Harlow have [advocated] a strong form of complementarity that can be described by saying each causal patch has its own quantum description,” Susskind wrote. “In [Screwed's] quantum mechanics, B is entangled with A and not with the outgoing radiation. In [Safe's] description, B is entangled with R.… It's obviously premature to declare the paradox resolved, but the validity of the HH conjecture would allow the strong complementarity of Bousso and Harlow to be consistent, without the need for firewalls. For these reasons I believe that black hole complementarity, as originally envisioned by Preskill, 't Hooft, and Susskind-Thorlacius-Uglum, is still alive and kicking.”

Susskind said it was premature to declare victory, but as far as I was concerned, Susskind, Bousso, Harlow, and Hayden had put out the fire. And with firewalls out of the way, my father's and my mission was back on track.

At the same time, I realized there was a lesson to be learned from the whole fiasco. The firewall paradox wasn't trying to tell us something about black holes. It was trying to tell us something about quantum mechanics.

If each observer has his or her own quantum description, as strong complementarity demanded and as Banks had been claiming all along, we were going to need a new understanding of quantum physics. In ordinary quantum theory, there's one Hilbert space and entanglement is absolute. In a firewall-free, holographic world, there's one Hilbert space
per observer
and entanglement is relative to a given reference frame. Things were going to have to change.

Luckily, I was pretty sure it was exactly the kind of change we needed to finally get to the bottom of ultimate reality and the origin of existence. In our quest, my father and I had found that invariant after invariant gave way to observer-dependence. But every clue we uncovered was rooted in the assumption that reality is governed by quantum mechanics. Hawking radiation, the holographic principle, top-down cosmology, M-theory, holographic spacetime, strong complementarity—every last one of them assumed quantum mechanics
from the start. If they withered down the ontology of the universe, it was because quantum mechanics withered down the ontology of the universe. I could see clearly now that if we wanted answers, they were going to come from one question alone, the same one that Wheeler had asked that day in Princeton, the one he had decided to focus on when he knew time was ticking down:
How come the quantum?

“If different observers give different accounts of the same sequence of events, then each quantum mechanical description has to be understood as relative to a particular observer. Thus, a quantum mechanical description of a certain system (state and/or values of physical quantities) cannot be taken as an ‘absolute' (observer-independent) description of reality, but rather as a formalization, or codification, of properties of a system
relative
to a given observer.… In quantum mechanics, ‘state' as well as ‘value of a variable'—or ‘outcome of a measurement'—are relational notions.”

As I read Carlo Rovelli's paper, a gospel choir sang “Hallelujah” in my head.

How had I never heard of this before? It was so simple. It was so brilliant. It was exactly what we needed.

As Wheeler had emphasized in his journals, the central problem of quantum mechanics was coauthorship—the problem of the second observer. Or, as Wheeler put it, “What happens when several observers are ‘working on' the same universe?” It was precisely this problem that Rovelli had set out to solve in his 1997 paper “Relational Quantum Mechanics,” which I had stumbled upon amid a desperate search of the physics literature for some new insight into the quantum mystery.

Rovelli began by comparing the problem of the second observer to the problem of Lorentz transformations in special relativity. To account for the fact, first observed in the 1887 Michelson-Morley experiment, that all observers measure light to be moving at the same speed regardless of their own state of motion, Hendrik Lorentz proposed that objects will physically contract or stretch in exactly the right proportion to cancel out the effect of an observer's motion and leave the speed of light constant. That was in 1892, more than a decade before Einstein published his special theory of relativity. These Lorentz transformations successfully accounted for the constancy of light's speed, but you only had to think about it for a second to realize that it was completely fucking insane. If I'm measuring how long it takes a light beam to travel the length of a road, and I'm running down the road as I measure it, how the hell would the road
know
to shorten itself by the exact right amount to cancel out the effects of my speed relative to the light's speed as it conspires to fool me into thinking that light always travels at 186,000 miles per second? Not to mention the question of what physical process the road would employ to shorten itself at will. Lorentz transformations produced the right answers, but, like quantum mechanics, they seemed bat-shit crazy.

If the equations of special relativity had already been written down by Lorentz in 1892, Rovelli asked, “What was Einstein's contribution? It was to understand the physical meaning of the Lorentz transformations.” Lorentz had the right structure but the wrong story. It was, Rovelli said, “quite an unattractive interpretation, remarkably similar to certain interpretations of the wavefunction collapse presently investigated. Einstein's 1905 paper suddenly clarified the matter by pointing out the reason for the unease in taking Lorentz transformations seriously: the implicit use of a concept (observer-independent time) inappropriate to describe reality.”

In other words, it wasn't that the lengths of objects were magically changing to fool observers. It was that space and time were observer-dependent concepts. Give up their invariance, and suddenly everything starts to make a lot more sense.

Could a similar reinterpretation of quantum phenomena make sense out of all the bizarre, ad hoc explanations for wavefunction collapse
and the paradox of the second observer? To Rovelli, previous solutions, such as Bohr's ontological divide between observer and observed or Wigner's privileging of consciousness as some metaphysical force, “look very much like Lorentz's attempt to postulate a mysterious interaction that Lorentz-contracts physical bodies.”

“My effort here is not to modify quantum mechanics to make it consistent with my view of the world,” Rovelli wrote, “but to modify my view of the world to make it consistent with quantum mechanics.”

So what was it that had to be modified? “The notion rejected here is the notion of an absolute, or observer-independent, state of a system; equivalently, the notion of observer-independent values of physical quantities.” In other words, Rovelli wrote, “a universal observer-independent description of the state of affairs of the world does not exist.”

That day back in IHOP when my father and I made our list of possible ingredients of ultimate reality, we didn't bother listing reality itself. “It would be like listing cake as an ingredient in cake,” my father had said. But now it was looking as though we should have, if only to have the mind-melting pleasure of crossing it off the list. According to Rovelli, reality itself was observer-dependent. Which meant, however insane it sounded, that reality itself
wasn't real.

Once you abandon the notion of observer-independent quantum states, the paradox of the second observer disappears. After all, the paradox comes from the contradictory descriptions that Wigner and his friend give of the same events. But the descriptions are contradictory only if we assume that there's a single reality they are both describing. Wigner's friend says the atom's wavefunction collapsed; Wigner says it hasn't and that the atom and his friend are now in a superposition state. Which is it
really
? According to Rovelli, there's no
really.
It collapsed relative to Wigner's friend. It didn't collapse relative to Wigner. End of story.

“Bohr and Heisenberg's key idea that ‘no phenomenon is a phenomenon until it is an observed phenomenon' must therefore apply to each observer independently,” Rovelli wrote. “This description of physical reality, though fundamentally fragmented … is complete.”