The black hole firewall paradox
You may have seen the interesting article floating around about the black hole firewall paradox written by Jennifer Ouellette. Sean Carroll (who also happens to be Jennifer’s husband) posted something on Facebook about it that led to a discussion in which I think I identified a path to follow toward the solution. It seems to me that the solution to this problem lies in quantum resource theory. But we’re getting ahead of ourselves. Just what is this paradox to begin with?
Well, imagine Alice and Bob are hanging out in the vicinity of a black hole and, perhaps for reasons Shakespearean, Alice heads off toward the black hole and starts falling in. In theory, a black hole’s event horizon has always been treated as just a gravitational boundary. In other words, Alice shouldn’t notice anything when crossing it if it’s big enough. It’s just that the escape velocity has suddenly become essentially infinite so she’s kind of stuck (technically it’s a little more than that, but that’s good enough for now).
But, then Polchinski, Almheiri, Marolf, and Sully (AMPS) proposed this past summer that Alice should actually experience a wall of fire and be incinerated on the spot. Hence it was dubbed the firewall. As with everything in physics, the argument really boils down to information. There are all sorts of odd problems that arise when you start to think hard about this problem and given that it is late and I’m tired, I’ll let you read Jennifer’s excellent article in order to get the details. What I want to offer (and what I did offer on Sean’s Facebook thread) is a suggested starting place for finding a solution: quantum resource theory.
Fundamentally, the problem is that the event horizon is like a barrier that normally prevents communication across it. If Alice is on one side and Bob is on the other, they should not be able to communicate which means they cannot fundamentally agree on a common reference frame, at least classically. Thus the event horizon (firewall) is equivalent to a superselection rule (see this paper for more details on this point). Ah, but that means one should be able, in theory, to develop a quantum reference frame and build a resource from it to overcome the superselection rule. But how?
Well, I think the answer is staring us in the face (though I will have to run through the math to be sure): Hawking radiation. In Hawking radiation, virtual pair production occurs near the horizon of a black hole, but before the particle and anti-particle can annihilate each other, the anti-particle tunnels through the horizon and annihilates something on the other side leaving the particle outside the horizon where it is viewed as Hawking radiation. Based on a paper I’m working on with Barry Sanders, Michael Skotiniotis, and Borzu Toloui, the particle–anti-particle pair acts as a resource for overcoming CPT superselection. In a sense, the firewall is a bit like a CPT superselection rule. Now, how, precisely, Alice and Bob could use this pair to actually communicate in a practical sense is something I haven’t worked out yet. But it offers a new starting point for thinking about the problem, in my opinion.
In addition, if you take the Feynman-Stueckelberg interpretation of anti-particles literally and assume that an anti-particle is a particle moving backward in time, you could view these virtual pairs as particles on closed time-like curves. In other words, instead of seeing two things (a particle and an anti-particle) you’re really only seeing one but you’re seeing it in a superposition of moving forward in time and moving backward in time. Heck, the Feynman diagram even looks like a CTC (not that that proves anything, but it is suggestive nevertheless, particularly in light of our soon-to-be-released results).