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).


9 thoughts on “The black hole firewall paradox

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  1. Hello Sir,

    From this entire article the one stuff that is not clear to me that for what reason exactly you inferred the Event Horizon of a Black hole to be a sort of a SUPERSELECTION boundary..

    Is it is differentiating the respective Quantum states of the Normal Matter Particle and it’s anti Counterpart and subsequently preventing them from annihilating each other ??

    But then again, if that is to be believed, if Alice is crossing the event horizon in our usual thought experiment, then wouldn’t there be an Anti-Alice appearing in our Universe who will be having some real Power destructing his friend Bob with a touch..he he..a bit of humor at last !!!

    1. Actually, this is not even my idea. There are a number of papers out there that consider this from a slightly different POV, but with the basic notion that the inside and outside of a BH event horizon constitute different superselection sectors. In fact I think Polchinski’s paper that started this whole thing mentions it, though I’d have to double-check.

  2. The article by Jennifer Ouellette is the best I have seen. Of the three “cherished notions in theoretical physics” 1. the equivalence principle, 2. the unitarity postulate, and 3. the normalcy expectation of physics far away from a black hole, the 3rd one is only approximately true. The reason is that the zero point vacuum energy obeying a w^3 frequency spectrum would be Lorentz invariant for all energies if it would not be cut off at the Planck energy. The cut-off leads to a prefeered absolute reference system in which this energy is at rest. Because the Planck energy is so high, special and general relativity remain extremely good approximations, but it is not possible simply to transform away an event horizon where the absolute velocity of an infalling elementary particle against this reference system reaches the velocity of light and the Planck energy. In the transition from absolute subluminal to superluminal velocities the differential equation describing the 4-potential (if formulated in the pre-Einstein absolute ether theory of relativity by Lorentz and Poincare) goes over from an elliptic differential equation into a hyperbolic differential equation with no static equilibrium solutions for matter held together by electromagnetic forces. This is what happens at the event horizon where the absolute velocity of an infalling elementary particle reaches the Planck energy , and where it decays into electromagnetic radiation for the above given reason. The same would happen if an elementary particle is accelerated by any means to absolute velocities where it reaches the Planck energy. With the event horizon in a collapsing body appearing first as a point in its center, the body will in a short time decay into a burst of gamma rays. This preserves unitarity and explains the gamma ray bursters where in one observed case 50 solar masses were in a short time completely converted into radiation. This is the firewall which has nothing to do with Hawking radiation. But the mass of very large black holes can be also slowly converted into radiation which may explain the stream of hydrogen flowing out of the galactic center, where Eddington had speculated that it may come from a higher dimension, rather than pushed out by radiation pressure from the gamma rays released at the event horizon of a large black hole. F. Winterberg, Professor of Physics University of Nevada.

  3. Heh, remember that one “The second postulate is unitarity, the assumption, in keeping with a fundamental tenet of quantum mechanics, that information that falls into a black hole is not irretrievably lost.”

    It’s good fun reading Moxie. Never seen anyone succeeding in defining how that Hawking information could be ‘decrypted’, into whatever one would like to define as its origins though? Actually you can as easily use an equation made on ice, that you then melt, asking yourself where that information went?

    the pair production (Hawking radiation) assume a entanglement as I get it? But how that entanglement relate to for example my ice block with the equation falling in I’m unsure?

  4. That’s one I’ve been wondering about too “This is what happens at the event horizon where the absolute velocity of an infalling elementary particle reaches the Planck energy , and where it decays into electromagnetic radiation for the above given reason.”

    I thought about it in matter of reaching ‘c’, but I defined that to the singularity, not to the event horizon, unless that too can be defined as being a ‘center’? And yes, passing ‘c’ should have consequences ‘out’a’this universe’, but I don’t expect mass to do that? A in-falling, gravitationally accelerating, piece of matter is not accelerating, no matter what ‘speed’ one may measure from some arbitrarily defined, inertial or not, platform. It’s in a ‘free fall’ naively speaking and assuming no strong tidal forces, the equivalence principle will hold. It’s easy to test, check your wristwatch.

  5. Meant ” It’s in a ‘free fall’ naively speaking and assuming no strong tidal forces, you will ‘fall’ in peace, the equivalence principle holding. It’s easy to test, check your wristwatch.”

    And that is a simple proof, locally defined you connect your local clock to ‘c’. then you start to fall toward a ‘center’. Doing so you locally defined will find yourself in a free fall, no existent gravity. Unless you assume that ‘c’ no longer is ‘c’ in your free (uniform) fall, you should be able to find that your clock ticks as ‘always’, in good accordance with ‘c’, that you now spit into even ‘chunks’ using it as a time device. So according to yourself, locally measured, time, and ‘c’, ‘ticks away’ as normally. And you, depending on if you close your eyes or not, either define yourself as being still ‘floating’ in a space,, or falling toward some ‘center’ and therefore weightless.

  6. The point is that there is no way for you, enclosed in a ‘black box’ to measure whether your free fall is in a gravitational potential or not, ignoring spin (tidal forces) for this. And that should hold at a appropriate event horizon too, as I see it. The other assumption I make is that ‘c’ will be ‘c’. And that one I also expect to hold. The third is connecting ‘c’ to your local clock, just to show that nothing ‘freeze’, locally defined. (and it should have ‘split’, not ‘spit’ 🙂

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