It's not my area, but I always take notice when part of the physics community is

abuzz about a thought experiment that seems to expose flaws in our understanding. At issue is whether something dramatic (involving quantum gravitational effects) takes place at the event horizon of a black hole, from the point of view of an infalling observer. Way back when I took a general relativity course, I learned that, because of the way spacetime works, the more massive the black hole, the more mild the actual curvature of spacetime at the horizon. Tiny blackholes = tightly curved spacetime at the horizon; galactic-mass blackholes = nearly flat spacetime at the horizon. (The horizon is the location where, in the usual Schwarzchild treatment, the sign of the metric components flips; that's another way of saying that once you cross the horizon, classically you are inevitably going to hit the singularity. Avoiding it is mathematically as hard as avoiding next Tuesday in flat spacetime, as my professor had said.) So, the old-school classical picture says, a freely falling observer can cross the event horizon and not even realize it. Moreover, classically, an observer at rest relative to the black hole outside the horizon never actually sees anything cross the horizon - from such a perspective, a clock falling toward the horizon gets progressively more red-shifted and runs slower and slower, stopping altogether at the horizon after being infinitely red-shifted.

I freely admit that I don't understand Hawking radiation beyond a handwave level. Still, I would be grateful if someone could explain to me, even more clearly than the article linked above, what the big deal is. Arguments about entanglement across the horizon sound almost theological to me - if it's by definition

**impossible** to check to see if measurements inside the horizon are quantum-correlated with measurements outside the horizon, then such discussions don't seem scientifically meaningful.

## 5 comments:

http://arxiv.org/pdf/1207.3123.pdf “Black Holes: Complementarity or Firewalls”

"... almost theological ..." According to Martinus Veltman, “If we do away with the experiments, science becomes religion. From that moment on it won’t be the facts that count when we are trying to determine what’s true, but the opinions of someone’s who’s been elected pope. … Theoretical physics is not worth anything until the laboratory has shown that it’s correct.”

Quoted from Bennie Mols’s blog, Feb 8. 2008, “Theory of Everything of Nothing – An exchange of views on string theory”

I say that the string theorists and quantum gravitational theorists have unfortunately ignored the work of Vera Rubin and Mordehai Milgrom. Rubin and Milgrom are correct, and the string theorists have made a huge mistake.

If not by theological means, how else are string theorists supposed to make a living?

The entanglement picture is one way to look at the paradox, but there's another way which AMPS initially talk about in their paper and which I find more intuitive.

The first thing is the claim that quantum mechanics always works, hence a pure state always evolves into a pure state (unitary time evolution). Now, if we have a system in pure state which collapses into a black hole and eventually evaporates away via Hawking radiation, the total radiation would have to be in a pure state, which means if we take a subsystem it will be entangled with the rest of the system. (This is a common theme when we talk about entanglement entropy in condensed matter systems.)

Now if I look at the Hawking radiation, I can define a small subsystem to be the radiation emitted in the last few moments of the black hole, with the rest of the system being everything that was emitted before. The fact that the small subsystem is entangled with the rest of the subsystem means that measuring the rest of the subsystem, one can know the state of the small subsystem. Hence, an observer measuring the early radiation will know what to expect in a particular mode of the late radiation.

Now let's say an observer does measure the early state, and hence knows that the a particular mode of the late radiation is a specific energy eigenstate in his frame of reference for some operator that he can define. If the observer now decides to jump into the black hole, the mode he should be seeing is a energy eigenstate for an observer at rest. But for a quantum field theory in curved spacetime, the eigenstate for an observer at rest is a linear superposition of various frequency states for an accelerated observer. (This, in fact, is the origin of Hawking radiation as well as the Unruh effect.)

Hence, as the state is an energy eigenstate for an observer at rest, the infalling observer will see quanta at all frequencies, and hence, will also see high energy (frequency) quanta as claimed by AMPS. This is the notion of so called "firewall".

I wonder if this explanation was somewhat clearer than the entanglement argument!

PS : The arguments across the horizon are not entirely "unphysical" as both sides of the horizon are accessible to an infalling observer, and if the infalling observer sees no drama at the horizon, that inevitably implies the entanglement across horizon in the frame of reference of an observer at rest w.r.t. the black hole. That simply follows from the fact that field operators for infalling observer are Bogoliubov transforms of the operators for the observer at rest.

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