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0 pointsa13692099937y ago0 comments

This is a significantly more... more response than I was expecting, thank you.

I do have a couple of quibbles, though:

> Hawking radiation converts a pure state into a mixed state. A cryptographic mixing function converts a pure state into a pure state in a way which is hard to trace.

This is actually specifically what I meant by "the physics equivalent of"; that is, a quantum-computational mixing function that converts a arbitrary, possibly mixed state to another, probably[0] mixed state, such that a hypothetical extra-physical observer with full knowledge of both states would see the result as uniformly pseudorandom from the range of all possible output states.

Also, I take as a sort of provisional axiom[1] that physics is time-reverible (not necessarily symmetric, although probably CPT symmetric) and therefore cannot throw away or generate new any (quantum mechanical/qubit-based, so orthogonal-basis measurements aren't) information. (Given this and something like the Bekenstein bound, that a evaporating black hole must be leaking its information to somewhere, and its radiation must be getting its information content from somewhere, are seemingly trivial.)

0: In the thermodynamics/statistical mechanics "almost certainly" sense. 1: similar to and as serious as Conservation of Energy or "Scientists are made out of atoms and cannot cause magical non-(unitary/linear/differentiable/local/CPT symmetric/Liouville uniform/deterministic/etc) events by looking at things."

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raattgift7y ago

> more response than I was expecting, thank you.

You're welcome.

> evaporating black hole must be leaking its information to somewhere

The information about the contents of the BH during its formation and growth is in the region of strong gravity. Classically, it's squashed into the gravitational singularity; fully classically the singularity is always hidden behind an event horizon, so it does no harm to predicting events outside the horizon.

However, we now add a quantum field theory to the picture.

The origin of Hawking radiation is the acceleration between observers before the formation of the strong gravity and the observers after that; the accelerated (later) observers see particles where the non-accelerated (early) observers see none. The particles appear in the dynamical spacetime around (but outside) the horizon. The reason they are there is (rougly) that the creation and annihiliation operators that line up in "unstretched" vacuum separate in "stretched" vacuum, and annihilation operators miss the created particles (that is, the annihilation happens at the right spatial coordinate, but too early or too late: the created particle is elsewhere). The analogy with Unruh radiation, which appears for accelerated observers in flat spacetime but not for unaccelerated observers in the same spacetime is not accidental. In the Unruh case, the acceleration mechanism (say, a rocket engine) is the reason the accelerated observer sees the extra particles. In the Hawking case, the acceleration mechanism for later observers is the dynamically collapsing spacetime.

If nothing exits the horizon of a black hole (at least until final evaporation; and for that we are stuck with not knowing enough about the behaviour of quantum fields in strong gravity) then the only parameters available at any instant in the (QED-filled) dynamical spacetime that is the origin of Hawking radiation are mass (1 component), charge (1 component), angular momentum (3 components), linear momentum (3 components), and spatial position (3 components). The last six components fall away for some families of observers with a suitable choice of spatial coordinates. ("Instant" in this context is a coordinate time defining a spacelike hypersurface, and one has lots of freedom there). You get a handful of extra components (individual "charges") as you go from QED to the standard model.

There have been attempts to break this picture by inter alia having things never enter the horizon in the first place, by implanting extra information in the spacetime around the black hole ("hair"), and by locking up all the infalling matter into a crystal that preserves details of the matter's microscopic states either forever or until evaporation is almost entirely complete. It is extremely hard to do this without introducing unlikely observables.

> Conservation of Energy

... is not a global symmetry of a dynamically collapsing spacetime. You only get conservation of energy locally within a suitably small region of spacetime (which can be quite large far from the collapse, assuming asymptotic flatness).

> time-reverible

Locally. This is most sharply obvious in strong curvature.

> CPT symmetric

This is a problem with unitary time evolution of any quantum system in this setting; CPT doesn't enter into it. There is neither antimatter nor chirality in the model non-interacting scalar field that exposes the information loss problem for a collapsing black hole. ("Negative energy" is only a trick used when one wants to use a static background instead of a dynamical one; it does not interact at all with its pair-partner or other "negative energy" quanta; there is no local symmetry, it is the global symmetries of the Schwarzschild solution that are being preserved through the trick. You entangle the real Hawking quanta with false quanta instead of entangling the real Hawking quanta with the spacetime (which would change the metric, which is exactly what one is trying to avoid in some studies)).

Indeed, the problem is mostly centred on "time" in the first sentence of the previous paragraph. There is no unique slicing of a general curved 4-spacetime into 3-spaces, and if one does it wrong, one gets problems (see ref to Giddings 2006 below). This is in some ways an argument that black hole information loss is mainly about the https://en.wikipedia.org/wiki/Problem_of_time .

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