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Black Holes: Thought Labs at the Horizon

The extreme properties of black holes make them ideal laboratories for thought experiments, allowing us to test our best theories against the edge of what we know. Paradoxes thus brought to light are shaking up the world of theoretical physics in exciting ways.

Published August 15, 2013

Black Holes: Thought Labs at the Horizon

The New York Times recently ran a fascinating article on the black hole firewall paradox. The  puzzle and the contradictions it seems to imply are being debated this week at UC Santa Barbara's Kavli Institute for Theoretical Physics.

The crux of the issue is a conflict between central tenets of general relativity theory and quantum mechanics. Basically, either the equivalence principle (a foundational concept for general relativity) doesn't hold, entangled particles can "cheat" on each other, or information can be lost. The latter two are both forbidden by quantum mechanics.

This probably needs some explanation! Joseph Polchinksi, a theoretical physicist at the Kavli Institute and one of the authors of the paper that pointed out the firewall paradox, describes the conundrum in this guest blog for Cosmic Variance.

Briefly, in 1974, Stephen Hawking showed that, contrary to the nomenclature, black holes are not black. In fact, they radiate a constant stream of particles known now as Hawking radiation. When virtual particle pairs pop into existence near an event horizon, one can fall into the black hole, leaving the other to radiate away from the black hole rather than annihilate with its twin. Problematically, Hawking said, the radiation would be totally random, containing no information about the states of its composite particles and their anti-twins, which is anathema to quantum mechanics. "There is strong evidence that [the conservation of quantum information] is an inviolable principle of physics, and we don't really know how to make sense of quantum mechanics without it," says Cal Tech theoretical physicist John Preskill in this Quantum Frontiers post.

Juan Maldacena, a theoretical physicist now with the Institute for Advanced Study, explains,

"In quantum mechanics (as in classical mechanics) the information about a system is not lost. Different initial conditions lead to different outcomes...The radiation coming out of black holes would be completely thermal and devoid of the information of what fell into black holes. Thus, black holes appear to be sinks of information, perverse monsters that threaten the fundamental laws of quantum mechanics."

Maldacena implied a solution with the anti-de Sitter/conformal field theory correspondence (AdS/CFT for short), which offers elegant mathematical demonstrations of the holographic principle. The idea is that everything occurring in 3D space is actually a projection of things happening on a 2D boundary, and you can translate between the two using the AdS/CFT. If that sounds conceptually bizarre and unconvincing, fair enough! But the math is so compelling as to have been near-universally accepted in the theoretical physics community.

"This meant that even 3D black-hole evaporation could be described in the 2D world, where there is no gravity, where quantum laws reign supreme and where information can never be lost. And if information is preserved there, then it must also be preserved in the 3D world. Somehow, information must be escaping from the black holes," explains Zeeya Merali in Nature.

The "how" turned out to be less straightforward. (I know: Straightforward?! Bah!) Stanford physicist Leonard Susskind proposed that information could be salvaged from black holes via quantum entanglement between radiated particles. But this ends up violating another core concept of quantum mechanics, monogamous entanglement. A radiating particle can't be entangled with another, earlier radiated particle, because it was born entangled with its anti-twin (remember, the one that fell into the black hole?). Preskill explains the monogamous entanglement issue in more detail here. (H/T Jennifer Ouellette)

Polchinski—along with colleagues Ahmed Almheiri, Donald Marolf, and James Sully— published a paper stating that, in order to preserve information, the entanglement between the virtual particles formed near the event horizon has to be severed. This is where the challenge to relativity comes in. Merali elaborates,

"'It's a violent process, like breaking the bonds of a molecule, and it releases energy,' says Polchinski. The energy generated by severing lots of twins would be enormous. 'The event horizon would literally be a ring of fire that burns anyone falling through,' he says. And that, in turn, violates the equivalence principle and its assertion that free-fall should feel the same as floating in empty space—impossible when the former ends in incineration."

A possible solution to the puzzle lies in the idea, formulated by Susskind and Maldacena, that wormholes connect particles on either side of an event horizon. "The conjecture seems to allow us to view the early radiation with which the black hole is entangled as a complementary description of the black hole interior," explains Preskill. This would mean that one particle could be faithfully entangled with two joined particles on either side of the event horizon, because the connected particles would actually be the same.

This could have some revolutionary implications for cosmology—the wormholes connecting all these entangled units of information might turn out to be the very stuff of space! "If true, this insight would be a step toward a longtime dream of theorists of explaining how space and time emerge from some more basic property of reality, in this case, bits of quantum information," explains NYT author Dennis Overbye.

Stay tuned for more on the subject after the Kavli program adjourns later this week!

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