One of the biggest paradoxes in physics is the black hole information paradox, but new research from a team of physicists at Case Western Reserve University may have resolved it. As I have mentioned in previous articles, physics is fractured. It has produced two theories that are shining beacons of modern science: quantum mechanics and general relativity. Both are accurate to the limits of our ability to measure them, and both have predicted results that were years ahead of their time and later experimentally verified. However, the similarities end there. At the heart of quantum mechanics is a mathematical framework of linear equations that describes the very small bits of the universe as probabilistic. General relativity is described by an elegant set of highly nonlinear equations that detail the very big in a completely deterministic manner: polar opposites that stand in stark contrast with one another. This discrepancy has reared its ugly head every now and again, but one place it is clearly demonstrated is the "information loss paradox."
Black holes truly are the vacuums of the universe: once—or if, more on that later—you cross the event horizon, neither you nor anything that originates from you will ever come back. As my general relativity professor quipped one day in class, "If you cross the event horizon, you won't know anything has happened. You'll still get the morning paper; you just won't ever be able to tell anyone on the outside." The information contained in an object that falls into a black hole is lost to the universe forever. However, this poses a problem, as quantum mechanics states that information cannot be destroyed.
The black hole information paradox began life, so to speak, in 1975, when Stephen Hawking and Jacob Bekenstein proved that black holes were not really black, but that they emitted thermal radiation and eventually evaporated. This leads to a problem; other cosmological tenets (the no-hair theorem) suggest that the Hawking radiation that leaves a black hole should be independent of the material that goes in. This is problematic, because if one could have an initial quantum state where everything is known with exact certainty and send it into a black hole, then as the black hole evaporates and evolves, the final state of the system cannot be predicted. In this case, the best result is that a probable outcome can be computed. Here information has been lost: you knew exactly what went in, but you don't know exactly what may come out—quantum mechanics has been violated. Here's how it looks when stated in a different manner by an expert in the field, CalTech Professor John Preskill in a 1992 review paper on the information paradox:
This is the information loss paradox. The paradox is that if we try to analyze the evolution of a black hole using the usual principles of relativity and quantum theory, we are led to a contradiction, for these principles forbid the evolution of a pure state to a mixed state.
Reconciling the contradictory
Over the course of the past 30 years, people have sought to reconcile these apparently contradictory predictions. It has been suggested that the "lost" information actually ends up in parallel universes where no black holes exist, or that Hawking radiation is not entirely thermal but has some quantum effects as well. In 2005 Prof. Hawking published a paper that suggested quantum perturbations of the event horizon of a black hole would allow information to escape, hence resolving the paradox. However, that theory has not yet been widely accepted by the scientific community. New work released this week by a team of physicists at Case Western Reserve University offers a revolutionary new proposal to solving this paradox: information is not lost in black holes because nothing ever crosses the event horizon!
The Case Western Team approached the problem from a relatively uncommon perspective. Instead of taking the view of an observer falling into a black hole, they took the more physically relevant viewpoint of the asymptotic observer: one who is so far away from all the action that s/he is not affected by it and cannot affect the process. From this viewpoint, they work out the mathematics that describes what happens when one starts with non-singular matter and tries to collapse it. In order to describe the system, the team used the Schwarzschild metric of spacetime.
As an aside, when working in curved space as described by general relativity, a metric gives one a way to measure distances in both space and time dimensions. Initially this approach gave me cause for concern, since the Schwarzschild metric is such a (relatively) simplistic one. It ignores charge and angular momentum and can lead to unphysical results depending on the coordinate system one works in. The researchers here state that they did not encounter any of the difficulties typically seen when working in this metric, suggesting that their calculations are self-consistent.
The physical equivalent problem that the researchers address is that of a shell of collapsing matter, or more technically a vacuum domain wall. Applying the equations of general relativity to this problem in the Schwarzschild metric, the team produced an expected result: the formation of the event horizon takes an infinite Schwarzschild time. Given that this result is well known, the researchers expanded their field of inquiry to include quantum effects. To see if this result still holds true in the quantum realm, the team made some assumptions and used what is known as the functional Schroedinger equation. They found that even when accounting for quantum effects, the black hole still takes an infinite amount of (Schwarzschild) time to form. Taking their results a step further, the physicists find that the collapsing shell will radiate away its energy in a finite amount of time. They found that the amount time needed to radiate away all of the shell's energy is shorter than the time needed for an object to fall through the event horizon. This leads to one of their major conclusions: an observer sufficiently far away "will see the evaporation of the collapsing shell before he can see any objects disappear".
According to Dejan Stojkovic, one of the paper's authors, "An outside observer will never lose an object down a black hole. If you are sitting outside and throwing something into the black hole, it will never pass over but will stay outside the event horizon even if one considers the effects of quantum mechanics. In fact, since in quantum mechanics the observer plays an important role in measurement, the question of formation of an event horizon is much more subtle to consider." What does this have to do with the information paradox? Since the outside observer never sees the formation of the event horizon in a finite time, the radiation that they can measure is not fully thermal, and can still carry information about the object that was tossed towards the black hole. Thus, information has not been lost, only changed; which is fine by all physical laws.
This research, if correct, could be the solution to one of the biggest paradoxes encountered in modern physics. The work is freely available as a pre-print on the arXiv.org servers (must like mathematics to read), but has been accepted for publication in an upcoming edition of Physical Review D. The authors make it very clear what assumptions have been made in their work and what effects those may have. Although they feel that many of the assumptions will not significantly alter the final outcome, they admit that some could directly lead to the formation of an event horizon in a finite amount of time.
They also mention ongoing efforts to remove some of the assumptions that went into this work. The researchers are also quick to point out that a theory is not complete without an experimental verification. Since Earth-bound lab created black holes don't exist yet—the Large Hadron Collider may change that—the authors suggest that a sonic equivalent of a black hole, a dumbhole, may provide a testing ground for their theory. While it is not currently feasible to create such an event in a lab, the authors point out that one need not create a fully realized dumbhole. They say that one only need to create the beginning stages of collapse towards a dumbhole to observes the equivalent acoustic radiation. This acoustic "pre-Hawking" radiation would carry the sonic information of the sound that is falling into the dumbhole in a manner akin to losing quantum information to a black hole. If they're right, their theory should be experimentally verifiable.