Black-hole information

I recently stumbled upon a post by a blogger I really love who claimed that the black-hole information loss problem is the most overhyped problem in science, ever. This was very interesting to me: at last, some prominent figure of the physics community was going to set the record straight and recognize what I have long thought to be the truth concerning black-hole information. But as read on I realized that what the author believes is not that there is no real problem, but that the problem is actually unsolvable. I was truly amazed and shocked: people still don’t understand that there is no loss of information for the matter that crosses the event horizon of a black hole. The irreversibility of the process is still believed to illustrate the existence of a fundamental asymmetry with respect to the direction of time.

What the author suggested is that mathematical consistency alone is not constraining enough to allow one to identify the appropriate solution to that “problem” and that all the solutions which have been, or which will be proposed in order to address the issue are pointless, because we will not be able to carry out the experiments that could reveal which solution is right in the foreseeable future. But I believe that what is problematic is not reliance on logical consistency to assess the plausibility of some proposal for a solution to this or any other problem in fundamental theoretical physics, but the application of a mathematically consistent theory outside the limits where it is known to be physically relevant. It should be clear, indeed, that the real problem here concerns relativity theory, because this is where the fundamental irreversibility comes from (growth of event horizon, production of thermal radiation).

Thus, it is incorrect to argue that, given that the process of black-hole evaporation (by which the information about what fell into a black hole appears to be made irretrievable) is derived from standard quantum field theory and classical relativity theory, then it follows that quantum gravity has nothing to do with the black hole information problem. We already know in effect that relativity theory is not appropriate on the scale of microscopic elementary-particle processes and therefore what is truly incorrect is our use of a classical field theory to determine the outcome of a certain phenomenon that involves information about the microscopic state of the elementary particles that emerge from a black-hole event horizon. We know with absolute certainty that this is wrong and therefore it is really the classical nature of our current theory of gravitation that explains that there seems to be a paradox. As is the case for all thermodynamic processes, we are in fact allowed to expect with absolute certainty that the information about what happened in the past to those particles that crossed the event horizon of a black hole is contained in the microscopic state of the thermal radiation that later emerges from it and that none of the elementary processes involved is truly irreversible. The point with all this is that once we recognize those limitations, then it emerges that there is no paradox.

Given that measures of distance are contracted in the radial direction, towards the center of a black hole, it follows that from the viewpoint of an observer outside the object, everything that happens to the matter that crosses its event horizon actually happens on the surface itself. Therefore, the microscopic quantum-gravitational degrees of freedom on the surface of a black hole must contain information about the state of the matter particles which crossed its event horizon, even if this information cannot be communicated to an observer outside this surface before it is released as thermal radiation. The unavailability of this information for any observer not directly in contact with the surface of the object is merely a practical limitation which is attributable to time dilation and even if we do not yet have knowledge of how exactly information about the matter inside any surface is encoded in the microscopic state of the gravitational field on this surface, the existence of this information must be considered a consistency requirement, because when this surface is not an event horizon, the information can, in principle, be obtained through careful measurements performed on the quantum-gravitational scale. But we do not need to wait until we are able to perform detailed observations on the Planck scale to understand this and therefore it is misleading to argue that the black-hole information loss “problem” is basically unsolvable, because, in fact, current experimental knowledge and the constraint of logical consistency indicate that there is not even a real problem here.

In any case, it is certainly not useless to try to find out how it is exactly that a theory of gravitation that would obey the principles of quantum theory could allow information to be encoded in the microscopic (quantum-mechanical) state of the gravitational field, because even in the quantum-gravitational realm unavoidable consistency requirements would apply. In other words, most of the time, the problem is not that we rely too much on mathematical consistency, but that we do not apply the logical constraints imposed by what we already know of physical reality consistently and rigorously enough to all aspects of physical theory (which would actually allow to rule out certain mathematically motivated schemes like the original string theories and other such supposedly beautiful theories).