Black Holes in a Tub and the Church of Unitarity

May 24, 2010
by Florin Moldoveanu

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Recently I attended the New Directions in the Foundations of Physics conference in Washington DC organized by the Foundations of Physics Group (University of Maryland - College Park, Johns Hopkins University, Georgetown University).

The talks were relatively long with enough time allocated for questions which allowed an in-depth understanding of the topics at hand. In the first morning, there were philosophical presentations about the early history of quantum mechanics, and while I am not an expert by any stretch in the history of this early period, I could understand for example how von Neumann's approach of introducing the Hilbert spaces was at that time superior to Jordan's approach (although the later C* algebraic approach stemming in part form Jordan algebras is arguably the better approach).

In the afternoon the focus of the conference switched to black holes and the relationship between entanglement and entropy.

Black holes: amazing objects. Any object falling in is erased out of existence in a finite amount of time. Not unlike falling off the edge of the universe. So where did the information about the falling matter go? Is it really encoded in Hawking radiation? In the absence of the ultimate theory of nature, we don't really know. But maybe we can perform experiments and ask nature instead.

Bill Unruh presented preliminary experimental direct observations of Hawking radiation of a "black hole". Since creating a black hole is completely beyond our current technological abilities, what he was doing was simulating the event horizon of a black hole by waves propagating against a flowing liquid which was passing over a submerged barrier. What was remarkable was that the wave measurements provide the Bogoliubov coefficients in field theory and to the degree that the model is correct one does observe the actual Hawking radiation which is many-many orders of magnitude smaller than the environment temperature of 300K. Bill informally reported three tentative experimental facts: (1) Hawking radiations _is_ thermal, (2) the radiation originates in vacuum fluctuations before the event horizon is formed, and (3) after the event horizon is formed, the radiation outside and inside are and remain correlated after they start to move away from the horizon, although there is no communication possible between them. (The report is preliminary work in progress and should not be quoted officially as the analysis is not yet complete.)

From this, Bill stated provocatively that the real puzzle of information loss is why people consider this a problem. As evidence he presented an argument about how coherence can be lost _with_ energy conservation. Historically, the main argument against information loss in black hole evaporation is that coherence cannot be lost without a change in energy. The temperature of a black hole is inverse proportional to its mass, and in the final stages of evaporation one sees quite an explosion. And if information is not conserved, from vacuum fluctuations, one would expect random black hole formation and evaporation and consequently random explosions should be detected all over the place.

The argument Bill presented was the (old) argument of heating a lump of coal with a laser: A laser starts in a coherent state, heats the coal which cools down and gives away random thermal radiation while is returning to its original state. So what do we have? Loss of coherence with energy conservation. But the counter argument was made from the audience that the information lost by the laser is actually encoded in the phonons in the lump of coal. Therefore this argument is not transferable to space-time itself, unless the vacuum state has a microstate structure able to hide this information. (If at this point you feel that this is similar in nature with Verlinde's entropic gravity proposal--described in this blog post and article--you are right.) To counter the phonon argument, Bill stated that the vacuum state should be unique and that measuring the actual information loss is physically impossible due to time-energy uncertainty relations.

Personally, I strongly disagree with Bill's argument. Why? Because information preservation and unitarity is such a cornerstone of quantum field theory that it is simply inconceivable it is not obeyed, and any alternative looks like using voodoo to explaining nature.

On the other hand, Bill's position is not insane at all. Let's draw a parallel between what happens in real life and what happens in black hole physics. Taxes and death are the only certain things. For the atheist, death does cause the soul to be lost and information is not conserved. But how the rest of society deals with it? Through a grieving process which "sets things in proper order" and allow us to let go and carry on. What would be the "grieving process" for black holes? It is the event horizon and the red shifting process which gradually turns off ("let go") the communication between us and the infalling objects. And despite our mortality and information loss in society, we are able to carry on our daily lives. So perhaps the doom and gloom picture of impossibility to create a valid quantum field theory with information loss is not true when the information loss occurs behind event horizons through "grieving" red shifting (no naked singularities). Do we really need the religious "immortal soul" idea to spare us descending into madness in our day to day activities? And do we need the church of unitarity under any condition? Hawking recanted and paid his information conservation bet which made Bill quip: Galileo recanted as well, we all know how these turn out over time. The answers may well be found in a tub of water.