Annual Question:
In 1974, Stephen Hawking proved that black holes were not black. Rather, quantum mechanics required that black holes would slowly lose their mass via a really neat mechanism: the gravity of a black hole would create a pair of particles outside the black hole, one particle with negative mass and the other with positive mass, and the former would fall inside the black hole, and the latter would move away from the black hole. The net effect was to decrease the mass of the black hole, and its mass would go to zero eventually.
Hawking realized that a zero-mass black hole was a big no-no, because such an entity could only be a naked singularity that completely destroyed the information inside the black hole. One of the fundamental principles of quantum mechanics—the same theory that tells us black holes evaporate—is “unitarity”, which means that information is conserved. But if a black hole destroys information in the final stages of its evaporation, then information cannot be conserved. Unitarity would be violated if a black hole were to evaporate completely.
Hawking then made a mistake: he argued that we have to accept a violation of unitarity in black hole evaporation. But unitarity is a really fundamental principle of quantum physics. Unitarity has many implications, one of which is that if unitarity is violated, so is the conservation of energy. And a little violation of unitarity is like being “just a little pregnant;” it has a tendency to get larger, very much larger. Leonard Susskind of Stanford University pointed out that a tiny violation of unitarity would give rise to a disastrous positive feedback of violation of energy: if one were to turn on a microwave oven, so much energy would be created out of nothing—conservation of energy does not hold, remember—that the Earth would be blown apart!
Obviously, this cannot happen. Information and hence energy must be conserved. But many black holes have been detected, so they must evaporate. How is this dilemma to be resolved?
There is an obvious resolution, namely that all observed black holes are the mass of the Sun or larger, and such black holes will last billions of trillions of years before they approach a naked singularity. What if the universe came to an end in a Big Crunch singularity before any black holes had time to evaporate completely?
This resolution of the black hole evaporation dilemma has a host of fascinating implications. First, it means that the Dark Energy, whatever it is, will eventually turn off. In an ever-accelerating universe, there will be no Big Crunch singularity, and all black holes will eventually evaporate.
Second, the great Israeli physicist Jacob Bekenstein—the man whose work suggested to Hawking that he should investigate the possibility of black hole evaporation—has proved mathematically that if event horizons exist, then the entropy of the universe must approach zero as a Big Crunch singularity is approached. But the Second Law of Thermodynamics says that entropy can never decrease, much less approach zero at the end of time. Thus, if the Second Law holds forever—which it does—then event horizons cannot exist. The absence of event horizons can be shown mathematically to imply that the universe must be spatially finite.
The absence of event horizons also incidentally, almost in passing, resolves the problem of how the information inside a black hole gets out: if there are no event horizons, there is literally no barrier to getting out. We should keep in mind that the assumption that a black hole is bounded by an event horizon is just that: an assumption, not an observed fact. If the universe ends in a Big Crunch, the information inside a black hole just would not get out until near the Big Crunch. No observation today can show that the information is forever bound to being inside the black hole. A claim that event horizons exist is like a guy’s claim that he is immortal: one would have to wait until the end of time to confirm the claim.
So by merely accepting the obvious resolution of Hawking’s Dilemma, and applying the standard laws of physics, we infer that the universe is spatially finite, that the Dark Energy will eventually turn off, that the universe will end in a Big Crunch, and that event horizons do not exist. Various physicists have pointed each of these facts over the past decade, but these implications seem to have escaped the science journalists. Eventually, the information will leak out. Hopefully before the end of time.
