Once Before Time - Martin Bojowald [110]
Black holes would constitute gigantic information shredders, representing a big problem in quantum theory. Although one does not know the precise equations describing the complete quantum state or the wave function of a black hole, one can show that no equations as they otherwise appear in quantum theories can lead to such an extreme destruction of information. Here it is important to emphasize that the information is not just difficult to access; it cannot be reconstructed even in principle. If a book is burned, the information it contains is no longer readable, but with subtle techniques it may still be recovered from the charred pages. Information destruction in a black hole is much more thorough: There are simply no information carriers by which lost data could be saved.
Perhaps the problem is more tangible when formulated by means of conserved quantities. Certain numbers in physics, characterizing the total matter content of the universe, are not allowed to change in any known process. An example is energy, which is also constant in the Hawking process. Other conserved quantities are electric charge, or the total number of protons, neutrons, and heavier partners of those particles, called the baryon number. Their antiparticles count negatively, keeping the whole number unchanged during pair creation, for instance of a proton and an antiproton. Now, nothing prevents us from sending more protons than antiprotons down into a black hole; this is likely to happen anyway, since as far as we know, there is much more matter than antimatter in our universe. A black hole would then contain a surplus of protons. Hawking radiation, on the other hand, treats matter and antimatter democratically, holding that it is just as likely for the particle half of a particle-antiparticle pair near the horizon to fall into the black hole and the antiparticle to escape as radiation as vice versa. (Electric charge might distinguish the partners, by preferred attraction or repulsion, but black holes are not strongly charged.) Should the black hole evaporate completely and leave only Hawking particles, one important conservation law would be violated.
One can solve this problem only by assuming a stable remainder of the black hole at the end of evaporation. But what object could this remainder be, and why should evaporation then stop? Only quantum gravity phenomena can help, for general relativity allows no end to evaporation and no remainder either. Once matter has collapsed, the classical theory admits only the possibility of black holes with a Hawking-evaporating horizon. A compact core left after evaporation could be explained only by a quantum theory of gravity. But if quantum gravity, as often expected, becomes relevant only at the scale of the Planck length, this residue must be tiny. The question then arises whether it can, even if it is stable, shelter a sufficiently large part of the fallen-in information to make the process consistent with quantum theory.
As with the big bang singularity, we cannot evade quantum gravity and an investigation of its details. Again, we are dealing with a problem of time: Space-time has a border that, behind the horizon, does not grant enough time for, say, light to escape. Discrete time can eliminate the big bang singularity, providing additional time beyond it;