Once Before Time - Martin Bojowald [113]
The fundamental phenomenon is once again the discreteness of time. Not all possible points in time are allowed; instead, time jumps in fixed, precisely controlled steps. Although the step size is very small—playing hardly any role outside the black hole, at the horizon, or even in most of the interior of large black holes—it does become essential near the singularity. In contrast to the continuous time of general relativity, which is doomed to stop after a finite interval and to break down with the theory itself, discrete time keeps on running. The elimination of some points in time on microscopically small scales implies the occurrence of a new, much wider, macroscopic time frame beyond the classical singularity of a black hole. In a Penrose diagram, this is represented on the left-hand side of figure 28. For the extension of time, it is crucial that the singularity inside a black hole is a point in time but not, like the center of a star, a point in space. Only this way can it be possible for discrete time to jump across the singularity and unlock a new world in the future.
We have here one of the important realizations of consistency, guiding theoretical developments in the absence of direct observations: Precise details of the classical theory play a decisive role for the concrete mechanism of the quantum theory, extending it in a way that could not have been foreseen while quantum gravity was set up. Black holes in general relativity, as they arise from the collapse of matter, are distinguished by a point-in-time singularity behind the horizon, penetrated by the discrete time just like the big bang singularity of cosmology. If the singularity of a black hole were a point in space like the center of a star, time would run parallel to it and have no chance of piercing and eliminating the singularity. Naked singularities would persist in quantum gravity—unless they were already forbidden by cosmic censorship in general relativity.
28. The two possibilities of connecting the singularity-free black hole interior of quantum gravity with the exterior. Either there is a branching point to a daughter universe beyond the dash-dotted singularity, or the interior simply sits in a space-time that surrounds it completely.
Classical characteristics and those of quantum theory play important, closely entwined roles, illustrating the elegance and consistency of the ideas involved. Quantum gravity is effective and unforgiving in the elimination of dangerous singularities, but at the same time economical when it comes to singularities already dissolved classically. The fate of singularities in quantum gravity, despite that theory’s current incompleteness, provides a test to be taken seriously, one that has been passed in the form of early mathematical derivations. The more such passed tests pile up over time, the stronger one’s trust in the theory becomes. Should a test fail, the first recourse would be to improve the theory in such a way that this test can yield a positive result while the earlier test results remain valid as well. Should this not be possible or should the modification make the theory look too artificial, one would eventually drop it altogether. Even without observations, there is thus strong selective pressure on theoretical speculations.
If the singularity as a point in time is now eliminated, there is a time with space behind the singularity or, seen from outside the black