Once Before Time - Martin Bojowald [60]
In contrast to quantum cosmology, whose time is passing discretely at a fundamental level, an hourglass only measures time discretely. Choose more finely grained sand, and time would be measured ever more continuously. The graininess is naturally limited by the atomic structure of matter, but other methods, such as modern atomic clocks, allow much more precise time measurements than are possible with the falling time of sand grains through an hourglass’s opening. With these technologies, one can further subdivide the time steps. But at the level of the quantum theory of space-time, all attempts to divide units of time any further reach a final limit. There is literally nothing between two successive atomic points of time in the discrete lattice of quantum gravity.
At the level of a discrete structure of time, the prevented big bang singularity is connected with a further phenomenon: Time before the big bang implies a reversal of spatial orientation. It is as if the history of the universe before the big bang would, viewed from the present, have happened in a mirror. A right-handed person who survived the big bang would thereafter be left-handed. Space is inverted on itself, like a sphere turned inside out. Here, the collapsing universe resembles the surface of a deflating balloon. After some time, the rubber would collapse airlessly, ending the process just as the classical collapse of a universe would end in a singularity. But if we assume that the rubber pieces could somehow penetrate each other in an uninhibited way, the balloon would reinflate after the collapse. If, moreover, the rubber simply follows its initial motion by inertia, the former inside must now point outward: Orientation reverses. In the same way, spatial atoms penetrate one another at the big bang and invert space.
How is it possible that the universe avoids total collapse into the nothingness of space, and yet inverts itself? Would it not be required for space to shrink to a point at the moment of inversion, or at least be squashed down to vanishing volume, if the collapse happens anisotropically? Also here, the discreteness of time, combined with other key properties presented by quantum theory, is crucial. The balloon does not deflate continuously but in a jumpy way, much like a movie made with a finite number of frames. It turns out that the elementary dynamics of loop quantum cosmology, which already gave rise to the discreteness in the form of having only finitely many frames, automatically takes out the one that would correspond to a completely collapsed balloon. Even if one tries to arrange the time steps in such a way that time zero, when the full collapse is reached, would be included as a frame, that frame is automatically detached from the rest and does not cause a singularity. The resulting movie shows a deflating balloon, that never collapses completely and yet inverts itself and reinflates.
Finally, in addition to discrete time, there is a further mechanism causing a repulsive force—a kind of double insurance by quantum theory against total collapse into a singularity. Not only does the space-time lattice show clear deviations from the known macroscopic behavior at small distances, but matter energies in such realms also behave differently than expected classically. In this context, it is useful to remember the behavior of black body radiation, as explained by Planck: According to classical expectations, its energy density should grow without bounds at small distances, presenting an example