Once Before Time - Martin Bojowald [56]
All this happened before the introduction of Ashtekar’s formulation of general relativity and of loop quantum gravity by Rovelli and Smolin, and so this form of quantum cosmology was not based on discrete space. How, precisely, space on small scales looked in this theory was largely unknown: The theory could reliably be formulated only for the homogeneous spaces of cosmology, but not more generally. At the end of the twentieth century, the prevailing belief among researchers, aware of the old quantum cosmology as well as of loop quantum gravity, was that these are two sides of a single theory: For solutions without any symmetry, one would have loop quantum gravity with its complicated construction of space from discrete building blocks. But when space is washed out by enforcing symmetry, affording a view of it only on scales much larger than the extension of spatial atoms, one would obtain the old quantum cosmology. A further analysis of the symmetrized equations of loop quantum gravity would have been futile, for it could not have resulted in anything new. Indeed, leading figures in loop quantum gravity at that time had repeatedly advised me against wasting my time by further following the symmetrization.
A direct reproduction of the old quantum cosmology as the symmetrical special case of loop quantum gravity would, in the context of the singularity problem, be devastating. If the old theory were the unavoidable description of cosmological space-times in quantum gravity, singularities could not be removed, for this problem remained unresolved: As a possible quantum theory of the universe, quantum cosmology as developed by Wheeler and DeWitt does lead to a wave function and quantum theoretical uncertainty. But its washed-out wave packets simply run into a singularity comparable with the classical one. There is still a point in time when—disregarding the unavoidable uncertainty—the volume of the universe vanishes and its temperature diverges. Nor can the quantum cosmological equations of old, like Einstein’s, withstand this situation: They lose their mathematical validity, keeping shrouded what happened at the big bang.
In retrospect, the explanation of this failure is simple: The initial version of quantum cosmology introduces some quantum effects, but it hesitates before the decisive step. It overlooks the discrete nature of space and time, as later demonstrated by loop quantum gravity. Near the singularity, the behavior changes slightly compared to general relativity, but not crucially so. Only loop quantum cosmology was able to highlight this fact, and to provide a concrete physical mechanism for preventing singularities.
To see all this, one must first solve the equations of loop quantum cosmology, a seemingly difficult task. And yet it did turn out to be possible; this is where chance entered the game. After I had constructed the symmetrical formulation of loop quantum gravity, or loop quantum cosmology, for my Ph.D. degree with Hans Kastrup at RWTH Aachen, Germany, I was for some time distracted from its equations. In 2000, I was moving to Pennsylvania State University, where Ashtekar had offered me a postdoc position. (He did so even though he was then among those not convinced of the promise of loop quantum cosmology. After a great deal of explaining and persuading on my part,8 he is now vigorously using loop quantum cosmology in his own research and has contributed to several recent developments in the field.)
After the move, I had to return to work, but was no longer familiar with all the details. In particular, I had briefly forgotten the reason for the apparent