Once Before Time - Martin Bojowald [142]
DYNAMIC INITIAL CONDITIONS: STATELY LAWS
MANTO: I stand still; around me circles time.
—GOETHE, Faust
While a strict derivation of quantum cosmology from a complete theory of quantum gravity is still lacking, there are, by now, numerous indications of important phenomena. In a concrete way, loop quantum gravity provides equations extending those of general relativity. Though not yet fully formulated, they have been tested theoretically in a variety of ways. In this process, different corrections to the classical equations have crystallized and can be considered characteristic of such theories of quantum gravity. We have already seen implications for the elimination of singularities at the big bang as well as in black holes; now we shall turn to the question of uniqueness.
Equations of loop quantum gravity are not yet available in full generality; its effects can rather be seen in different models. An analysis tells us that indeed conditions on the wave function of the universe automatically arise. In their details, they are closest to a mixture of DeWitt’s condition and the no-boundary condition of Hartle and Hawking. The problems of DeWitt’s original condition are avoided since the equations deviate from those used by him owing to quantum corrections, including the important repulsive forces at small sizes of the universe. Loop quantum gravity thus offers a possibility to walk the path proposed by Conradi and Zeh in a systematic manner. The similarity to the no-boundary condition then shows up in the further course of the wave function farther away from the singularity, where its height increases in both cases. By describing the wave function as the tail of a tunneled universe, the tunneling condition, by contrast, would lead to a wave function of a different shape, its size decreasing at larger distances from the wave function’s bulk situated in “nothing.” Older proposals can thus clearly be distinguished from one another and made concrete.
In contrast to the old conditions, there are two crucial differences in loop quantum cosmology. First, the big bang singularity does not occur as a beginning or a boundary of the universe, but is merely a transitory phase—one of extremely high density and violence, but transient nonetheless. And yet this classically singular phase has implications for the wave function and is responsible for the constraints it is subject to. Second, these constraints are no longer imposed as physically motivated conditions; rather, they follow from the quantized Einstein equations themselves. Even though the exact form and strength of the conditions—whether there is always a unique wave function or possibly a constrained but larger class—is not yet clarified, an outlook to something very new in physics is nonetheless offered: a system whose theoretical description is not split into dynamic laws of nature and initial conditions in the hands of a physicist, but where initial conditions follow, as it were, dynamically, as a consequence of the laws. That alone would be the exemplar of a cosmology, the realization of the dream of an ultimate theory explaining not only the temporal course of the universe but also the fact that there is only a single universe.
Here, on the most elementary level of the wave function, we are led back once again to the singularity problem. In spite of the existence of repulsive forces to prevent the collapse of the universe into a singularity, a regular behavior of the universe’s wave function is not yet guaranteed. Repulsive forces build up barriers that are too high for the universe to surpass in its collapse; instead it is, once it has collapsed, pushed back at a certain minimal extension to reexpand. This is the situation shown to us by effective forces of loop quantum cosmology. But a quantum mechanical wave function is rarely impressed by a barrier, through which it can simply tunnel. We have so far