Once Before Time - Martin Bojowald [139]
THE WAVE FUNCTION OF THE UNIVERSE:
GRASPING EVERYTHING
At first glance, quantum cosmology may look like a harmless application of quantum mechanical rules to the whole universe—especially if the cosmological principle of homogeneity is appealed to, making one consider only the total volume but no finer details. Quantum mechanics was originally developed for atomic physics, but it soon turned out to be a much wider framework that could encompass all physical processes. Not only are emission spectra of atoms explained by quantum mechanics, but also the rich and various phenomena of solids, for instance, electric conductivity in metals. Even astrophysical objects, most importantly white dwarfs and neutron stars, can be understood only by means of quantum physics. From here, applying quantum theory to the whole universe is not too long a step away.
On closer view, however, this ultimate step does have a special flavor. Here, at the outermost frontier of scientific knowledge, the remarkable but rather strange properties of the quantum mechanical wave function become a severe problem. After all, the wave function is not directly observable but instead, as it were, keeps a record of all information possibly gained from measurements on the system it describes—with all the limitations arising from uncertainty relations. It is an administrator with built-in ignorance. In the interpretation accepted in the course of time, the wave function describes accessible properties of the quantum system as it was prepared by an experimenter, who now begins to undertake measurements from outside the system.
Such a viewpoint can be applied without any problems even to “large” systems such as a piece of metal or a whole neutron star. A metal physicist does not stand in the metal, and an astronomer is far away from a neutron star. A cosmologist, however, cannot be separated from the object studied: the universe. In contrast to all other examples of quantum physics, quantum cosmology must always grapple with an observer who is necessarily a part of the investigated system. It is impossible to split quantum cosmology into a wave function on the one hand and an observer measuring its properties on the other. There is only a wave function of the universe, supposed to describe everything including us as observers (or theorists).
In full generality, all this information is certainly impossible to compute, and one must rely on extreme simplifications and approximations to make any progress at all with such questions. But in all these models, one can never avoid eventually dealing with the peculiarity of an observer within the system—an all-encompassing wave function that, in a sense, measures itself. One can occasionally find a possible escape route in the suggestion to assume a superordinate observer who would powerfully watch the whole universe and its wave function, all at once and from outside. One could then use the usual rules of quantum theory at least without mathematical problems; but even so one does not fundamentally avoid the question of what we—as observers in the system, not as external observers—can measure about the wave function of the universe.
While of general nature, these questions play a role especially for the problem of uniqueness and quantum gravity. For the desire for a unique solution starts from the fact that we as observers in the universe can see just one universe. Were we to pose this question for a superordinate observer, we would have no indication whatsoever how many universes could be seen. If an imaginary superordinate observer can see our universe as a whole, why not others, too, or even all possible ones? Although such observers are sometimes assumed in physical investigations—mostly as a last (cheap) refuge from daunting conceptual difficulties—they have no relevance for physical questions. Physically, only what we can perceive