Clock dependence and unitarity in quantum cosmology

Tuesday, Mar 22nd
Lucía Menéndez-Pidal, Nottingham University

Clock dependence and unitarity in quantum cosmology
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By Jorge Pullin, LSU

In ordinary physics, time (and space) are given once and for all. They are "background" quantities that do not evolve. In theories of gravity like general relativity, where one describes gravitational effects not as the result of a force but as a deformation of space-time, things are different. To begin with, unless one considers a concrete gravitational configuration (a concrete space-time), time (and space) simply do not exist. Even after considering a given space-time, to interpret it as "an evolution" of space (and matter) as "a function of time", requires some care, especially when one is considering the quantum version of things. The most obvious procedure is to consider some variable of the problem, like the value of a matter field, and use it to "keep time". Some such choices can obviously be very bad. For instance, if one chooses the position of a rock that does not move as one's "time", the resulting "evolution" of what one is trying to study will not be something easily recognizable. Even if one makes "judicious" choices, it is not at all clear that the resulting evolutions can be considered physically equivalent. Difficulties are further compounded by details of how the Einstein equations operate.

This talk considered these questions in the simplified setting of homogeneous cosmologies, where spatial dependence is very simple, allowing to make calculations explicit and controlled. Even in this simplified setting, the talk showed there are several subtleties. One of the central properties of ordinary quantum systems, called unitarity, that essentially implies that information is not destroyed, is not automatically guaranteed. In loop quantum gravity applied to cosmology (loop quantum cosmology) the Big Bang singularity usually is eliminated and evolution is regular where in classical general relativity infinities appear. The talk showed that this feature is not guaranteed and depends on the choice of time made.