Once Before Time - Martin Bojowald [123]
It may sound surprising, but the only alternative to directed time, which would make space and time play no different roles, is the impossibility of motion of any kind. Having time but being able to decide arbitrarily between stepping toward the future or the past is impossible; one would literally be paralyzed, unable to choose. For what would be the reference for a step back in time? What happened to me five minutes ago is the influence of the world (including my own body) on myself, when I was in a certain state characterizing my age five minutes ago. In different states, other acts occur, perceived by us as the flow of time since the mind is influenced by its own body to partially memorize past states. Time itself is an abstracted quantity: It is a parameter, in its special form chosen conventionally and used to determine motion; motion itself is fundamentally relational and describes a complex interplay between different things, not between a thing and time. In the same way, the psychological perception of time as the organizing principle of memory contents is ultimately grounded on an evolutionarily buttressed convention whose destruction would render impossible any recognition of motion. If a change of time’s direction were to be allowed, this convention would be toppled. None of these relational states can be changed by conscious choice; but that would be required for a reversion of time subject to the will, truly constituting a return to past and potentially remembered states.
When attempting to explain the directedness of time, one is ultimately led to a problem much older than the relativistic theories of space and time: the problem of the existence of motion and change, a problem that was vexing philosophers as far back as Parmenides. He saw only one solution: a complete denial of motion, called by him pure illusion. Despite the obvious difficulty of reconciling this view with the most elementary observations, this hypothesis retained its influence through the centuries—starting with Parmenides’ immediate successor, Zeno, and the atomists Leucippus and Democritus, then via philosophers such as Schopenhauer to physicists like Schrödinger. The problem is still open from a philosophical viewpoint, but here we are already treading outside physics, whose task it is to describe change and motion, thus accepting them as already given.
A final chance to speculate about turning time’s arrow around is sometimes seen in quantum cosmology. Again for mathematical reasons, it is often useful to take the volume of the universe as a parameter to describe temporal change relationally. This time surely progresses in an expanding universe, but what happens when the universe one day stops its expansion and then collapses? Its volume would start to decrease and develop backward—and with it perhaps time. This hypothesis was first postulated even before the advent of quantum cosmology, by Thomas Gold in 1958.
Such a behavior of the volume of the universe is easily possible in general relativity, even though current estimates of cosmological parameters, as they appear to be established for our universe, may not make it likely. Does time then turn around at this point of inversion,