Deriving the Arrow of Time

Humanity has long struggled over the nature of time. In the last century, physicists were shocked to discover that the arrow of time cannot be derived from the laws of physics which appear perfectly symmetric. For every solution for t, there seems to be an equally valid solution for -t (except in a few cases involving the weak force in which case the symmetry is more complex, involving charge, parity and time)

At first glance that looks puzzling. But after a few years reflection, most physicists agreed that it’s perfectly possible for symmetric laws to give rise to asymmetric phenomena. Physicists have identified a number of such asymmetric phenomena that represent “arrows of time”, says Claus Kiefer at the Institut fur Theoretische Physik in Cologne, Germany.

Perhaps the most famous is the thermodynamic arrow of time in which the entropy of a closed system must always increase. But there is also a quantum mechanical arrow of time in which a preferred direction of time is determined by decoherence and a gravitational arrow of time in which the preferred direction is determined by gravitational collapse.

“What is peculiar is the fact that the time direction of the phenomena is always the same,” says Kiefer. It’s almost as if the arrow of time were predetermined in some way. “The question raised by the presence of all these arrows is whether a common master arrow of time is behind all of them,” he asks.

What master law might be responsible? Kiefer’s conjecture is that the direction of time arises when quantum mechanics is applied to the universe as a whole, a branch of science known as quantum cosmology.

Central to this idea is the Wheeler-DeWitt equation that describes the quantum state of the universe as a whole, including both its gravitational and non-gravitational states.

This equation does not contain any parameter that is equivalent to our classical notion of time. In the Wheeler-DeWitt formulation, spacetime does not exist in any classical sense and particles do not have traditional trajectories in spacetime, just as particles do not have traditional trajectories in ordinary quantum mechanics. Instead all the information about the universe is encoded in its wavefunction

So how might an arrow of time arise? While the universe is considered homogeneous to the first degree, there is no preferred direction of time, says Kiefer. But he shows that when small inhomogeneities are taken into account, an asymmetry arises in this wavefunction.

He even says that with slight elaborations, this idea could be applied to an arrow of time in the multiverse.

What he fails to do, however, is provide a way of testing this idea. There is no way of determining experimentally whether the Wheeler-DeWitt formulation is really the origin of the arrow of time.

Of course, that’s a common failure of most thinking about quantum cosmology (not to mention cosmology in general). And until physicists find a way to prune their ideas about time with experimental data, we can merely marvel at their creativity.

Ref: arxiv.org/abs/0910.5836 : Can the Arrow of Time be Understood from Quantum Cosmology?