Why time keeps going forwards

This week New Scientist has an article entitled Why time keeps going forwards, in which the reason why time flows in one direction (i.e. from past to future) is explained.

Why is this a puzzle? The problem is that the basic laws of physics, which are so successful at explaining experimental results, are written in a way that makes no distinction between time going forwards and time going backwards.

What does that mean? It means that if the laws of physics allow something to occur, then they also allow the the time-reversed version of that "something" to occur (technically it's a bit more complicated than just time-reversal, but the essence is right).

But that's crazy! If a tea cup falls on the floor then it breaks, but we never see the reverse chain of events occurring. So the laws of physics must be wrong.

Not so! The key point to realise is that the following two items are not the same thing:

1. Equations that describe how things behave in general.
2. Solutions of those equations that describe specific instances of how things behave.

The solutions must be consistent with the equations, and they must also be consistent with any additional conditions that are imposed on them.

In the case of the flow of time, the asymmetry between the forwards and backwards flow directions is caused by the imposition of an initial condition, in which the universe initially has a highly ordered state. Of all the possible solutions to the equations of the whole universe, only an extremely small number of solutions that respect the highly ordered initial condition are allowed. These are exactly the solutions that we (i.e. our brains) interpret as having a forwards flow of time.

The phrase "flow of time" is a subjective quantity that we can use to summarise the asymmetric behaviour of systems generally. At the level of the whole universe the flow of time is a reliable quantity that goes on and on seemingly for ever, because human time scales are much shorter than the age of the universe. At the level of a small system that we prepare ourselves in a highly ordered initial state and then allow it to evolve (i.e. rather like a mini universe), such as gas atoms in a box with an initial condition that they are all in one corner of the box, there is a clear flow in one direction away from the initial condition as the gas atoms spread out inside the box. However, the small system behaves differently from the whole universe, because very soon the gas atoms come into equilibrium and uniformly fill the box, after which the gas behaves the same way whether you look at it running forwards or running backwards in time, so the flow of time as defined by the behaviour of the gas atoms no longer has a clearly defined direction. From the point of view of a gas atom there is no flow of time when the gas is in equilibrium; that is why "flow of time" is subjective.