The Arrow of Time

Last week I explored the idea of time irreversibility in the universe. Our laws of physics are invariant over a T-transformation; whatever a particle does is not affected by whether it is moving forwards or backwards in time. Yet why do we still see an obvious ‘arrow of time’ in real life?

On the Earth there is an obvious up and down, but were you to be zapped into outer space, you would not be able to tell – all directions would appear the same. And the only reason why we could initially tell that there was an up or down is because there is a massive planet in our vicinity that acts as a reference.

The same applies to time, but this time the ‘reference’ is the big bang. The big bang is proposed to have a highly ordered state (and therefore a very low entropy), and due to the second law of thermodynamics, entropy must increase over time. This gives time a direction, i.e. the same direction as that in which entropy increases. The direction of time in which entropy increases is known as the thermodynamic arrow of time.

The thermodynamic arrow of time is very significant as it underpins the majority of the other arrows of time. Surprisingly, this implies that time is based on entropy as opposed to the other way round, and it’s possible that if entropy remained constant, there would be no strong arrow of time. However the question of why the big bang had a very low entropy to start with remains unanswered, which is why we don’t yet fully understand the thermodynamic arrow of time (or any arrow of time for that matter).

How about why we remember the past but not the future? This links to the psychological arrow of time. There is a strong argument to show that the psychological arrow of time necessarily points in the same direction as the thermodynamic arrow of time, although it isn’t perfectly well-grounded as our knowledge of the perception of time in the brain is not advanced enough.

If our brains are anything like how a computer works (which is not a completely unreasonable assumption), then we need to put in energy to generate and store a memory. This energy will dissipate as heat into the surroundings and thus raise the entropy of surroundings, showing that the direction in which you remember the past is the same direction in which entropy increases. Or for a computer, at least. And so in order to have a clear perception of time, there needs to be a strong thermodynamic arrow of time.

There is another arrow of time that we call the cosmological arrow of time, which is the direction of time in which the universe is expanding. We can use the anthropic principle to argue why the cosmological arrow of time and the thermodynamic arrow of time point in the same direction, and how we can conclude that we are currently in the expanding phase of the universe.

The anthropic principle states that the fundamental properties of the universe that we observe are as so because we exist to observe them. In other words, our universe has the right conditions to allow conscious life to rise, and if the conditions were different, we wouldn’t be here to observe those ‘different’ conditions.

In order to survive, humans must consume food and generate energy. This is essentially converting an ordered form of energy into a more disordered form (yes, you are correctly anticipating entropy!). Humans must exist in a universe where entropy is increasing, and entropy only increases in an expanding universe.

I guess that in the end, there is one physical law that violates a T-transformation, and that is the second law of thermodynamics. However entropy is only visible on a macroscopic scale, which is why processes such as friction make time irreversible. And the reason why we can be here to ask all these questions is because entropy is increasing. All hail entropy.

Yanhao