Order is a slippery concept. It can mean several different things depending on what you’re talking about, and there are even multiple things it can mean in physics! Because its meaning can be subtle, the term is prone to misuse. I hope in this article to shed a bit of light on how we can understand how entropy can be seen as a measure of order in physics, and whether it can be applied coherently to the universe as a whole.

## Entropy and Order

The physical quantity which is often seen as synonymous with order is entropy. A system with low entropy is more ordered than a system with a high entropy But what actually is entropy, and why is it used as a measure of order?

An intuitive, but precise way of interpreting what entropy is as the number of particle arrangements (microstates) that produce the same overall structure (macrostate).

Consider something very mundane – like filing. Say you’re filing a load of papers, job applications perhaps, and want to organise them in alphabetical order by surname. We have two macrostates in this case: one in which the folder is alphabetically ordered, and one where it is not. In terms of microstates though, there are lots of ways the papers could all fit into the folder in any old order, but only one way of arranging them alphabetically. So we say that the unordered folder has a high entropy, but the alphabetically arranged folder has a very low entropy, it’s very ordered.

## Entropy and Earth

At this point you should hopefully be able to see why entropy is thought of as a measure of the “order” of a system. If we start thinking about systems in the universe, we see things with varying degrees of order. The Sun has a very high entropy. It’s a highly disordered system. The human body by contrast has a far lower entropy, and so is very ordered.

If you’ve heard of entropy before, you will be familiar with the infamous second law of thermodynamics, which states that:

2nd Law: In an isolated system, entropy must always increase or stay the same.

People often get worried about this in relation to life on Earth. If the order in the universe is always decreasing, then how is it possible for highly ordered humans to evolve over time? I’ve already addressed this important question in detail here, but I’ll go over the reasons briefly now:

The reason that complex life can develop on Earth is because the Earth is not an isolated system. In order to decrease entropy, one has to do work. This is the principle behind a fridge. A fridge keeps things cool (at a lower entropy), but at the expense of pumping out a large amount of hot air into the surroundings. The overall effect is that the contents of the fridge decrease in entropy, but the entropy of the surroundings increases by more. The overall effect is that total entropy increases, but in a certain region (the fridge), it can decrease. Fortunately for us, the Sun increases entropy so much that the decrease in entropy due to life on Earth is cancelled out, ironically the Sun plays the role of a fridge!

## Entropy and the Universe

Now that we have a good idea of what entropy is, and hence a physical notion of order, how ordered is our universe?

We can ask this question in two ways. Firstly we can ask whether things within our universe, like a human brain, is ordered. Life on Earth is by far the most ordered thing we’ve found so far in the universe. At the other end of the scale  black holes, stars and most celestial bodies are very disordered.

But there’s something that was far more ordered than anything we see around us today, and that thing is the Big Bang singularity itself. Since entropy must always increase, we can interpolate back to the beginning of the universe, and we find that in order to produce the kind of entropy levels we see in the universe round us today the original Big Bang singularity had to be ridiculously ordered. This is a problem that modern cosmologists are well aware of, but don’t yet have an explanation for – how come the original singularity is so ordered? What could have produced such an ordered initial state?

## Why the Universe isn’t Necessarily Ordered

While this is an interesting and legitimate problem in cosmology, it should be taken with a grain of salt. The term “order” is a very emotive word for theists, and it is at this point theists will pounce onto the conversation with: “The fact that the Big Bang was so ordered is proof that there had to have been an orderer, and this orderer is God”. But there are numerous problems with this assertion.

For a start, the second law of thermodynamics is a theorem from classical statistical mechanics. We don’t know much about the time close to the Big Bang, because our current laws of physics aren’t valid in such high energy environments, so it’s almost certainly the case that the second law of thermodynamics isn’t perfectly accurate at the time of the Big Bang either. Once we have a more fundamental theory of Physics, and a better understanding of entropy, which we can apply to early times, the problem may well disappear.

But the problem with this claim that I most want to draw attention to is the fact that there is no meaningful way of saying that the universe is ordered at all! There’s no objective measure of how ordered the universe is.

What theists want to argue is that the universe we live in is objectively ordered and that the presence of order is very good evidence of God’s existence. But although we have a good measure of what order is within the universe (entropy), and even though we know that the initial entropy of our patch of observable universe was much lower in the past, we don’t have any objective measure of order when applied to the universe as a whole. We simply don’t know if this universe can justifiably be called ordered or not, because we have no other universe with which to compare it!

If we knew of the existence of a multiverse, and could compare the entropies of initial states of different universes in the multiverse, then we would have a measure of “order of universes” and would be able to meaningfully say whether this universe was particularly ordered or not. Since this universe is currently the only one who’s existence we know about, we have no meaningful way to determine whether this universe as a whole is particularly ordered or not. It’s like there being only one lump of rock in the universe and calling it small – you have nothing to compare it to!

So when people tell you that the universe is amazingly ordered, just remember. The initial state of the universe was far more ordered than anything we see in the universe today, but that doesn’t mean we can meaningfully say that the universe as a whole is ordered.