In Physics, most processes are time reversible. That might seem like a really strange concept, but it’s fairly easy if you consider the example of dropping a book. You convert gravitational potential energy into kinetic energy which is then dissipated as heat and sound (generally) when the book hits the floor. Whilst this does not actually happen – what if all that dissipated sound and heat energy was focused in reverse (from the original sequence of events), with the same point of action on the book? Well the book would have precisely the right amount of energy to return to the original place it was dropped from, which would be quite wonderful to watch. Surprisingly no physical laws are violated by the process I have just described – you can go back and forwards and the universe does not break. Well almost – there is a big exception when it comes to reversibility (known as time symmetry) which is entropy. Entropy requires the property which is most excellently named, the arrow of time.
Within a closed system entropy can increase but never decrease, according to the second law of thermodynamics (don’t worry about that (yet)).
Entropy is the level of disorder – but that definition can lead to some misleading ideas. Sometimes it is easier to think of it as being the tendency for things to wander over time. I hate to use this phrase, but it is a tendency towards randomness. Anyone who has looked after more than one child will tell you they have a tenancy to disappear in increasingly random directions – this is kind of the idea! There are many crude examples that illustrate this point, so I will give another one here but should caveat these examples are not actual entropy changes, rather a metaphor for randomness in the system to help explain the point. Take the pyramids in Egypt – and perform a thought experiment where the pyramids were not attacked by grotty tourists but instead crumble naturally over time. We fast forward to say 2416 and all we have left is a big pile of crumbled pyramid. If I asked you to sit and wait until the process flowed the other way and reassembled into a pyramid how long would you wait? If the answer involves more than a second you are either in the wrong place; or place far too much faith in people on the internet. The disorder of the system goes one way – a tenancy to crumble.
Often when people think about the principle of entropy, and a system becoming increasingly random over time with no reversibility they point to examples where this logic is flawed. The formation of a crystal is the single best example – a lovely ordered crystalline array in which over time the arrangement becomes more and more regular. It really is very special if you ever get the chance to watch a sped up video. The key difference is that this is an open system – there is an environment around the crystal to which it is open (i.e. the system is not self contained in some imaginary sealed box) so the law need not hold as described above. As we stated the law is for closed systems. So whilst yes you are seeing a reduction in the entropy for the crystal, the poor environment takes the hit with entropy increasing. Overall the second law of thermodynamics has been maintained on the macroscopic scale.
Now before someone of knowledge reads this and calls me up on it – let me highlight that this isn’t a law in the most regular of senses. Do another thought experiment where you place two molecules in a box and leave them on the left hand side. Say there were three possible positions for each molecule – left, center and right. You start with LL and expect entropy to increase as they follow the arrow of time and take one of the other 8 arrangements – although there is nothing preventing the original arrangement. There is actually a 1 in 9 chance you would find them back in their original starting place at any one time, so if 9 people did the experiment 1 might conclude the second law of thermodynamics is totally flawed! But relax – the law of large numbers makes this a law, in the systems of interest to us everything will works the way it should. When you talk about systems with say a mole of particles, you are quite safe to state the increase in entropy as a law; you can try and re-perform the thought experiment with a mole of particles, the numbers will get ugly.
So what is the point of all of this post? The most interesting application of this is the fact that the universe itself forms a closed system in which entropy can increase but not decrease. This is the descent into chaos in which we are all trapped. What’s more, as the only physical process with an arrow of time it may well be the very reason that you cannot remember the future. What started as a rather dull look at 19th century thermodynamics has transformed into a beautiful butterfly. Quiz question; entropy in a black hole, high or low? No peeking.
(I watched interstellar last weekend). The answer is high – very very high, which I hope is what you would expect. Don’t worry if not however; intuition and black holes often don’t often go hand in hand. In fact, nearly all of the entropy in the universe is holed up in a singularity. Whilst you can identify micro-systems within the universe which are open and the second law of thermodynamics is invalid, the sum of it all is a big closed system in which the amount of disorder must be increasing with time. This is the reality we have in our universe.
I have stated the above about fact – but it is actually subject to some fairly current debate. In the most recent advances in Physics there are some mutterings that there may be mechanisms by which the arrow is violated – in a very strange way whereby any trace of it would necessarily be erased from human detection. This is of course highly speculative, however it does have the feel of something we are yet to fully understand. Stephen Hawking does believe that if entropy were to run backwards, as far as we were concerned time would also be running backwards. If we are to take this view point (which is generally accepted) then as the only time asymmetric process we know of should be the very thing that gives time the illusion of flowing in the direction it does (side note: you need to adjust the definition of a flow, because a flow requires time itself to be a flow. Confusing). The core reason that remember the past but not the future may well be the simple fact that entropy was lower in the past but is higher in the future fixed by the arrow of time – rather than this human construction we have invented so it fits inside our brains better. We must fit to nature, nature will never fit to us.
There is an argument that states a thermodynamic arrow of time is essential for life to develop. If you are a supporter of the anthropic basis you might like this as it must be so because if it were not we wouldn’t be here to question it; as discussed in this post. I wouldn’t like to start an argument because I don’t necessarily disagree with the logic I just don’t think that this is the full answer. I do of course agree we must for put the thermodynamic arrow of time of the list of factors that allows our universe to be in existence. Without its presence you wouldn’t be able to do so many of the things you need to do in order to sustain life as we know it – converting food to energy is a good example. It feels like the arrow of time will be a focus in the coming years, as our understanding of the universe just like entropy increases with time.