Why must we follow time’s arrow?

An analysis the significance of entropy as an obstacle to time travel in a macroscopic world

By Luke Kurowski-Ford

The concept of an ‘arrow of time’ is very instinctive. It matches what we have experienced since our first moments in this world; the past is always behind us, immutable, and the future always ahead, a constant mystery. But why is it that the arrow is so uncompromisingly fixed forwards? Why are we unable to change the direction of the arrow and travel backwards in time? A world moving backwards in time would behave how a video plays when it is rewound. It would be a very strange place to live; there would be numerous events that would seemingly defy the laws of physics, such as a pile of bricks spontaneously rising to form a block of flats or an apple suddenly leaping up and attaching itself to tree branch. While these events may seem unlikely, they are not impossible. For an apple to jump back, heat energy around the apple would converge into it and be converted into kinetic energy. Under Newton’s laws of mechanics, it would be feasible for a world to exist where time was reversed. In our world, however, heat – being the random motion of particles – always disperses, and so we never see it converge on objects to cause them to move spontaneously. This is because everything in the universe is far more likely to become disordered over time; it is more probable that a structure of objects will collapse into a disorderly heap than it is that the heap will gather itself back into the original structure. In physics, the amount of disorder is called entropy, and one of the fundamental laws of thermodynamics states that entropy always increases over time. This is the only law of physics that is directional in time, with all other laws of physics operating in the same way when time runs backwards. And so, entropy is the only law in physics requiring the arrow of time to only point forwards. It is the only thing preventing us from freely moving through time in any direction. A good example of entropy is shuffling a pack of cards. It makes intuitive sense that a pack arranged with alternating black and red cards is ordered, and then becomes more disordered as the pack is shuffled and all the cards randomly intermingle. However, all the possible arrangements of the cards are just as unique as one another – there’s nothing special about the initial arrangement we described. The only reason why the shuffled arrangements appear so ‘disordered’ is because they are harder to distinguish than the ‘ordered’ ones, such as alternating black and red cards or all the cards in numerical order. These so called “ordered systems” have a large-scale pattern or structure that allows us to identify them, without having to worry about the much more complicated small-scale arrangement. And this is the problem with entropy – it arises from an approximate, low-resolution view of the universe. We live in a macroscopic world and so are unable to see all its details. For example, if you zoom in on glass, you will find that its molecules are in constant turmoil, randomly moving and colliding with each other. Regardless of whether the glass may seem to be ordered, such as in the shape of a stein, or more disordered, such as in pieces on the floor, the molecules behave the same. As you go to smaller and smaller scales, entropy becomes increasingly difficult to define, as does time. This is why in quantum mechanics, on the smallest scale of the universe, time behaves in a very strange way. In some equations in quantum mechanics, such as the Wheeler-Dewitt equation for quantum gravity, time does not even seem to exist. Time, despite its seemingly vital importance in the functioning of our world, might not actually be a fundamental property of the universe. It seems to only emerge on large scales, where the intricacies of the small-scale composition of the universe are inconsequential, and the world is governed by macroscopic structures. Unfortunately, we inhabit the large-scale domain, and so are led along a narrow path through time. To escape the path, and travel freely through time, would require us to experience the universe on the quantum scale – an experience very different to what we are used to. We would have to see our world not as a collection of well-defined objects, but a chaotic sea of an uncountable number of particles. The world without the arrow of time would be a world unrecognisable as our own.

From Issue 16