The Arrow of Time (Script) (Patreon)

Ever wish you could travel backwards in time and do things differently? Good news: the laws of physics seem to say traveling backwards in time is the same as traveling forwards. So why do we seem to be stuck in this inexorable flow towards the future? It's time to begin our journey towards really understanding time.

The laws of physics describe how the universe at one instant evolves into the universe at the next. But those laws don’t distinguish the future and the past. Reverse the flow of time and their equations work exactly the same to describe a universe in rewind. That’s true from the subatomic realm of quantum mechanics to the cosmic realm of Einstein’s general relativity. But if time doesn’t have a preferred direction in physics, why does time seem to drag us with it, and only in one direction? Why is there an arrow of time?

There are two distinct ways in which we perceive the unidirectionality of time. One is external: an egg  might splatter when you drop it, but will never spontaneously reassemble. Our whole universe decays in the inexorable rise in entropy as time ticks forward. The other place we perceive the arrow of time is internal: we lay down our memories in an ordered sequence of prior events. We remember the past, but not the future.

Today we’re going to dive into the first part of this - How does entropy break the symmetry of time, and cause the future to differ from the past.  We’ll follow with an episode exploring why this breaking of time symmetry on the cosmic scale defines the experience of time that we experience in our own brains.

So what exactly do we mean when we say the laws of physics don’t care about the direction of time? Basically, if you reversed the motion of all particles in the universe - sent them back exactly in the direction they came, and used the laws of physics to calculate what would happen - you’d predict that those particles should perfectly retrace their steps, all the way to the Big Bang if you calculated that far.

Let’s look at a simple example. We’re going to use our good-old block universe picture, where we have 2-dimensions of space and one dimension of time, with time flowing upwards. The block universe just sort of exists a-temporally. The experience of time is had by looking at time-slices in a particular sequence, like a flip book. OK, so imagine two particles moving towards each other - let’s say, electrons. They move up in time and towards each other in space. When they get close they deflect due to the repulsive electrostatic force between them.

Newton’s laws of motion combined with Coulomb’s law perfectly describe how the electrons’ positions change over time. But if we flip this diagram on its head - reverse the flow of time, it still looks like two electrons bouncing off each other. The same equations perfectly describe the bounce in both directions, and those equations don’t seem to prefer one direction or the other.

So the laws of physics don’t care about the direction of time. They just describe the relationship between time slices of our block universe. Time has a symmetry in the sense that the past and future aren’t differentiated by the laws of physics. And those laws don’t even require time to “flow” - it’s just another dimension like space.

There is a powerful exception to this. The second law of thermodynamics states that this stuff called entropy must always increase or stay constant - entropy never decreases over time. So the 2nd law DOES dictate a direction for time - it breaks the symmetry. To see why, we’ll need to review entropy. We’ve talked about it before, and this is a great episode for a refresher. There are actually several ways to think about entropy. Today we’ll talk about it in terms of distribution of energy. Energy can take many forms, and can be transferred between forms and between objects. For example, kinetic energy is transferred between our electrons when they collide.

Over time, energy tends to get shared out as evenly as possible due to, say,  collisions. So if you had many electrons in a box, and half of them had a lot of kinetic energy - were moving fast, while the others had none - pretty quick energy would be shared out and it would stay shared out. It’s very unlikely that through random collisions, half the electrons would get all the energy and the other half end up with none.

So if you start from a situation where energy is not perfectly randomly spread out, then over time it’ll become more spread out. Entropy measures how randomly distributed the energy in a system is. Higher entropy means more random. The second law of thermodynamics tells us that entropy must increase over time - which just means that a system that starts out in a very specific, non-random state will tend to become more random. It’s a statistical effect - it’s possible for small fluctuations to happen, local drops in entropy, but the larger the system the less likely it is for entropy to reverse.

So how does this set the forward direction of time? Actually, it doesn’t. The 2nd law just tells us how a system is likely to change from a position of low entropy - in either time direction. To understand why one particular direction ends up being chosen, we need to return to the block universe.

Let’s start with a handful of particles with low entropy. You can do low entropy by having a weird distribution of velocities, but you can also do it by clustering the particles in one spot in the available space. Let’s give those particles random velocities and see what happens in the following time steps. Even though the velocities pointed in random directions, the cluster will inevitably disperse. Entropy increases as energy spreads out to all possible states - in this case towards all possible locations the particles could occupy.

In this case, we defined the “up” time direction in the block universe as “towards the future”. But what does this look like going backwards in time? Uh, exactly the same actually. Random velocity directions will tend to spread this cluster apart in both time directions.

Again: if you take any low-entropy system and look at steps either before or after it in time, entropy is likely to be higher. Entropy actually doesn’t care about the direction of time any more than the other laws of physics - it just wants to increase in adjacent time-steps, in either direction.

But if you live on either side of the starting, low-entropy point, you perceive an asymmetry in time - particles expanding, entropy increasing on one side, or particles converging,and  entropy decreasing on the other. Zoom in to individual particle interactions and you see perfect reversibility of the laws of physics, but zoom out and time’s arrow emerges. The presence of an entropy minimum dictates the arrow of time - on either side, the universe is overwhelmingly likely to evolve in a very particular way.

The real-world situation represented by this diagram is called an entropy fluctuation. We expect entropy to decrease occasionally and, typically, on very small scales due to random alignments of particle trajectories or however else energy is moving around. Entropy can decrease, reach a minimum, and then will be seen to increase - now on both sides of the point in time of that minimum.

OK, what does all of this mean for our universe and the universal arrow of time? Well it’s no accident I chose “expanding particles” to illustrate evolving entropy. When we measure the velocities of particles across our universe - in the form of galaxies rather than electrons - we don’t see random motion. We see galaxies racing away from each other, which means they were once more closely clustered. This is the expansion of the universe, and it’s the manifestation of the 2nd law on the largest of scales. We know that entropy was lower in the past because we can trace the positions of galaxies and the particles that comprise them back and calculate a much denser, more “special” arrangement - in fact an incredibly low entropy arrangement. That would be the Big Bang. Given that knowledge, it’s not surprising that entropy is increasing in what we now think of as the forward direction of time in our universe.

So this is one argument for the direction of the arrow of time. If we think of time as just a series of instances - slices of the block universe connected by the laws of physics, then we can break the symmetry in the direction of time if one of those slices has a very unusual arrangement. The universe must get less special in either direction, so someone looking at the universe from either side would see a directionality to time. OK, so in our universe, what caused this initial special arrangement, the extreme density of the Big Bang and its corresponding ridiculously low entropy? This is actually an open question in physics, and we’re not going to address it right now. But one possible consequence is that if you trace all particles backwards in time to this original “special” slice, at which velocities are all random, and keep tracing out the other side then you should see entropy increasing again, but now backwards in time. It’s not crazy to imagine a symmetric universe in which those particles fan out again like a reverse Big Bang. This might be the case if the Big Bang resulted from an insanely improbable, universe-sized entropy fluctuation.

There’s no evidence that this isq true - but if it was true we’re presented with a fun scenario. If entropy increases backwards in time before the big bang, does that mean time runs in reverse back then? Would that reverse Big Bang lead to a time-reversed universe? It’s not entirely crazy to think so - but first you need to explain one thing. How is the thermodynamic arrow of time - the flow of time defined by increasing entropy - connected to our sense of the flow of time? Why do we feel like we time passes in the same order as increasing entropy?  To understand why we only remember the past, not the future, we need to delve deeper. In fact it involves information theory and quantum entanglement, so we need another episode. Or more than one. Because on Space Time we’ve always given plenty of time to space, but it’s timely to spend time on that fascinating dimension that deserves more space: time.