0:00 You're looking at light doing something it's not supposed to do. Instead of spreading out smoothly, it's collapsing into bright branching paths. And this isn't because it's following hidden fibers or channels or anything. Quite the opposite, actually. It's passing through invisible random variations that counterintuitively focus the light's energy into distinct paths instead of spreading it out. This phenomenon is called branched flow. In this video, I'm going to show you how it works and why it shows up on scales as small as the quantum realm with electron waves up to worldsiz scales and tsunami waves crossing the ocean and even on intergalactic scales where energy is focused and branches by random variations in the universe. In the early 2000s, researchers were
0:46 running what seemed like a routine experiment. They were injecting electrons into semiconductors at a tiny point of contact called a quantum point contact. Based on decades of theory, they expected these electrons to spread as waves through the semiconductor. Instead, when they imaged where the electrons actually went, they saw something completely unexpected. The electrons organized themselves into long branching filaments, even though there were no channels in the material guiding them. When researchers saw this data, it quickly became clear that this was a new type of transport phenomenon that previously had not been documented. But how do evenly distributed waves start forming distinct lines? Well, if you have a wave spreading through a medium that's completely uniform, then you have
1:32 predictable wave mechanics that guide the wave through the medium. If the wave hits a new medium with a different density, then there will be some reflection and refraction at the surface and the wave will continue onward. This is well understood and documented. For example, you can see that a wave of light bends when it hits a surface. This is due to the effect of speed of light changing in the material. So when light hits different materials of different density or refractive index, you always get some bending of that light at a given angle. We don't even have to look at its waves. We can just look at it as a ray of light following Snell's law and we see the same thing reflection and refraction. But what if instead of hard boundaries with changing properties like density at a surface, there's a gradual
2:18 change in density. Well, then you wouldn't get hard boundaries of refraction and reflection, but you would get gradual turning. You can see this when I make a liquid that gradually increases in density toward the bottom. It bends my beam of light. But now imagine that instead of one gradient of density from high to low, you had random variations of density like this. So imagine I have some material where the density varies according to this graph here where the z-axis up is density or refractive index and it's spread out over a 2D plane like this. Now using this matrix, I can model what happens when a beam of light goes through this randomly varying density matrix. a beam that moves through the medium but kind of follows these density gradients in the local vicinity. So overall the beam
3:06 passes through it but it has these random looking deviations. And if we have two beams then we get the same thing. Three, four, five, all kinds of random movements through the material. And you don't really see a pattern yet. But watch this. Something amazing happens when we add thousands of individual beams. The beams congregate into channels and branches. These branches propagate and split through the material. Change the beam angle ever so slightly and you get a new pattern of branching. This is branched flow. It's an emergent phenomenon that seems fully chaotic. Yet, it's not quite chaotic. As the original researchers described it, branch flow is on the way to full chaos, but it's not there yet. This branch flow
3:52 is surprising because there are no channels of density in this medium. The density changes are random with no paths. But because those variations are smooth, nearby beams experience the same gentle bends. So instead of scattering independently, many beams stay correlated and gradually drift together. One way to see this branch flow in real life is to make a soap bubble. The surface of the bubble looks pretty uniform, but it's not actually. There are locations on the bubble that are slightly thicker and thinner than other areas. Because of this, light caught in the middle of the bubble's water layer will reflect inside that layer. But since some places are thicker than others, the light has to zigzag longer distances in some regions than others.
4:38 So, the thickness of the bubble slows down the effective wave propagation of the light, similar to how a change in density affects waves. This gives us the exact conditions we need to see branched flow. So now if I just take my green laser pointer and shine the light right into the middle of that bubble film. Let's check what we see. But before we do that, I want to thank the sponsor for this video, BetterHelp. BetterHelp is the world's largest therapy service and it's 100% online. With BetterHelp, you can tap into a network of over 30,000 licensed and experienced therapists who can help you with a wide range of issues. To get started, you just answer a few questions about your needs and preferences in therapy. That way, BetterHelp can match you with the right therapist from their network. Then, you
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6:10 10% off your first month at betterhelp.com/actionlab or just click the link in the description. And thanks to BetterHelp for sponsoring this video. Now, let's get back to our experiment. Now, the key to making this work is to shine the laser pointer directly through the thin water film of the bubble. Now, that's actually pretty hard to do, but if you just get something like a glass cup and dip it in your bubble solution, it'll make this bubble film on top. And what you're going to want to do is shine the laser through the glass right where the film of the bubble is. Okay, let's shine the light in here. Whoa, look at that. I can totally see the branches forming. The branch patterns are continually shifting and changing because the locations of those thick and
6:56 thin spots on the bubble are changing and flowing with air currents. This phenomenon that I'm showing here was first seen with light using the same method only in 2020 when it was published in the journal Nature. It's amazing to me that we're still finding phenomena like this that were hiding in plain sight. Once branch flow was discovered, we started finding it everywhere. For example, in 2011, tsunami researchers were surprised to find that tsunami wave energy formed branching patterns as it traveled across the ocean. And it became clear that these branches were examples of branch flow caused by smooth random variations in ocean depth. Even the familiar pattern of sunlight on the bottom of a swimming pool is related. It's essentially a slice of branch flow
7:44 created as sunlight passes through water with slight smoothly varying density and depth. Branch flow even shows up in sound waves. For example, if I record a plane flying overhead and then look at its spectrogram in Audacity with frequency on the y-axis, time on the x-axis, and color representing loudness, you see these vertical streaks where all frequencies get louder suddenly. So, you kind of hear loudness pulses in the sound when planes fly overhead. That's due to the small variations in air density and temperature concentrating the sound waves on the way to the ground. kind of a sound version of one point in space at the light at the bottom of a pool. Again, these air variations are not branched. They're actually randomly distributed, but they cause the sound energy to be branched in
8:29 specific locations. Branch flow is an amazing phenomenon that appears wherever waves travel through a medium with small smooth variations in density or speed, especially when those variations occur on length scales larger than the wavelength. We even see similar branching behavior on cosmic scales where small gravitational variation focused matter into the filamentary large scale structure of the universe. However, despite how universal this phenomenon is, it was only recently discovered and even now is still barely touched on in modern physics compared to other fields. The reason for this is because it's easy to miss. If you zoom out far enough, branch flow just becomes diffuse waves spreading. You have to catch it at the right scale to notice
9:16 it. And another reason is is that whenever we model waves, we typically assign the medium they're propagating through some average density or refractive index or thickness. We don't include the small continuous variations that exist in real life. And the result of this is clear. For example, here are two models with the same average density. In one of them, there's purposeful variation in the refractive index, but the same average. and in the other there's no variation. So you don't see branch flow unless you model the small imperfections that exist in real life. Branch flow is the perfect example of a phenomenon that emerges when you include the random imperfections found in nature. The real world is an imperfect mess of interactions. But somehow out of this chaos, order
10:02 emerges. And to get that order, you need the chaos. And thanks for watching another episode of the Action Lab. I hope you enjoyed it. If you haven't subscribed to my channel yet, consider hitting the subscribe button and we'll see you next time.
