Thanks to Brilliant for sponsoring this episode. Hey Crazies. Mirrors are useful tools, especially in the bathroom. They seem like they’re pretty easy to understand. Or are they?! Rule number 8 here in the asylum is question everything. You think you understand mirrors, but all it takes it takes is just the right question to destroy everything you think you know. So let’s start with the stuff everyone knows. Mirrors flip things left-to-right, which makes those things look backward. The you that you see in the mirror is not the you that other people see when they look at you. Here’s what Albert Einstein looked like. This is how he looked to himself in the mirror. They’re backwards from each other. It’s at least part of the reason that many people don’t like pictures or video of themselves. That’s just not how we’re used to seeing our own faces. You’re used to seeing your own face the other way around and, since no one is perfectly symmetric, our subconscious notices the difference, even if our conscious mind can’t quite tell what’s wrong. You can get used to it though. After years of staring at myself like this, I’ve gotten comfortable with both directions. What’s so crazy about all that though? Well, I lied a little bit. Mirrors don’t actually flip anything. You heard me right! Mirrors don’t flip. The reflect. Your brain just thinks it’s a flip. Back at the mirror, my clone was holding a piece of paper with the word “things” on it. It looks backward from how you would normally read the word. But the word already isn’t facing you. It’s facing the mirror. If you could see the word through the paper, you’d see the reflection is actually the same direction as the word. If you flip the paper around so the word is facing you, the word in the reflection is also the right way. You can read it. The light just goes to the mirror and comes back. There is no flip. The real problem here is your expectations. And those aren’t going to serve you very well over the next few minutes. Speaking of expectations, in this painting, a little girl is looking at herself in a mirror. Right? Wrong! She’s looking at you. Mirrors let us see ourselves, but only if we’re looking directly at them. The direction a mirror faces is given by an arrow or line called the normal, which just means that it makes a 90 degree angle with the surface of the mirror. It’s from the old Latin meaning of the word. We measure all angles from that normal line. See, if light shines on a mirror, it reflects off at very specific angle: The angle it came in at, but on the opposite side of that normal line. These two angles must be the same. It’s called the law of reflection and it’s true for any incoming angle. Even if we curve the mirror, the law of reflection must be obeyed. So let’s take another look at that painting. This little girl is not directly facing her mirror. The mirror is at an angle. If she’s seeing light coming from the mirror, according to the law of reflection, that light has to come from a different place. It came from the front of the painting where we happen to be standing. We can see her in the mirror, but she sees us. I can easily demonstrate this with my own mirror. But why though? Why does that law look that way? Why is the reflected angle always the same as the incoming angle? Um, it just is? OK OK, I’ll give this a shot. We need to go deep for this, so don’t say I didn’t warn you. To even begin to answer this, we need more than just light rays. Light is disturbance in the electromagnetic or EM field. It’s a wave. These disturbances move outward from whatever source is causing them and they move at the speed of light. They are light. But having all those arrows, exes, and dots all over the place is going to get confusing. Instead, let’s abstract all that away and just keep track of the wave peaks. Think of these like the water waves you’d see approaching a shore line. They’re called wave fronts and they’re going to help us keep things simple. Now let’s look at what happens when one these wave fronts hits a mirror. If the wave front comes in at an angle, one end of it will hit the mirror first. That part will reflect before the rest of the wave front. To understand why that reflection even happens, we need to look even closer. Super zoom! The mirror’s surface is covered in silver atoms. I know it’s not always silver. Just go with it. Each of those silver atoms is made of a positively-charged nucleus surrounded by a cloud of negatively-charged electrons. And, in case you didn’t know, charges are affected by the EM field. When the wave front hits an atom, the charges inside that atom begin to vibrate. That vibrating charge makes its own light that goes out in all directions. Here’s the thing though: While each atom creates it’s own disturbances in the EM field, there is only one EM field, so it can only respond to the total of all the disturbances together. Many of those disturbances are going to be out of sync. They’ll cancel each other out. It just so happens those disturbances cancel everywhere except one specific angle: The angle predicted by the law of reflection. How cool is that!?! But if we’re looking at atoms, shouldn’t we be using quantum mechanics? I can’t get away with anything around here, can I? Alight, so I cheated a little. This method is called Huygens principle and was developed all the way back in 1678. It was updated in 1818, but, needless to say, it’s a bit old. If we’re going to explain the law of reflection with quantum mechanics, we need to reframe the question a little. Say we’ve got a laser that can point in any direction we’d like, but we need it to get to some detector. Just for fun, we’ll make the detector a micro black hole. If light goes in, the black hole grows and we count that as a detection. It’s a boring example, OK? I’ve got to spice it up somehow. Now let’s put a wall in the way, so the laser can’t go directly to the black hole. We need the light to go around the wall. That’s where our mirror comes in. We can reflect the light off of the mirror and get it to our black hole. If you’ve been paying attention, you know the angles must be equal, so the light has to hit the mirror at a very specific place to reach the black hole. Or does it?! Instead of imagining this laser beam as a ray or a wave, we’re going to imagine it as a stream of photons: little packets of probability. If one of those photons enters our black hole, it’ll grow. To keep things simple, we’re only going to consider one photon at a time. This photon exits the laser and hits the mirror. Our expectation is that the photon should obey the law of reflection, but that’s not necessarily what happens. What did I tell you earlier about your expectations? Let them go! Our photon knows nothing about the law of reflection and neither does the atom it hits. If a photon exits a laser and enters our micro black hole, there’s a chance it could have taken any path between them, even if those paths don’t obey the law of reflection. Does it take all the available paths simultaneously? Yes. Kind of. Well, not really. Eh, maybe. I hate quantum mechanics. What’s physically happening depends on your favorite interpretation. All we know for sure, is that we must consider all the paths in our calculation. “Shut up and calculate” is a famous motto in quantum mechanics. If we want to know the probability that a photon will reach the black hole, then all these paths contribute something to that probability, even if those paths don’t obey the law of reflection. We just need to figure out how much each of those paths contribute. We could do the math outright, adding up exponentials like this, but we’re not going to. I mean, why do math with symbols when you can do it visually instead? Let’s imagine this thing is just an arrow with a particular length, something we’d call a phase vector or phasor for short. Over time, the arrow spins around at a pace given by the frequency of the photon. Visible light frequencies are pretty high though, so this arrow is zipping around like crazy. Zoom zoom zoom zoom zoom zoom zoom. But, ultimately, each available path for the photon takes a different amount of time, so those spinning arrows end up in different orientations when they’re done. Remember though, these arrows are a visual way of representing the photon’s wave. A wave of probability. To find the total probability the photon will arrive at the black hole, we need to add all these arrows together. Visually, we just put all the arrows in order, tail to head, because that’s how you add vectors together. The arrows caught up in the spirals tend to cancel themselves out, so only the arrows near the center contribute to the probability. That’s exactly the location we’d expect given the law of reflection. The law of reflection just comes from the probabilities of photons. It’s just probabilities. But that’s just a math trick, right? The photon is really only taking the middle path, right?! Nope! The photon interacts with the entire mirror and I can prove it. If we exclude the middle path by removing some mirror, the law of reflection tells us that no photons should reach the black hole, but some of them do. Some of the remaining paths still create a non-zero probability. That single photon still interacts with the other parts of the mirror, like, for real, even on the edges! Let’s say we only have a mirrored surface on the far left edge of the screen. That way we’re only including a spiral of cancelling arrows. In that case, as you’d expect, we do not receive a photon at the black hole, unless we tweak the mirror. Let’s say we know the locations where the quantum arrows point left and we remove those sections of the mirror as well. Now the arrows don’t cancel in a spiral. Even though none of the paths are even remotely obeying the law of reflection, they add up to a non-zero probability anyway. The photon can still arrive at the black hole. Classically, these situations would be called diffraction, but, in quantum mechanics, it’s just probabilities. Mirrors violate our expectations at every turn. Sometimes, we can figure it out if we draw a ray diagram. Other times, we need to consider the wave nature of light. But, in some circumstances, not even that will work. That’s when we resort to quantum mechanics because reflection is ultimately probabilistic. The point is, we didn’t really understand mirrors until the last century. Don’t feel too bad if your instincts failed you today. So, do you feel like you understand mirrors a little better? Let us know in the comments. Thanks for liking and sharing this video. Don’t forget to subscribe if you’d like to keep up with us. And until next time, remember, it’s OK to be a little crazy. Brilliant is a problem solving based website and app with a hands-on approach. There are over 60 courses in math, science, and computer science. Stimulate your brain with logic puzzles or check out their course on waves and light. Start with the basics, the things that are common to all waves, and then learn the ways that light is unique. They regularly add content too and give you an idea of what’s coming, so watch out for that. Brilliant puzzles you, surprises you, and expands your understanding of the modern world. It’s a great complement to watching educational videos, with well-curated sequences of problems that help you master all sorts of technical subjects. If this sounds like a service you’d like to use, go to brilliant dot org slash Science Asylum today. The first 200 subscribers will get 20 percent off an annual subscription. It's Okay To Be Smart mentioned that RuBisCO doesn't get enough credit. And I agree. I wish I had more time to talk about the Calvin cycle in the video. Collab? And to everyone asking about quantum entanglement, there will be a video. I promise! Anyway, thanks for watching.
