If light always travels at the speed of light, how does it slow down when passing through air or water? Does it matter if light is made of particles or waves? What’s the difference between phase velocity and group velocity, and how does that all play into this? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPT (AUTO-GENERATED)

One of my favorite aspects of all of science and especially physics and let's face it, physics is the best of the sciences, is that it offers multiple ways to look at the same problem. Now a less charitable view of that would be to say that we have no idea what's going on, which is well, well, kind of true. Do we ever really understand nature? But it also means that we can deploy different arguments, different mathematical tools, and different pictures to tackle the same underlying scenario. This may seem like a disadvantage as in we have no idea what's going on, but in reality, this is an asset.

Our knowledge of physics is flexible and adaptable offering us many different insights and ways to solve challenging problems. As an example, let's talk about gravity. You know, you often say you often hear that Einstein's general theory of relativity is an improvement or an update or a replacement to Newton's model of gravity. And that's true ish. It's only half true.

G r is an improvement to Newton's gravity but only in certain situations. Let's say I have, I don't know, a pie launching device, and I want to calculate how far my pie will travel for a given level of launch power. Now ignoring the details of aerodynamics of launched pies, which I admit are critically important in reality, but not for the point I'm trying to make, ultimately, I have to solve a problem involving gravity. The pie launcher launches a pie at a particular angle and speed. The earth's gravity is pulling downwards on the pie.

Eventually, the pie will hit the ground. Now I have a choice to calculate how far this pie will go. I can use Newton's formulation of gravity or Einstein's. And these two formulations of gravity give radically different views of what gravity is and how it operates. Newton says it's this invisible force that operates instantaneously.

It's like these long strings connecting every object in the universe. And Einstein says, no, no, no. It's the bending and warping of space time. But in this pie specific case, these two radically different conceptions of nature will give essentially the same answer. Yes, there might be a slight difference in the 16th decimal of the final resting position of the pie on the ground, but if you're never going to achieve the sensitivity to measure that difference experimentally, then that difference is meaningless.

Which means we don't care. And it's true, if I were to take my Pi launcher and launch a Pi near the surface of a black hole, Newton's view and Einstein's view would provide very different answers, and Einstein's would be closer to correct. But we're not near a black hole. We're right here on the earth launching pis. So in the case of the earth, is GR an improvement on Newton or just an alternative way to look at the same scenario and arrive at an answer through a different set of mathematical tools?

It it's the second one. It's the the second one. Does anyone argue that we don't really understand gravity because we have different descriptions of it? No. We don't understand gravity because of other reasons, but that's a different episode.

We understand gravity, and we have different lenses to look at the same situation. Sometimes those lenses give the same answer, and in some interesting cases, they don't. This is simply the nature of our physical understanding of the universe. In other words, there's more than one way to skin a cat. If this were an episode on quantum mechanics, I'd make some joke about Schrodinger's cat, but it's not.

So we'll just have to save that for later. I'm doing all this prep about different viewpoints and models and mathematical tools because today's question, how does light slow down when traveling through a material, has not 1, not 2, but 3 different answers. And these three answers come from different approaches to the same problem. In most cases, the 3 approaches give the same result, but in some special cases, one approach is more useful, like it's easier to deal with mathematically. It may be more intuitive, it gives a clear physical picture of what's going on.

Or more correct, able to better match up with experiment in a specific scenario. But at the end of the day, there is one question, how does light slow down when traveling through a material and there are three answers. Just like if I launch a pie and I ask, okay, what happens to that pie? What causes that pie to hit the ground? I have 2 very, very different answers.

I have Newton's answer and Einstein's answer. And in the case of a pie launched near the surface of the earth, those two answers will give the same result. At least up to the level that we can measure in an experiment. So which is more correct on the surface of the Earth, Einstein or Newton? You can't say.

And in this case, with light slowing down, we have three answers. And the reason we have 3 answers is because light is really fun. It is both a particle and a wave, which we have explored before. You can either view light as this wave of electricity and magnetism, or you can view light as this flood of tiny little particles called photons. And sometimes you need to view them as both at at the same time, and that's when it gets a little weird.

So with our three answers, we have one answer where we don't even talk about photons and just deal with waves of of electricity and magnetism. In the second answer, we get to not talk about waves at all and only talk about photons. And the third, well, that one is special, so I'll save that one for last. I told you physics is awesome, and and it is the best of the sciences, although I may be a little biased. But to talk about light slowing down, I first have to talk about speed.

We all know that the speed of light is the speed of light. We actually define the speed of light to be precisely 299,000,792,458 meters per second because we said so. And in fact, we use that definition to turn around and define the meter, but that's a different episode. So ask if you want how we define things like seconds and meters. And we all know that that speed is the speed of light in a vacuum with which means there's nothing else surrounding the light.

It is just light traveling completely absent of anything else. The great friend of the show, even though he's been dead for something like a 150 years, James Clerk Maxwell, was the first to discover, a, light, and b, that it moves with a constant speed and vacuum. He discovered that light is made of waves of electricity and magnetism and that it travels at this fixed speed. But light travels much slower through other substances. It's a few percent slower when traveling through air, and it's like 30% slower when traveling in water, which is wild.

And some materials completely block the passage of light. What gives? What? Why are some things transparent, some opaque? Who gets to decide light speed limit through all this stuff?

Today, I'm going to focus on the speed of light through transparent materials like glass and water. If you're interested in the more general question of what makes a material opaque versus transparent, just let me know, and I'll add it to the list of future episodes. And it's through James Clerk Maxwell's work that we arrive at our first explanation for why light moves slower in glass and water. When we ask what does light do when it passes through matter, we first have to define what is light. And Maxwell gave us a picture for, you know, we spent millennia wondering what the heck is light.

Maxwell was the first one to give us a correct answer. Light, what we call light, when you switch on a light bulb and it flashes in your eyes, when you get an x-ray at the doctor, when you hear a radio broadcast, these are all different forms of light. Just some of it you can see, some of it you can't. And all of it all of it is waves of electricity and magnetism. What does that mean?

Well, think of electricity. You know, you get zapped with a little little bit of shock of electricity. Now think of magnetism, you know, the force that, holds a magnet to a fridge. Now think of these things changing with time. Think of the strength of the magnet that's holding on to the fridge varying in time.

It's getting stronger and weaker, stronger and weaker. And think of an electric shock that's getting stronger and weaker and stronger and weaker. And think of these going together that there's a little bit of electricity and a little bit of magnetism. They're, changing in time together. And you're wondering, chi, I wonder what that would look like If electricity and magnetism were both changing at the same time, the answer is light.

Light is what that looks like. Once you start wiggling electric and magnetic fields, you get the phenomenon of radiation. Matter, is we need to define what is matter. Well, it's a bunch of stuff with atoms. Right?

You you zoom down, you get your molecules. You zoom into those, you get your atoms. You peek inside the atoms. What do you have? You have a bunch of particles.

You have electrons in their orbitals. You have the nuclei with the protons and neutrons. You have charged particles. The electrons and protons are charged. They have an electric charge.

That part is important because charged particles don't just see passing light and ignore it, they interact with it. A charged particle reacts to electric and magnetic forces. So when light comes in, you imagine light shining in through a window or through a pond, these are waves of electricity and magnetism. They enter the material. They are still waves of electricity and magnetism, they're doing their waving thing as usual, not minding anyone's business, but the charged particles notice.

They respond to the waves passing over them. Charged particles feel a force from all that electricity and magnetism, like like buoys on an ocean. When the wave comes through, the buoys will rise up and down. They react to the passing of that wave. When the wave of electricity and magnetism passes through the substance, the charged particles, the electrons, the protons, they react to it and they start moving.

They start wiggling up and down, back and forth, left and right. Who cares? They respond. And now here's where it gets weird because charged particles emit waves of electricity and magnetism on their own. You take an electron, a charged particle, shake it back and forth, up and down, up and down, up and down, up and down, or back and forth, like I said.

Back and forth, back and forth, back and forth, back and forth. That will create changing electric and magnetic fields. It will create electromagnetic radiation. This is in fact how all the electromagnetic radiation in the universe is created through the motion of charged particles, back and forth back and forth part back and forth. So the, what we have here is a picture where the waves of electricity and magnetism encounter the material.

They start wiggling and jiggling those charged particles, but then charged particles themselves emit their own waves of electricity and magnetism. And this is where chaos ensues because these charged particles have a little bit of mass. Not much, but it's enough. And they have to move. They have inertia.

It takes time. When the wave hits them, they don't just like snap to it and they're like, okay, okay, okay, let's go. No. They're like, fine, fine. Okay.

I get it. Light radiation. I get it. I'll start moving, but it takes a while for them to move. So there's a little bit of delay.

The wave comes in, starts moving the charged particles, but the charged particles have a little bit of a delay because they have mass. They have inertia. They need to start moving. And so they start moving and they start generating their own waves, but their own waves are coming a little bit after the original wave. There's a little bit delay.

And when you add up all of this, you get patreon. Patreon.com/pmsutter is how you keep this show going. When you sign up, you get early access to episodes. You get ad free episodes, direct access to me on the patreon chat thingy, and you get the satisfaction of knowing that you are supporting this show for yet another month. And I I I can't thank you enough.

Patreon.com/pmsutter. Now what you get is chaos. Total insanity. All these wiggling, sloshing charged particles create their own electromagnetic waves that then start traveling through the rest of the material, and then you've got the neighbors of the charged particles that are responding to the original electromagnetic wave and the electromagnetic wave set up by its neighbors. It is a hot giant mess of electricity and magnetism.

Waves going back and forth generated everywhere, particles responding to the original electromagnetic wave and the ones generated by their neighbors. Luckily for us, most of those waves cancel each other out. You've got one wave coming from one direction that's peaking right when it hits you, and then you've got another wave coming from the opposite direction that's, troughing, an ant of whatever the opposite of peaking is, and then they cancel each other outright when they hit you. So most of those waves are gonna cancel each other out. But the, oh, waves that are going in the original direction of the original light are going to be preserved because there's nothing to cancel out because everything's moving forward.

So there isn't radiation coming from the charged particles that haven't been hit yet coming back. And so so it all goes forward. But all of that jiggling, all of that motion takes time. The original electromagnetic wave gets scrambled up and bogged down. It doesn't get to exist on its own, but now it's the combined effort of that original wave plus all the waves generated by all the charged particles, which is a lot.

And because they always respond with a little bit of lag, the total amount of radiation moving through the material is slowed down. An example I like to have in my head that doesn't really convey this well, but it's the best I can do, is you know the wave at stadiums? You know, someone starts and everyone stands up, and then the person next to them stands up, and then and then you see this rolling wave through the stadium. Imagine you're in the center of the stadium, and you point and you start the wave, and then you're gonna draw your circle in a finger and you're gonna direct that wave. That is the original wave that you are putting in on this stadium.

You're gonna create a wave that's moving through this material, this material made of people. Now imagine that every person who stands up to start the wave is the origin point for a new wave. So you point at someone, they stand up, and it takes them a little while. They got put down their their their hot dog and their drink, and then they they, you know, scrape the the popcorn off their shirt, and then they stand up. Oh.

There's a little bit of lag time. Now imagine that person, all their neighbors say, oh, my neighbor's standing up, so I better stand up and start a wave of my own. And then that person starts a new wave. And what you end up with is just a hot mess, but people start getting conflicting information. Like, they see someone standing up next to them.

Oh, I gotta start away. But then someone else, like, to the right of them is now sitting down. Oh, now I gotta sit down. So they get confused. There's a big hot tangled mess.

What you will get at the end of it, after everything cancels and averages out, is a wave that moves through the stadium but slower than you anticipated. The end result is that light slows down because all these waves cancel out, all the waves tangle up, and ultimately the charged particles respond slowly. This picture works well in almost all cases so it's often used. But I know what you're thinking. Paul Paul Paul Paul Paul Paul Paul.

A little while ago, we sat through 9 episodes on quantum mechanics. We live in a quantum world, Paul. We know that light isn't just an electromagnetic wave. It's a bunch of little photons. So how does quantum mechanics treat this problem?

Okay. Okay. Fair. You want the quantum version? You're gonna get the quantum version.

Here's picture number 2. Let's look at photons. Bits of light that add together to give a the wavy features that we're used to. Instead of waves, we're dealing with a bunch of little tiny bullets that go zipping into the material, zip, zip, zip, zip, zip. But occasionally those bullets hit something, a molecule, a nucleus, an electron, something, and then bam, it stops.

It goes away. The energy of that photon gets absorbed, and the photon disappears because that's what photons do. Fundamental particles can be created and destroyed willy nilly. They can transfer their energy. They can reabsorb their energy.

No big deal. The energy of that photon is absorbed and it goes away. And then a little while later, that molecule or nucleus or electron wiggles around and spits out a new photon at the same energy. I wanna be very careful here. This is not atomic orbital absorption and emission.

This is other energy levels. This is a more, based on what's called quantum electrodynamics picture of interacting fundamental particles. So the original photon from the light we sent into the material goes away, it gets absorbed, and then a little while later, the electron or the nucleus or you know, just whatever spits out a new photon with the same energy, but that new photon is different. It's not a normal photon, like we think of a photon. It's a it's a virtual photon.

Now personally I hate this term, and everyone hates this term, but it is what it is, so please be patient because I'm trying to be patient. Here's a virtual photon. Photons do 2 things in this universe. They carry light, what we call electromagnetic radiation is really a sea of photons, and they also carry the electromagnetic force. When I feel an electric repulsion, or when I stick a magnet to a fridge, there is an electromagnetic interaction happening there that does not involve radiation, that does not involve light, but there's still photons there because the photons job is to carry the electromagnetic force.

Sometimes photons travel through space and time and just live independently. We call that light. We call that radiation. Sometimes photons are just being exchanged in order to mediate the electromagnetic force. We call those virtual photons because they're not the photons that are used to carry light, they're the photons that are used to carry the electromagnetic force.

Really, they're just used for bookkeeping purposes in our equations to signal that there is some electromagnetic interaction going on. Like you can't zoom in with a microscope at a magnet in the fridge in between them and see a bunch of photons zipping back and forth. No. There's an electromagnetic interaction being mediated through quantum particles, but you can't actually see them or interact with them, so we call them virtual particles. When you can see them and can interact with them, we call them real particles AKA regular photons.

I know it's complicated. I know it's weird, but you wanted the quantum version so this is all your fault. So what happens in this material is that the electron or whatever absorbs a real photon, but it has to interact electromagnetically with its you know, all the other particles surrounding it. So it spits out virtual photons in some direction. So do its buddies.

When the original light enters the material, it immediately scatters and spreads out into this fireworks shower of virtual particles going every which way. And once again, we have a hot mess, but not a hot mess of waves canceling each other out. We have a hot mess of this sea of particles. Like imagine, you know, shining a laser into a pane of glass and then the moment it hits the glass, it just scatters in a 1000000 different directions. To figure out what's happening, to actually reign this in and try to make a prediction, we use Richard Feynman's prescription for quantum mechanics, which is to look at every single possible path of all the virtual and all the real photons, take everything that they can possibly do, every little path, every little movement, every little scatter, every single possible path through the glass, which is all of them.

There's actually an infinite number of paths that they can take, but Feynman developed developed a very clever way to average out all these infinities. Almost all of the paths cancel out. So there's a virtual photon going this way, but then over here, there's a virtual photon going that way. So on an average, they cancel each other out. Use Feynman's math to navigate this.

And then the end result is that some of the photons survive, which is the path that the light was going in anyway. But there's a catch. All this ping ponging and scattering and bouncing comes at a cost. The original photons don't get to follow a straight line. It's like trying to navigate a crowded room, you know, at a party or something.

You're trying to move in a straight line, but there are people in the way and who oh oh, hey. How's it going? I haven't seen you in forever. How are the kids? And then you have to stop and talk and then navigate around this big clump of people that have circled up and then and then even though you still travel at the same speed going from person to person to get across the room, you're going super slow.

This is the particle answer for why light slows down when traveling through a medium because the moment it touches the medium, all the photons get scattered and get mixed up with a bunch of virtual photons. And in fact, the light takes these photons take every possible path. I'm looking at a pane of glass right now and I'm imagining a laser hitting it and then immediately all the light just spreads out, taking every possible path, every possible zigzag, but all those paths, almost all those paths cancel each other out. They just average out and you're left with the original beam of light, but because of all that scattering, all that interaction, it slows down because light doesn't get to follow the straight and narrow path. So we've got 2 answers, the wavy answer and the particle y answer.

Both depend on the light interacting with material which generally causes a huge confusing traffic jam and slows down the movement of light. But you get to decide if you want to follow one picture over the other depending on which one makes more sense to you in the moment and or whichever is easier to compute for the problem at hand. You can imagine waves of radiation interacting with the material and then waves generated by the material and these all tangle up and introduce time delays and interference. Or you can imagine particles scattering everywhere and canceling each other out. And then there's a third picture, which is actually my favorite picture because it is by far the weirdest and the most mind blowing, to me at least.

But if you wanna stop and get off the ride right here, I'm not gonna blame you. But if you're gonna stick around, don't say I didn't warn you. So far in this episode we've been focusing on the properties of light. Is it a wave? Is it a particle?

Blah blah blah. But what about the material? Man, doesn't it get an identity? Doesn't it get to be somebody? Who's going to care about the material?

You know what? I am. Material can be something too. So far, we've just waved our hands and said, yeah. The material which is could be a glass, a bucket of water, whatever.

It's just a bunch of molecules, which are just a bunch of atoms, which are just a bunch of charged particles. And they respond to the incoming light, whether it's electromagnetic waves or whether it's a photon, it doesn't matter. They just respond and then start doing their own thing and start causing chaos. But let's not forget the materials are more than their fundamental constituents. Like a table is made of charged particles and a cat is also made of charged particles, but I'm pretty sure that tables are different than cats.

And what matters isn't the charged particles themselves. They are fundamental particles. An electron inside a cat is no different than an electron inside of a table. But what matters are the way they are arranged with themselves, the patterns and structures they form, their relationships matter. And if we want to properly look at a material like glass or water, we have to look at not just the fundamental particles, but the way these particles interact with each other and arrange themselves.

One kind of relationship that atoms in a material can have is how well they wiggle together. Everything. Everything in the world is constantly humming and vibrating. There are these little vibrations passing through every single object, every single material. The these vibrations come from seismic motions, from air molecules bouncing off, from the sound of your laughter hitting it.

And also everything is just warm, and anything that's warm is going to move at a molecular level, and that will introduce vibrations into a material. So I I look at a chair. There are millions of subtle vibrations going through that chair right now. I look at a pane of glass. There are millions of subtle vibrations going through that pane pane of glass right now.

And different materials will have different vibrational properties. Like certain frequencies might be preferred or not preferred in that particular material. Vibrations might last a very long time or not long at all. They might be able to go very far, travel very far in the material or just stop in a centimeter or whatever. All of this, the properties of these vibrational motions don't depend on the fundamental particles, the electrons, but the way those particles are arranged.

Different molecular structures, different chemical compounds, different states of matter will lead to different kinds of vibrations that a particular material can support. And when it comes to these vibrations, the vibrations in a material have names. They are called, are you ready for this, phonons. Not photons because that would be weird. Phonons.

Phonons are a way to describe the vibrations in a solid, that if I look at a pane of glass or a chair or I suppose a cat, I don't know if purrs count as phonons. We'll have to investigate that later. This material, this object can support, can allow certain kinds of frequencies of just natural vibrations within it. And if I were to smack the side of it, then a vibration would travel through that material. And I can describe those vibrations, both the natural ones and the ones that are forced from the outside like waves.

And in a purely quantum sense, all waves are really particles. I can actually describe these waves as what are called quasi particles, called phonons. These are not real particles like an electron. What they are are a convenient mathematical way to describe the behavior of a material. In this case, a quasi particle is a convenient mathematical way to describe the kinds of vibrations that are constantly happening inside of a material.

It's like a virtual particle. Like, it's a bookkeeping device. Like, I know phonons don't really exist in nature, but I can use these as a mathematical tool to describe what is actually happening in nature, which is a bunch of vibrations traveling through a solid or an object or a material. Now that we have a more sophisticated view of materials other than, I guess it's a bunch of charged particles, now we can ask this question again. What happens to light when it enters a material?

But we're not gonna ask what happens to the light. We're gonna ask what happens to the material. We have light, which is made of photons entering the material, and we have the material itself, which is made of phonons, these quasi particles that describe the vibrations in the material. It turns out that when photons and phonons love each other very much and get close to each other, they make something new. Are you ready for this?

Take a deep breath. A polariton. Now, what the heck is a polariton and why am I just making up names? Work with me here. Okay.

A polariton is another quasi particle. It's not a real particle, but it's one we can use to describe the behavior of material. You know, a phonon is a mathematical tool that looks and acts like a particle. That's why we call it a quasi particle because all the mathematical language that we assign to particles, we can assign to phonons, but it's used to describe something else, in this case, the vibrations in a material. A polariton is another quasi particle.

It's not a real existing physical entity. It is a mathematical tool I use to describe something that is actually happening. But in this case, a polariton describes the behavior of material with a bunch of light blasting through it. And in this picture, as soon as the light hits the material, the photon goes away. There are no more photons.

We're not dealing with virtual photons, real photons. We're not using Feynman's quantum mechanical path integral, you know, averaging out formula. No. We're not dealing with electromagnetic waves. No.

The the photons go away. And then when I look at the solid, I'm not dealing with charged particles anymore. I'm not dealing with vibrations. Those go away too. The photons disappear.

The phonons disappear. There's a new entity, a marriage of the 2 called a polariton. This polariton has its own properties, its own characteristics, its own identity and one of its properties is that it travels in the same direction as the original light but at a slower speed because it's a new thing. This makes the polariton very easy to work with and despite our the difficulty in wrapping our heads around it. Trust me, I have a hard time imagining this, but it's fun to try.

Once it springs into existence, it just does its thing. It moves in a straight line at a speed slower than the speed of light, and that speed depends on the phonon properties. So you you write down the phonon properties of this solid, and then the light hits it and then you create the polariton and boom, the polariton has its speed. As soon as the polariton hits the outer edge of the material, it goes away, transforms back into a normal photon. This picture is convenient and easy to model and it's easy to tackle many materials this way because the math comes out nice and easy because we designed the math to come out nice and easy.

And you don't need to keep track of all those annoying waves interfering or virtual particle nonsense. You know with the first two pictures, there's a lot of bookkeeping involved. And there's a lot of crossing your fingers that the math just comes out right, and that everything cancels out and you're able to explain what's going on. In this picture, it's much easy. You just say, well, the photon goes away.

There's no interference. There's no waves crashing into each other. There's no sea of virtual particles. No. The photon hits the material.

Now it's a polariton, and the polariton travels through, and then that's it. In this view, and I'll say it again because it's so awesome, when light when light encounters a material, it disappears. There are no photons anymore. The light goes bye bye and it's replaced by a new entity, a new thing, a new reality. Okay, well maybe not that far, but you get my point.

There's a new physical ingredient to the universe named the polariton, and that thing travels through the material. I know I just said that polaritons don't exist, but in this picture they do. You treat them as a particle that does exist. That's not far off from just actually existing. I mean, if this is all just mathematical models anyway, who are we to say that photons are real but polaritons are not, when they're all just mathematical conveniences for solving problems?

There are 3 answers. 1st answer, electromagnetic waves tingle up with the electromagnetic waves generated by the charged particles. The second answer is the photons scatter around with all the virtual photons created by the charged particles. The third answer, light disappears and is replaced by polaritons that move through the material. So which answer is correct?

Which answer is true? Those are 3 very, very different ways of looking at the same question. They couldn't be more different. One is based on classical waves of electricity and magnetism, another, the quantum picture of photons, and then the third, a new picture based on polaritons, a new entity that is created when light interacts with matter. These are all mathematical models.

They're all valid, but this can be frustrating. You walk up to a physicist, in this case me, with a very simple question. How does light slow down when moving through a material? You expect an answer. That that's your right to expect an answer.

The truth. An accounting of what's going on. But physics doesn't deal in truth. We deal in models. Our goal as physicists is to develop a mathematical understanding of the workings of the universe.

To serve that end, we develop models that approximate reality and allow us to make predictions that we can verify against experiment. And sometimes we can develop multiple models that all agree with experiment even when they offer completely different descriptions of the same phenomenon. The reason this is no problem is that we truly have no idea what's going on. I can't tell you what actually happens when light passes through a material. I don't know.

I just have a series of models that describe light and describe materials and I have models that describe how they interact. Try this on for size. Go up to a piece of glass. Walk up to a pond. Watch the light entering in it.

Imagine the 3 models in your head. Imagine waves, undulating waves of electricity and magnetism hitting the pond or passing through the glass and then activating those charged particles and then they send out ripples of their own and they all cancel out and the wave continues traveling through but at a slower speed. Imagine this stream of photons hitting the glass or the water and then scattering in a million, a 1,000,000,000,000, a trillion different directions, and then averaging out to the original path but slower because of the cost of all those interactions. And then imagine the light disappearing, creating a new entity, a polariton that is some hybrid mixture of the radiation of the light itself and the normal vibrations that exist in the material. And it creates a new entity, a polariton that travels through the material at a slower speed because that's what polaritons do And then when it hits the other side, the polariton disappears and the photon reemerges.

3 very very different pictures, all of them true. At least as true can be when it comes to models of nature. How do we know which one to use? Well, it depends. In physics, we don't care what's true.

We care about what's useful. Thank you to Kirk b on Patreon, Ryan l on Facebook, and Tim E on email for the questions that led to today's episode. And, of course, thank you to all my Patreon contributors. That's patreon.com/pmsutter, but especially my top contributors this month. We've got Justin g, Chris l, Barbara k, Duncan m, Corey d, Justin z, Nalia Scott m, Rob h, Justin Lewis m John w Alexis Gilbert m Joshua John s Thomas d Simon g Aaron j Jessica and Valerie h.

Thank you so much. Patreon.com/pm sir. Please keep sending me questions. Ask a spaceman@gmail.com. Go to the website, askaspaceman.com.

There's a form submission button if you want. Ask questions there. Keep following me on social media. Keep hey. Keep doing reviews on Itunes.

Those that is a huge help. That is how the biggest way that more people find out about this show. And I'll see you next time for more complete knowledge of time and space.

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