The physics of shadows

24:30You know what surprised me was the health side. Now, you know my sweet Holly was a medically complex poodle with her heart disease and her kidney disease, and she needed a lot of prescription meds and prescription food, and Chewy was outstanding and really went above and beyond to make sure that she had what she needed. So I appreciate that. And Chewy will take care of all prescriptions, pet insurance, telehealth, vet visits, the list goes on. And they're now rolling out actual vet clinics. So that is huge. And if Little turns her nose up at something, which she does quite often, I can return it within a year with no questions asked.

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25:34all right we're back and we're talking about light and shadows and kelly's comment reminds me that i actually have a solution to my existential angst about missing all those photons how are you going to collect all the photons daniel well look i figure if dyson can come up with this concept of dyson spheres which are basically just solar panels that surround the sun I'm just going to make a Whiteson sphere, which is basically space telescopes that surround the earth. Like let's just give up our vision of the night sky and replace it with like a solid bank of telescopes that gobble all that information.

26:08Imagine what we could learn. Every time we develop a space telescope that appears at one little corner of the sky, we have our minds blown by what we see out there. And so think about what we could learn if we had like a thousand, a billion times more capacity. It's never going to happen, but we're also never going to build the Dyson sphere. So I can put the Whiteson sphere into the same category of fantastical concepts. Yeah. If only we could collect all the photons and deprive the plants of them. I'm sure that would be great for all of us. I don't know who's less realistic, you or Dyson, but it's a fun idea to think about.

26:42All right. Maybe just half the earth then, you know, when the earth is in shadow. How about that? Oh, when it's in shadow. Okay. I was going And ask which hemisphere you're going to condemn to death. Let's have a vote. That's right. Obviously at night, yeah. So yeah, this project gets more complicated and less realistic as we think about it. But it was never going to happen anyway. Okay. I mean, people are upset enough about Starlink satellites going in orbit. I'm not sure. Anyway, let's move on. So, so far we've been talking about shadows from a sort of geometrical optics point of view. Shadows just travel in straight lines.

27:13And like at the edge of an object, either the light is absorbed or it passes. But the way light interacts with objects is more complicated than that, and it makes shadows fuzzier and weirdly surprising. So shadows played a really important role in the debate about the nature of light. Is it a particle or is it a wave? Is this the two-slit experiment? Yes, the two-slit experiment was part of it, but that actually didn't settle the question in most people's minds about whether light was a particle or wave until they did this crazy shadow experiment. So what's the connection between shadows and the particle or wave nature of light?

27:45Well, if light is a particle, then shadows should be very sharp, right? Either the particle light passes the edge of the object or it's absorbed. But if light is a wave, then it's more complicated because you get things like diffraction and interference. So in the early 1800s, people had done this experiment like the Young double slit experiment to show that light had this wave-like behavior, that it was interfering with itself. And so light was very likely a wave. And you can see the same thing, not just in interference, but in diffraction. Diffraction is like the big sister of interference. The way it works is imagine you have like a circular object and you shine a light on it and you have a screen behind it.

28:25What do you expect? Well, you expect a circular shadow, right? If light is a particle, that shadow should be perfect and crisp if you have a single light source because there's like an edge where the particles just barely make it around the object and a tiny bit further in, for example, they don't. So you get a very crisp shadow. You with me still? Yep, I'm with you. All right. But if light is a wave, that's not how light interacts with matter. What you need to do instead is imagine a bunch of sources of light all around the object. The same way as in the interference experiment where you have two slits.

28:57The way you think about that mathematically is each slit is now a source of light. The light makes it through the slit. You imagine that as a point source and then those two point sources interfere. Diffraction is like that, but now you have lots and lots and lots of sources of light all around the edge of this object. Everywhere the light is making it around is a point source of light, and those are all going to interfere. And so if you look very carefully at the edge of shadows, you can see this diffraction effect. There is no perfectly crisp shadow. Even in a room filled with black bodies and a single source of pinpoint light, you will still get these fringes at the edge of shadows.

29:35You'll have like a dark black center, and then you'll have a white band, and then a black ring, and then a white band. You get the zebra shadow effect from the diffraction edges. So I've got a bright light and I'm putting my hand under it and I'm not seeing the like, so in our outline, you have this great picture with ripples that, of course, our audience can't see. But imagine like you drop a rock in a lake and there's ripples. There's a black spot where the rock got dropped and then there's ripples coming out from there. But that's not what I feel like I'm seeing when I put my hand under the light.

30:05And so what was different about the lab conditions that find these ripples, obviously, relative to my office? Yeah. Well, you have to have a single source of light because otherwise you have all these penumbras which are overlapping and it's hard to isolate this effect. And you have to have a room with no other reflections because this is a subtle effect. It's not easy to see. But it was not so subtle that 200 years ago they couldn't do it. And so the interference experiment and this shadow diffraction experiment were very strong indicators that light was a wave, not a particle. And at the time, people really believed like Newton's idea that light was little corpuscules, right?

30:43It was this little bits of stuff. So these were hard to absorb. And there were lots of people who like really dug in and they were like, this is absurd. Light cannot be a wave. And one famous physicist Poisson of Poisson statistics and all sorts of stuff, he studied this theory in detail and he was trying to prove it wrong. I have a feeling I would have been on team Poisson. Light cannot be a wave. It doesn't make sense. That's just because Poisson means fish and you're always on team fish, Kelly. I am always on team fish. It's true. The number of jokes that fish people make about Poisson's statistics is maybe nauseating.

31:18Off the hook. Off the hook.

31:24Oh, thank you, Daniel. Okay, moving on. I had to dive into that one. Anyway, this is a great example of something that happens in physics all the time, that people look for a ridiculous prediction from a theory as a way to prove it wrong, but then it turns out to actually prove it right. So Poisson did the calculations and he discovered a weird prediction from the wave theory. He discovered that at the center of that shadow, the wave theory predicted a bright spot. Oh. So, you know, the particle theory was the shadow should be perfectly circular. And the wave theory predicted all these fringes, these zebra lines at the edge, but also at the very center, all of the waves add up and constructively interfere because they're all equidistant from the edge.

32:08And so all those photons should be in phase. And so Poisson was like, aha, this is a ridiculous prediction. You're telling me there should be a bright spot at the center of the shadow? Absurd. And so this obviously disproves the wave nature of light, right? That would be fishy. You're just waiting with that joke. I was. You can see it in my face. And so this was a very strong argument to reject the wave theory. But then a guy went out and actually did it. A guy called Arago. He went out and did this experiment. And there is a bright spot at the center of the shadow. What? If you Google this image, you can see there is a tiny white dot.

32:45This is now called the Arago dot. and it was very conclusive. And people were like, okay, well, we said that wave theory makes this absurd, nonsensical prediction, so therefore it can't be true. But then if the universe actually does it that way, that's a pretty clear indicator that the wave theory is correct. So while the Young's double slit experiment and these diffraction experiments were very strong evidence already of the wave nature of light, it wasn't until this shadow experiment, seeing a light at the center of the shadow that people were like, okay, fine, light is a wave. Was Poisson a good sport?

33:21And was he like, oh, you got me. Now I'm hooked on the wave theory. I know I took your joke. But was Poisson convinced after this, or was he long gone by then? Well, the historical summary I read suggests that he wasn't especially gracious about it. You know, he didn't like on the spot admit the wave theory. He was skeptical for a while. But, you know, he went on to have a perfectly fine reputation. So he definitely survived scientifically. Yeah, but, you know, I still, I like my scientists to be gracious when they're wrong. But anyway, what are you going to do? So first of all, you have blown my mind.

33:55Because when I first looked at this picture, I didn't see the little white dot in the center. I thought that it was a speck on my screen. And so while you were explaining it, I was moving the outline up and down. And I was like, that dot is actually on the image. Yeah. That's awesome. So shadows taught us something about the nature of light, right? The patterns of shadows are much more complex than you might imagine. And the wave nature of light really is revealed by the patterns of the shadows. Yeah. So this is all a little hard to believe, but I'm with you. But like what? Next are you going to tell me that shadows have colors?

34:24Shadows do have colors. Yes, absolutely. Yes. So far, we've only been thinking about single sources of white light and complete shadows, right? But remember, we talked about penumbras, right? You can have multiple sources of light. And so you can have intermediate shadows. Well, now take those multiple sources of light, say you have three of them, and you make those colors. You have a filter for each one. So you have like a red source, a green source, and a blue source. Anywhere where you can see all three sources, you'll be seeing white light. And anywhere all three sources are blocked, you'll be in shadow.

34:57But what happens if you're in a place where you're only blocking the red light? Then you have green and blue light, which make a cyan shadow. Or if you block the blue light, the red and green merge, making a yellow shadow. Or if you block the green, the red and blue combine to form a magenta shadow. Daniel! Right? I don't feel like I've ever seen... Yes, this is awesome. But this is totally going against my intuition. Shadows are black, Daniel. Is there a good video online? Yeah, I'm sure you can find a good video. But this sort of bends the definition of shadow, I think, is the issue. Because in these regions, is it really a magenta shadow?

35:35Well, you're shining a red and blue light on it. So people would say it's magenta because you're shining magenta light on it, not because you've blocked the green light, right? And so it really depends on how you define the things that are not fully illuminated or the things that are not fully blocked. Are they parts of the shadow? Are they the colored penumbras? Or are they partially illuminated? This is a physicist trick. I'm retreating into philosophy to avoid being proven wrong. All right, well, maybe I'll try this with my kids one day. Okay, so I have a son who loves swimming. Constantly he's swimming.

36:12Is there anything interesting or different about how shadows are cast underwater? Are their penumbras bigger or something because of how water defrex? Deflex? Oh, what is the word? Defrax? Bends. Refrax. Refrax. Thank you. So shadows and water are fascinating because it's a little bit counterintuitive, but water casts a shadow. Like if you pour water into a glass and you shine a light on it and then have a screen on the other side, you will see the shadow of the water. And at first you're like, wait a second, why would water have a shadow? Water is transparent, right? It's like glass. Light passes through it.

36:54Why is it making a shadow? What's going on? Did I find a glitch in the matrix? You have not found a glitch in the matrix. Water is transparent, but light does not pass through it without bending. And so what's happening here is that the light is acting like a lens and it's refracting a lot of that light away. And so the shadow there doesn't come from the object being completely opaque, but from it being darker behind the column of water because some of that light has been refracted away. So if you were to measure the light on the sides of the water, it would be brighter after you put the cup there?

37:26It might be a tiny bit, but it gets refracted in many, many directions. So most of it won't even hit the screen. Yeah. So when you are standing in the ocean, which I guess you get to do as a Californian probably pretty often. Whenever I want. Now I'm on my way to California. Here I come. All right. That is pretty solid. So you're standing in the ocean and it's a bright, sunny day and you can see shadows cast on the sand by the water. Yes. Is that just because like the way the waves build up, it's changing the patterns of how the light is bent? Yeah, exactly. Because the surface is not flat. If you stood in a perfectly still body of water, you would see no shadows from the water on the bottom of the pool, for example.

38:10But as soon as you make a ripple on the surface, then you're going to see shadows of those ripples for the same reason. That now when the light is hitting the surface of the water, it's not going straight down to the bottom anymore. It's getting bent away. And so when you have a pool that's just like sitting there and it's like gently fluctuating, you get these amazing patterns on the bottom of the pool, right? Brighter spots where the light is being concentrated and darker spots, shadows essentially, where the light is being bent away. And so again, this is a case, not a full obstruction, but of like a rearrangement of where the light is going, creating these patterns of light and shadow.

38:46It's really beautiful. One of my favorite things about water is that you're essentially seeing the surface, right? You're seeing the shadows of the surface. I like that it keeps me from dying. Water is good. Yes, we are definitely pro water on this podcast. Another place where I like looking at shadows is on a foggy day. So like we on our farm every once in a while, the fog will like come up from the bottom fields. And one, I like looking at my shadow in it. But two, I like imagining that a zombie movie is going to be filmed in my fields because it's kind of creepy. But so is there anything interesting about shadows in fog?

39:24Yeah, fog is wonderful for studying shadows because it shows you where the light is, right? It's like having a bunch of lasers and throwing up dust particles in front of them. You can see where the lasers are. And so fog is just like a bunch of particles of water suspended in the air. And they tell you where the light is. And you can have a shadow on the fog. And so there's a well-known effect called the Brockton specter effect, where you can have a shadow on a cloud, right? And so, for example, if you stand in front of a car with bright headlights in the fog, you'll see your shadow on the fog.

39:55And it can be this like huge looming shape, right? But also, if you stand in front of your headlights, you could see your shadow on a cloud in the sky if you do it right. Yeah. Cool. And that's the incredible thing about shadows is that, you know, there's this projection effect where your shadow can be so much bigger than you are, right? So you can wave your arms and then the huge sky version of you is also waving its arms. So I want to imagine that the Brock and Spectre effect is an effect from somebody who was studying ghosts and got confused about what was happening with the fog. But how did this actually get its name?

40:36Because Spectre always sounds sort of Ghostbuster-y to me. I don't know the exact history of it, but it shows up in like Lewis Carroll and Samuel Taylor Coleridge poems. So it's definitely a thing that's been around for quite a while. Okay. Awesome. It's sometimes called the Mountain Spectre or Spectre of the Brocken. Oh, that sounds even cooler. Spectre of the Brocken. That sounds like it should be in like a Viking tale. It comes from this mountain in Germany, the Brocken. It was first observed and described by Johann Schilberschlag in 1780. where he saw his shadow on the brocken. Ah, cool. All right.

41:11Learn something new every day. All right. So every once in a while, you'll hear about like pressure fronts coming through. And is that like air that is more or less dense? And could that change how shadows are made? I guess I'm trying to figure out if your neck's going to tell me that air can also impact shadows. Yes, air can have shadows for the same reason that water can, right? Because air is not a fluid of constant density. When it is, light just passes through it. But if some pockets of air have higher density or lower density, then the light bends in exactly the same way as it does when it hits the surface of the water.

41:47And you can already see this effect like when you look at heat rising above the road on a hot day, right? What you're seeing there are pressure waves in the air, and that's changing how light goes through. That's why you're able to see it, right? And it's similar consequences for how light moves through the air. This is why, for example, stars twinkle, right? Stars don't twinkle in space. They only twinkle through the atmosphere because their light is getting bent away from you in a sort of a chaotic, turbulent manner. This is why telescopes on the ground can't see as clearly as telescopes in the sky because light has passed through this complicated atmosphere.

42:23And they have these amazing adaptive optics to counteract for this, to like in real time, bend the path of the light back to regather all that light into a crisper image. But effectively, it's like a shadow. I mean, if you looked at the ground as light passes through it, you would see regions that are darker and regions that are lighter because of these density fluctuations in the air. That's amazing. And, you know, one of my favorite things about this time of year is that, so like I don't stay up late because I'm a total wimp, but in the winter and in the fall, you get, when I go out to do the animal chores, it's already dark.

42:56And so on clear days, I can see the stars twinkling. And the other day I was late to wake up my kids because the stars were twinkling and I was like totally enamored of it and forgot about what time it was and fell behind on my schedule. Well, this star twinkling effect is very cool. And it's, you know, the kind of physics you can enjoy any evening. But the same physics gives you a really weird effect during a lunar eclipse. What? I am dying to hear about that. So let's take a break to increase the suspense. And when we get back, you'll tell us all about it.

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47:20Okay, you were going to tell us about shadows and eclipses, Daniel. Yeah, so I'm lucky enough to have seen a total eclipse. This was in 2018. Amazing experience. And I went into it not preparing to be amazed. I was like, I know the physics. Yeah, it's cool. It's going to get darker, whatever. But there was something really moving about being in the totality, having the sun be so completely blocked momentarily. it just everything felt so odd and you know i'm not a religious person but i almost felt spiritual at that moment i tried to imagine what it might be like to not understand the physics at all and go through that experience feel like whoa something is happening today yes we are all gonna die that's absolutely what i would think have you seen totality no in virginia a year or two ago we got a partial eclipse but even that was pretty amazing and but you know as a biologist i was going on?

48:15And I think there was a little bit of that. I bet there was a lot more of that where you were. Actually, this was in Idaho, I believe it was, for the path of totality for that eclipse. Really amazing. Totally encourage everyone to see totality if they can. And there's a really cool effect, which I didn't see at the time, didn't even know about until preparing for this episode. But there are these things called shadow bands that happen during a total eclipse for the same reason as star twinkling. What's happening is that you have the sun now narrowed to a very, very very narrow source of light right instead of being a huge blob in the sky you have like a very thin crescent so now sunlight is very collimated all the rays are very very parallel and what happens is it creates these thin wavy lines of alternating dark and light that can be seen moving and undulating in parallel just before and just after the total solar eclipse so there's these like shadow bands of the eclipse.

49:10What? Just the same way that a solid object will have these diffraction patterns around it, these zebra patterns. The moon has those patterns, a shadow on the earth, but not for diffraction reasons. It's for the same reason as the star twinkling because now you have this column of light, which then gets bent randomly by the varying density of the air, but it all is moving in a column. So you get these bands. Really incredible. I want to see this in person. I want to see that also. And I also, for the first time, want to see our podcast as a video episode because the extent to which your arms were moving to try to explain that was really fantastic.

49:47That's the Italian in me coming out, you know. So the listener asked a question about what shadows would be like on the moon. And the context for the question was, you know, the moon has a very tiny, thin atmosphere, an exosphere. How does Earth's atmosphere impact the way shadows are made? and would it be different if you were on the moon? So like what did the Apollo astronauts see when they looked at their shadows? All right, well, I'm going to give you a pop quiz. I've taught you now enough physics on this episode to answer this question. What do you think, Kelly? Do you think shadows are crisper on the moon or less crisp?

50:21I think that it's probably about the same because you still have light reflecting from lots of different surfaces. And I bet the surface of the moon in particular is pretty reflective. I guess here when the atmosphere changes in density, that bounces light around and makes it a little bit less crisp. And so maybe with no atmosphere, I'm going to guess crisper. Crisper, yes, exactly. It's crisper. And the issue is the atmosphere. I mean, think about how if you're standing on the Earth, you look up the sky is blue, right? What's the color of the sky and the moon? Black? It's black, right? Because there's no atmosphere there to reflect light.

51:00And so the atmosphere here is blue. That means that you're getting light from all directions, right? Yes, it's mostly from the sun and you can see shadows. But the answer to Eric's other question is the reason you can see still light when you're standing behind a tree and the sun is blocked is because it's light reflecting everywhere on the earth from all over the sky. And yes, in all the buildings and whatever. But the atmosphere itself is like bouncing light everywhere. And on the moon, you have no atmosphere. And so it's much more geometric. Yes, you do have rocks that are reflecting light.

51:31And of course, during the nighttime, we see the reflection of the moon. But the atmosphere is a big contributor to making shadows fuzzy. And, of course, fluctuations in the atmosphere make that fuzzy. So, yes, the reason you still see stuff when you're standing in shadow is because it's light coming from many sources, not just one. And on the moon, shadows are crisper. But shadows are also important on the moon for another reason that you might find interesting, which is they provide place for water ice to accumulate, right? Because shadows on the moon are very, very cold. The moon's surface is crazy.

52:02It's super hot. It's super cold. It depends on are you in the blinding path of the sunlight? And if you're not, then water ice can survive. And isn't there a place like on the lunar pole where light never reaches? Yes, that's right. On both poles and places like Shackleton Crater. It's like eternal shadow or something really dark. Oh, craters of eternal darkness. There you go. Exactly. And shadows there are really important because they preserve water ice. And if we ever do live on the moon, that would be really valuable, right? So shadows could save our lives on the moon. Yeah, although I'll note that there's not a lot of water in those shadows.

52:37But there is some. It could get us started. We'd have to be real careful about recycling it. Shadows have also really helped us understand the nature of our place in the cosmos. Famously, more than 2 ,000 years ago, the Greeks used shadows to measure the radius of the earth. Greeks, so clever, so geometrical. they realized that the earth is probably a sphere because as you move around it you can see different kinds of stars right different constellations emerge as you move around the earth so the greeks much smarter than like you know certain rappers and youtube influencers who still deny that the earth is a sphere but they went beyond just saying oh the earth is likely a sphere they use the behavior of shadows and a little bit of geometry to measure the radius of the earth and got it pretty accurate, like more than 2 ,000 years ago.

53:31Well, okay. So can you give us more details about how they did that? Yeah. So imagine you're in a city where the sun is directly overhead. It's like high noon. And so all the shadows point straight down, right? There's basically no shadows. Then you have another city that's like a hundred kilometers away. And that city is not going to be at high noon. It's going to have some shadows, right? And you can measure the length of those shadows and now make a triangle where you know the distance between the two cities and you can measure the length of the shadow, the length of that shadow depends on the curvature of the earth.

54:03Because if the earth was very, very flat, that shadow would be small. And as the earth gets more and more curvature, that shadow would grow longer and longer. So by measuring the length of the shadow in Alexandria at the time that the sun was directly overhead in another city, which I can't pronounce, a Greek dude named Erastonese was able to measure the circumference of the earth just using like a stick and some geometry and measuring a shadow. So like Eratosthenes, I'm not going to say it right, called his friend down in Cyene and was like, we're both taking the measurements right now, go! I guess, did they also have really good clocks or they just were like, that is, okay.

54:43Yeah, exactly. That's amazing. So this is really cool. But the fascinating thing is that flat earthers have not let this point go. And they argue that this experiment doesn't actually prove that the earth is round. And They're kind of right. Oh, no. Because even if the Earth was flat, you would still have a shadow in one place when the sun is directly overhead in the other city. That's true. Essentially, it's like measuring the Earth to have an infinite radius. But you would definitely get a shadow because this whole method assumes that the sun is really, really far away and that the light is parallel, essentially.

55:18But in the flat Earth model, the sun is very, very close. and so you would still get a shadow in one place and not a shadow in the other. But there's a way around it. All you need to do is add a couple more sticks. So instead of just having two points, you have like three or four and the two models give different patterns of shadows. In the flat earth model, you get a linear relationship between the length of the shadows and in the spherical earth, you get a nonlinear relationship as things move around the curve of the earth. So anyway, we're pretty sure that the earth is not flat and you can actually prove it.

55:51using shadow and rod experiments. It's true, the two-point experiment doesn't refute the flat Earth. But anyway, shadows do show us that the Earth is round and allow us to measure the roundness of the Earth, which is kind of amazing. That is amazing. Way to go, shadows. So the last question the listener had was the trick question that we shared with our extraordinaries, which is, do shadows move faster than light? So, all right, now we have all of the background we need to understand the nuance to this question. So take it home, Daniel. The answer is yes, shadows do move faster than light. What?

56:31But the problem is that the rule says no thing can move faster than the speed of light relative to anything else. But shadows are not a thing. That's the problem. They're the absence of a thing. And as a shadow moves, it's not really the same object. So let's imagine a concrete scenario, right? Let's say you have a screen in the sky instead of the sky. You're like, you know, Daniel has built his telescopes that block the view of the world. And so you - Death is impending. Exactly. Right? And you can imagine a scenario with a bright source of light, and you can do like shadow puppets on the sky, right?

57:11Or imagine clouds or whatever. And you can move your hand a small amount, and the shadow will move a very large amount, right? Because the screen is very, very far away. And so this projection is far away and you get this multiplier effect. And then you can ask, well, if I move my hand really fast and the screen is really far away, could those shadows move faster than light? And the answer is yes, in the sense that like the image of your hand could be in one place and then faster than light could go from that one image to another image. The image, the shadow could appear somewhere else, right?

57:43Does that make sense? Like imagine somebody in the sky shooting a laser from one shadow to the other. the second shadow would appear before the laser arrived. In that sense, the shadow is moving faster than light. And you're wondering like, how does that make sense physically? What's really going on? And the issue is that the second shadow is not the same thing as the first shadow, right? Both of them are being created by the absence of light. Nothing is moving faster than light in this scenario. And there's no way to communicate between shadow one and shadow two. There's no information passing.

58:16It's just like if I shown a laser in one direction and then I turned it off and shown it in another direction, the laser spot would appear to move faster than light, but it's not the same spot, right? It's like I made a spot and then later I made another spot. I'm connecting them in my mind because they both came from the same laser, but it's not like anything moved from laser spot one to laser spot two. So in the same way, nothing went from the shadow's initial location to the shadow's final location. You have a wave of light that's obstructed and not obstructed that's creating the shadow and then a different wave of light that's creating a different shadow somewhere else.

58:49And your mind is like, shadows are a thing. And so it was here and it was there. And if I do distance divided by time, I get a number bigger than the speed of light. Yeah, that's true. But shadows aren't a thing. It's like comparing where one thing is and later something else is and calculating the velocity between those two. It doesn't really work. Is that like saying that the information that the photon has been stopped travels faster than a photon would travel. No, the information that the photon has been stopped isn't traveling from shadow one to shadow two. It's traveling from the source to shadow one and from the source to shadow two.

59:25Like you could signal somebody up there in the sky using shadows or not shadows, but that information obviously travels at the speed of light because you're either sending photons or you're stopping to send photons. But all that information travels at the speed of light. And you could do the same for person two, but you can't get information from shadow one to shadow two, right? There's no way for you to do that. You can send information. All the information is coming from the source of light to the shadows or the non-shadows, not between them. Got it. So the appearance of shadows can move faster than light, but shadows are not really a thing.

59:56They don't carry information. And so in that sense, you know, they're breaking the rules, but they're not really limited by the rules because they're not a thing. They don't have information. Well, thank you, Daniel, for illuminating all of our understanding of this question. I learned a lot and had a lot of fun talking about shadows because they're neat. Well, I hope that we can help bring shadows out of the darkness. Shadows are a wonderful way to think about light and to think about physics and just to like, you know, wonder in an everyday sense how everything works. There are fantastic mysteries of physics all around us.

1:00:28There are. And please send us your questions about the mysteries of, you know, physics, I guess, if that's what keeps you up at night. But definitely the questions that you have about biology, which is a fascinating topic. And if you're the descendant of the famous physicist Poisson and you want to write in to defend his legacy, please do. All right. Until next time, Extraordinaries.

1:00:55Daniel and Kelly's Extraordinary Universe is produced by iHeartRadio. We would love to hear from you. We really would. We want to know what questions you have about this extraordinary universe. We want to know your thoughts on recent shows, suggestions for future shows. If you contact us, we will get back to you. We really mean it. We answer every message. Email us at questions at danielandkelly.org. Or you can find us on social media. We have accounts on X, Instagram, Blue Sky, and on all of those platforms, you can find us at D &K Universe. Don't be shy. Write to us. The all-new Mazda CX-5. Featuring more connection.

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