Daniel and Jorge Explain the UniverseThe mysterious phenomenon of turning sound into light
Daniel and Jorge talk about sonoluminescence, a mystery that has evaded explanation for almost 100 years.
Learn more about your ad-choices at https://www.iheartpodcastnetwork.com
See omnystudio.com/listener for privacy information.
If you love iPhone, you'll love Apple Card. It's the credit card designed for iPhone. It gives you unlimited daily cash back that can earn four point four zero percent annual percentage yield. When you open a high Yield Savings account through Apple Card, apply for Applecard in the wallet app subject to credit approval. Savings is available to Apple Card owners subject to eligibility. Apple Card and Savings by Goldman Sachs Bank USA, Salt Lake City Branch, Member FDIC, terms and more at applecard dot com. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. How is US Dairy tackling greenhouse gases? Many farms use anaerobic digesters to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit us dairy dot COM's Last Sustainability to learn more.
Hey everyone, this is Joe Sweeten from how Rude Tanner Rito's Honday's most Electric ev lineup is going to change everything that you thought about. EV's one thing that you're absolutely gonna love and that's going to grab your attention is the Ultra Fast charging in the Ionic five and Ionic six. No more waiting around for your car to charge. These evs can go from ten to eighty percent in as little as eighteen minutes using a three hundred and fifty kilowat eight hundred volt DC Ultra Fast charger. Now that is fast.
Plus.
You get America's best warranty with a ten year, one hundred thousand mile limited electric battery warranty. Learn more about hundaievs at HYUNDAIUSA dot com. Called five six two three one four four six zero three for complete details. America's best warranty claim based on total package of warranty programs. See dealer for limited warranty details. See your hounday dealer for further details and limitations.
There are children, friends, and families walking, riding on paths and roads every day. Remember they are real people with loved ones who need them to.
Get home safely.
Protect our cyclists and pedestrians because they're people too, Go safely. California From the California Office of traffic safety and caltrans.
A Jorge, Are you a sinnisthete Oh, is that like a religiously No, it's a person who can see sounds.
Like do I see a symphony of colors when I hear classical music?
Yeah? Exactly. I know that a lot of visual artists have some of that.
Well, I do see red when my kids are too loud. Does that count?
I don't know. Maybe it just means you're singing the parental blues.
Well, orange, you smart?
Those are all the color jokes I could think of.
Yeah, let's not get into off color jokes. I am Orham, a cartoonist and the creator of PhD comics.
Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine.
What color would you describe your job as?
Blue and gold? Of course, the colors of UC.
Wow, you got the school spared to the core.
I do believe in the mission of the University of California. Actually, we are the biggest public school system I think in the world, educate lots of people who otherwise couldn't afford to go to college. So, yeah, that's why I'm at a public university.
Yeah, UC's are awesome. And now do you identify as an art varc or a bear because I know you went to Berkeley, but now you work at Ucy Irvine.
Well, i'd like to say bear to stand up against your Stanford tree. Is it a tree?
It is? Unfortunately, the Stanford mascot is a tree.
Is it a shivering seater or something.
That it actually changes every year? Yeah, it's a different tree each year.
No, but it's been a long time since I was at Berkeley, so I definitely associate with you. See irvines ardvark. I like a mascot that's not ferocious but a little bit kooky.
Right, and then eats that's pretty cool.
I've eaten ants myself. They're actually quite tasty.
You have turned into an art bark, maybe, Zaza zod Welcome to our podcast Daniel and Jorge Explain the Universe, a production of iHeartRadio.
In which we feed you tasty little tidbits of knowledge about the universe. No ants here, but lots of amazing facts about our bunkers universe. The crazy things that happen all over the universe, from the cosmic scale of the large scale structure of the biggest things in the universe to how the tiniest things buzz around and work together to make you and me and ice cream. We take all that together, sprinkle some ants on top, and spoon feed it to you.
Yeah, because the universe is crawling with anti particles, isn't it.
It's mostly particles, but there are a lot of anti particles out there as well, that's true.
And ants also in uncles.
That's right. So those of us who are both physicists and art barks are very into those anti particles. What would you call a human artvark combination. It's not like a.
Ware or bark argument or art person. But it is an incredibly large and amazing universe, full of huge and almost hard to grasp phenomenon and exploding stars and supernovas and big black holes. But it's also filled with small phenomenon that can also make you go wow and gasp and wonder.
That's right. The mysteries of the universe are not just inside black holes or in the deep reaches of space or underground in billion dollar particle accelerators. They can also be found everywhere around you. It's possible to create things that physics hasn't quite yet figured out. With just a few hundred dollars of equipment in your garage.
Yeah, and there are deep mysteries in terms of the particles and the very makeup of reality, but there are also sort of interesting miracles and mysteries in our everyday lives. If we just look around, there are things that even professional art art physicists can explain.
That's right, because physics is sort of a patchwork of different ideas. You know, the full universe, in all of it to glory is this incredibly complex, buzzing quantum soup of particles we'll never hope to understand. But the job of physics is to distill from that a few mathematical stories ideas about emergent phenomena, simplify things that we can pull out of this crazy chaos and tell little stories about. And sometimes those stories fit together, and sometimes we find things that fall between the cracks that can't really be described by any of the ideas we have so far.
Yeah, and it's pretty cool to talk about these because I feel like it opens people's eyes to the mystery that surrounds them. You know, once you find out there are mysteries in every corner of your house, you sort of keep an eye out after that to look for them and to have sort of an open eye for a wonder and awe.
Yep. So when you go hunting for big physics mysteries, you don't have to bag yourself and elk. You can pick up tiny little ants around the house.
So in this episode, we'll be talking about one particular interesting physics mystery or phenomenon that kind of involves all of the senses. It's tasty, it's tasty, and it feel good, but mostly involved a sight and sound.
Without any special effects.
So to the on the program, we'll be talking about can sound turn into light? That sounds pretty cool, Daniel. It sounds illuminating.
It does sound illuminating. And when I first heard about this, actually as a teenager, a high school student doing science reacher for the summer at Los Amos National Labs, I thought it was bonkers. I thought it was crazy you could turn sound waves into flashes of light. Frankly, I thought I was having my leg pulled.
WHOA, So this has been a mystery since you were a grad student. That's a long time.
Are you calling me old? I think you're calling me old?
Well, you're old, apm old because I know where the same age.
That's true. You know. I was recently accidentally c seed on an email about me where I was described as a junior ish scientist.
Oh interesting, that's good. Well I guess it, and said, who was calling you?
That?
Was it an older professor or like a hip young grad student.
It was definitely a very senior professor.
Yes, there you go. Yeah, I don't know how you should take that.
I took it as a compliment, like the way I take everything.
So you're a junior, that means there's still a lot ahead of you in terms of science.
That's right. It's gonna be decades before I'm that old and krusty. But this has been a fascinating mystery since long before I was doing physics and long before I was born. This has been something of a mystery for almost a century since it was discovered.
Yeah, and so it's a pretty fascinating phenomenon. And what's kind of cool is that, you know, it's not something that you need a billion dollar particle collider to explore or to see or to kind of try to figure out. It's something you can do in like your garage, right for a few hundred bucks.
Yeah, there are folks out there on YouTube that have instructions for how to make this happen. You get the right equipment and assemble it in a little bit of sophistication within a selloscope and you can create flashes of light from sound in your own garage.
So the idea is that you can turn sound into light, and so that happens. And there's a name for that phenomenon, right.
That's right. It's a pretty cool name too. I'm curious to hear what you're going to think of it. It's called so No luminescence.
It sounds like son of luminescence, like the sequel maybe to Luminescence the movie.
I see Luminescence's back and it's pissed off.
Yeah, its son wants revenge now Sono. I guess that makes sense right. It's like sound, right, and the luminescence means the light.
Yeah, it means glowing. It means Sonic glowing. So you know this is when you're playing Sonic the video game and you get that extra boost and Sonic starts to.
Glow and your eyes get crossed from all that video game playing. But yeah, it's called son luminescence. And it's kind of an interesting phenomenon that apparently physicists can't explain quite fully. And so we were wondering how many people out there had heard of this term, this phenomenon and or have any ideas about what it could be. So Daniel went out there to the internet to ask people what is so no luminescence?
And I'm still looking for more volunteers for people who are willing to to play our game of answer a random physics question without any preparation. It's fun, it's easy, it's no stress. If you'd like to participate, please write me to questions at Danielionhorge dot com.
Yeah, so think about it for a second. What do you think causes son no luminescence? Here's what people had to say.
I've never heard of sono luminescence before. It sounds like something that has to do with both.
Sound and light.
So maybe sound that somehow emits light, or maybe vice versa.
I've never heard of sona luminescence, but since so no implies sound, might it be that something lights up when you shoot.
Sound waves at it?
So something that causes light under the influence of sound.
I know what luminescence is, which is basically just when something gives off light. Find out what sonar is, But that sounds different than what sono means, So for that I have no idea.
It must be something to do with sound and light, but I'm not sure what.
I've never heard of son or liluminescence before, but I'm wondering by the name. If it has to do with something glowing in sound, I look forward to learning.
I know that luminescence is some kind of light in those neon color lights you have in like parties or like pain people with. So no is sound, so I know that much. So I could, I would say that it has to do with sound and light, like how the photons are moving or changing for variations of sound.
I assume that this has something to do with light radiation or the afterglow that results from some form of heat concentration, like in a body or body of massive body.
So no, like sound, luminoscence like light.
Maybe is that the way in which sound creates lights or something observable?
I think there's so.
No.
Luminescence is what happens when you vibrate something, maybe like a gaseous cloud in space and it begins to glow.
All right, some pretty interesting answers. A lot of people made the connection that it's sound and light. So kudos on the naming of this phenomena.
I'm sorry, what'd you say? I couldn't quite hear that. Can you repeat that?
I said, you did a good job made this physical phenomena.
I'm so glad I have that on tape.
You just copy and paste it every time.
That's right. We did it once successfully, so we can now retire.
That's right, it's possible.
I guess that's how you go from being a junior physicist to being junior ish. You accomplish something.
We did it twice, you maybe get to junior certified.
But people are right, this is a connection between sound and light. So even though nobody had actually heard of this specific phenomena, pretty much everybody guessed it just from the name. So good job everyone as all around.
Yeah, and so this is not just the thing where you have sound and light. This is like how do you transform one type of energy or one type of phenomenon into another type of phenomenon? Like how do you go from sound to light or light to sound?
Mm hmm. And it's really kind of dramatic. You take these ingredients that you never imagine you could get them to glow, but you can create the conditions to create these incredible flashes of light.
Yeah, so it's pretty cool effect. So let's dive into Daniel. What's like the basic experiment? How do you transform sound into light?
The basic idea is to take a small container of water, get a bubble to form in that container, and then shake that bubble using sound waves. Member sound waves are basically compression waves. So every time I speak, that energy is transmitted and that information moves through the air because the molecules are pushing on the next molecules, which push on the next molecules, sort of like waves in traffic. And so if you shake that water using sound, and you do it adjust the right resonant frequency with the little bubble that you have in the center of the water, you can cause that bubble to band and then collapse, and when it collapses, you get this bright flash of light that comes out of this bubble in your water.
Wait, what so you have a little like a glass of water, I guess you what? You put like speakers next to it or all around them, and then you basically send like vibrations into it, and they have to be kind of resonant or something right with the container. And if you have a bubble already in the water, then that bubble is gonna expand and then collapse suddenly.
Yeah, And you can do it several ways. You can either create the bubble in advance and then make the resonant frequency match the size of the bubble. Or if you have powerful enough sound, you can just start cranking up the sound waves and they will create their own bubbles. And then what happens is that those bubbles expand and collapse and you get this bright flash of light that's very very brief.
Wow. And I think it has to be supersonic sound, right, Like, it's not just like you know, turning on metallica and then you'll suddenly the water will glow.
Now, the sound doesn't have to be anything special, right. The sound waves are not traveling that fast. They're not traveling supersonically in the water. I mean you do need sort of fairly high frequency. It's not just like you know, if you turn on a glass of water near a speaker, it's gonna happen. But it's not like hypersonic. You can buy the equipment to generate these for you know, like one hundred bucks online. It's nothing that fancy.
Oh wow. And so the bubble expands and then collapses, and then when collapses, it actually it collapses so hard that it generates light.
It generates light. Yes, you get this flash of light, and it's really incredible because you know, there's not that much energy in this sound. It's not like you're blasting this with this incredible amount of energy. But what comes out of the bubble are UV photons. I mean some of them are visible, so you can see them with the naked eye, but it extends up into the ultra violet and ultraviolet are very high energy photons. We know from like looking out into space that the temperature of things connects with the energy of the photons. They emit, you know, the Earth emits in the infrared and the Sun emits it the visual and it takes like a super hot gas around black holes usually to generate ultraviolet radiation in this significant amount. And so these tiny little bubbles in your garage are generating UV photons.
Wow. And so is it like one bubble that's gonna blind you or is it like you need to see like a whole bunch of bubbles doing this at the same time to sort of see the actual glow.
Well, you should always wear safety goggles anytime you do a physics experiment, especially one that involves a glass and sound, because it could shatter, but it's not dangerous. But the other incredible thing about it is that it doesn't just happen once. If you set it up, then the bubble emits light when it collapses, and then it recovers, and it does it again and again and again, and you can do it like extremely regularly, so you get a continuous source of these flashes. So you set this thing up, you can see it with your naked eyes in an undarkened room.
Wow, Well, you won't see the bubble, right because the bubbles are super tiny, right, It's not like a giant bubble going exploding and expanding. It's like a bazillion tiny little bubbles.
You can't see the bubble with a naked eye because it's like a micrometer. But you can see the photons with your naked eye. Like what you will see is a glowing dot. And it depends exactly how you set it up until around thirty years ago, people were doing what you described. They would just like crash a bunch of sound into water and they would get a lot of little bubbles. But these days people are doing single bubble suno luminescence. They create the bubble using some other technique. You just like put a drop of water or something to get a bubble in there, and then you can get a single bubble sitting at the center of your glass of water, and when you turn on the sound, it starts to glow. Like you can see YouTube videos of this all over the place. It's not that complicated and it's really visible, like you can definitely see this bubble glowing.
Wow, that's crazy. I guess we'll get into it later. But you're making the air or you're making the water molecules glow.
Like.
The amazing thing is that we don't really understand the physical process. It's like somehow you've created a super tiny little star trapped in the bubble inside a glass of water in your garage, and so will have spent a lot of time trying to understand exactly how this works, what happens, and weather. It could possibly even be a way to do fusion on earth to create sources of energy.
Wow, sounds pretty cool, and you're telling me it's also pretty cool because it doesn't just happen in YouTuber's garages. It also happens in nature. Like there are animals who you sort of do this and use this phenomena to defend themselves.
Yeah, there are a few critters underwater that can create similar conditions, like the mantis shrimp and the pistol shrimp. They have these claws that can snap closed really really quickly. E's actively giving acoustic energy to little bubbles that exist already in the water. So they create these little collapse in bubbles, and they do it not just because they want to create flashes of light, but because they want to shoot these bubbles. And so, for example, the pistol shrimp can shoot these tiny little bubbles at sixty miles an hour that's one hundred kilometers per hour, and that kind of pressure can like kill a small fish. But at the same time, these bubbles also create SnO luminous and so you can see like a tiny little flash of light when they do this.
Whoa, It's like it levershrentp with superpowers. It can like shoot off light bullets.
Yeah, and the biologist to work on that call this shrimp a luminescence.
That sounds like a derice.
It sounds like a delicious thing to have for lunch.
Yo, really make your stomach glow, oh, bright up your day.
It's a brilliant choice.
Yeah, And so shrimp do it, and little critters do it, and you can do it in your garage. But it's still a big mystery to physicists, and so let's get into the physics of it and what could be happening there. But first let's take a quick break.
With big wireless providers, what you see is never what you get. Somewhere between the store and your first month's bill, the price you thought you were paying magically skyrockets. With Mint Mobile, You'll never have to worry about gotcha's ever again. When Mint Mobile says fifteen dollars a month for a three month plan, they really mean it. I've used Mint Mobile and the call quality is always so crisp and so clear. I can recommend it to you. So say bye bye to your overpriced wireless plans, jaw dropping monthly bills and unexpected overages. You can use your own phone with any Mint mobile plan and bring your phone number along with your existing contacts. So dit your overpriced wireless with Mint Mobiles deal and get three months a premium wireless service for fifteen bucks a month. To get this new customer offer and your new three month premium wireless plan for just fifteen bucks a month, go to mintmobile dot com slash universe. That's mintmobile dot com slash universe. Cut your wireless bill to fifteen bucks a month. At mintmobile dot com slash universe. Forty five dollars upfront payment required equivalent to fifteen dollars per month new customers on first three month plan only. Speeds slower about forty gigabytes on unlimited plan. Additional taxi, s, fees, and restrictions apply. See Mint mobile for details.
AI might be the most important new computer technology ever. It's storming every industry and literally billions of dollars are being invested, so buckle up. The problem is that AI needs a lot of speed and processing power, So how do you compete without cost spiraling out of control? It's time to upgrade to the next generation of the cloud. Oracle Cloud Infrastructure or OCI OCI is a single platform for your infrastructure, database application development and AI needs. OCI has four to eight times the bandwidth of other clouds, offers one consistent price instead of variable regional pricing, and of course nobody does data better than Oracle. So now you can train your AI models at twice the speed and less than half the cost of other clouds. If you want to do more and spend less, like Uber eight by eight and Data Bricks Mosaic, take a free test drive of OCI at Oracle dot com slash strategic. That's Oracle dot com slash Strategic Oracle dot com slash Strategic.
If you love iPhone, you'll love Apple Card. It's the credit card designed for iPhone. It gives you unlimited daily cash back that can earn four point four zero percent annual percentage yield. When you open a high Yield savings account through Applecard, apply for Applecard in the wallet app, subject to credit approval. Saving d is available to Apple Card owners subject to eligibility. Apple Card and Savings by Goldman Sachs Bank USA Salt Lake City Branch Member FDIC terms and more at applecar dot com. When you pop a piece of cheese into your mouth, or enjoy a rich spoonful of Greek yogurt. You're probably not thinking about the environmental impact of each and every bite, but the people in the dairy industry are. US Dairy has set themselves some ambitious sustainability goals, including being greenhouse gas neutral by twenty to fifty That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. Take water, for example, most dairy farms reuse water up to four times the same water cools the milk, cleans equipment, washes the barn, and irrigates the crops. How is US Dairy tackling greenhouse gases. Many farms use anaerobic digestors that turn the methane from maneuver into renewable energy that can power farms, towns, and electric cars. So the next time you grab a slice of pizza or lick an ice cream cone, know that dairy farmers and processors around the country are using the latest practices and innovations to provide the nutrient intense dairy products we love with less of an impact. Visit us dairy dot com slash sustainability to learn more.
All right, we're talking about trimpo luminescence, which sounds like it's a nice snack like shrimp chips kind of, but they glow.
That's right, they've tapped to that shrimp's proportional glowing ability.
Oh, I see, like maybe you got bin by one of these shrimps and now there's a superhero with that ability. But it would only work underwater, which is kind of a question that I had. Does this only work in water or is it other liquids too?
It does work in other liquids, for example, in sulfuric acid, it's even more powerful. But I do not recommend anybody get a container of sulfuric acid and try to do experiments with it. Then involve potentially shattering the glass or making it explode, so that's quite dangerous. But it's not limited to water, though most of the experiments have been done in water with varying amounts various gases dissolved into it.
Interesting, So is that a clue about what's going on? Like, it's not related to the actual water molecules. H two, but maybe it's something with what these bubbles are doing.
Yeah, people were wondering for a long time about where the light is coming from Is it coming from inside the bubble? Is it coming from the liquid just on the outside of the bubble. It's been something people have been wondering about for a long time, and this is something that's difficult, Like you might be wondering, like can't you just take a picture, like figure it out? Man, it's been going on for one hundred years, but it's hard because it's really tiny and it happens really really fast, and so getting like very accurate photography of what's going on is difficult. People use things like laser scattering to try to measure the size of this bubble is a function of time, So experimentally it's quite challenging. You know, until like twenty or so years ago, people couldn't even reliably make single bubbles on a luminescence, like create a bubble in a known location that you could like focus your cameras on to take pictures of that were resorting to this like multibubble luminescence, which makes it harder and harder. So we're sort of been making progress over the last one hundred years just in like getting data for what is going on, not to mention then building models to explain it.
Interesting because you know, we have telescopes that can look at black holes and other galaxy at the center of other galaxies, and we have you know, my electron microscopes that can look at basic media individual atoms. But you're saying this is kind of hard to take a look at.
It's difficult because of the speed. You know, the light that's emitted lasts for something like one hundred pico seconds, and so having cameras that are that high resolution is challenging. There are some measurements using streak photography that can get some information, but the best resolution it comes from laser scattering, because you can shine lasers at these bubbles and then the way the laser light bounces off depends, for example, on the size of the bubble at that time. So we do now have very precise measurements of the radius of the bubble as a function of time, so we can sort of see it collapsing. What we'd really like to know is like what's going on inside the bubble, what's the temperature of the gas or whatever is inside the bubble, And that's something we don't have direct measurements of.
Hmmm.
Interesting, So yeah, I think you sort of keyed into it is that what's going on inside of the bubble, right, because inside of the bubble is what like water vapor, right, that's what these bubbles are made out of.
Well, depends a little bit on how you create the bubble, but we think initially it's water vapor or gas that evaporates within the inside surface of the bubble when it's created. So it depends a little bit on like what's dissolved into the water. You know, is there argne or xenon trace amounts of that inside the water, But yeah, we think that essentially, have a very low pressure bubble that's formed, and then the sound waves come along and they pump some energy into that. It makes the bubble expand, right as you have this external pumping that pushes the bubble out, and it continues to expand because of its inertia while the pressure drops, and then eventually the water on the outside the pressure gets too great and it's like, hold on, we can't sustain this bubble any longer, and so it stops. Right. It grows from like, you know, a few microns to maybe ten microns and then it stops and it collapses. It crashes down, and we think that probably what's happening is that that gas, that small amount of gas inside the bubble is getting very rapidly compressed. But again, the details of how that generates these photons is not something we yet understand.
Interesting and it sounds like you don't even know what's inside of the bubble. It could be like a gas, or it could be like floating water molecules.
We don't understand. And the reason that this has been a puzzle for so long is for two reasons. One is it's hard to get data about what's going on exactly inside of it, and the other is that these conditions are really extreme. Like we have some theories for how bubbles work, and we have theories for like how gas can emit light, and we have some theories for like what happens to a plasma, but most of these make assumptions, like they assume that the gas is an equilibrium, or you know, the bubbles are a certain size or whatever, and this phenomenon seems to sit like outside of all of where those stories should work. You know, it happens really really fast, and happens really really small, and the gas doesn't have time to relax and come into equilibrium. So all the sort of mathematical stories we've been building up and telling ourselves, this patchwork of physics we've built over the last few hundred years, this falls like right in the middle of them. And so if you try to like build a numerical simulation of what's going on, we just don't really have physical laws that can tell us what's happening unless you go like way down to the individual particles. But it's impractical to simulate a bubble that has like ten to the ten particles in it using individual particle physics. So it's sort of like fallen in this crack between our knowledge of how fluids work and how gases work at various temperatures.
It's like it's too dynamic in a way, right, because physicists usually like to think about things once they're settled down or like at the super duper particle level. But this is you're saying this, this is somewhere in between.
It's somewhere in between, and we don't even know for example, is this bubble a sphere. Is it symmetric or does it collapse asymmetrically? Is there like a first point in the bubble where the collapse starts to happen, sort of like the way a big rock will crack and they'll start in one place and then really split there. Or is it completely spherical? And a lot of the calculations people have done assume a spherical bubble, and other people are like, what, you can't assume a spherical bubble. It's obviously asymmetric. So there, you know, shouting matches in the literature about how this might work.
Do they use all caps when these shout in papers this present is an idiot?
If they could make that text blink, they would do that, you know, bright red and blinking. Wow.
And it's kind of a big mystery because you're essentially taking the energy from sound waves and you're turning it into light. But that's kind of weird, right, Like sound doesn't have enough energy to do that.
Yeah, and there is sort of enough energy. It's about the energy density, Like sound waves have a good amount of energy, but you know, there's not a lot of energy in a very small space, and so if you talk about the energy density, then you need like a boost of a factor of ten to the twelve, like a trillion times more energy density to create UV photons from the energy in these sound waves, and so that's very impressive. Like these tiny little bubbles are like gathering the energy from the whole bubble and then compactifying it down really rapidly into a tiny spot that can release these high energy photons.
Wow, that's pretty cool. So it's some sort of mysterious process. Well, let's get into the mystery of it. But you were saying, the key is the temperature of the bubble.
Yeah, people really disagree about how hot it gets inside the bubble. You know, this is just normal water. You start with room temperature water, it's like thirty c you know, seventy degrees fahrenheit or whatever. You don't have to like heat this thing up. But what happens when you pump the sound waves into it is it grows and then collapses, and when the pressure increases, the temperature increases. Like why is it hot inside the Earth? It's hot partially because of radioactive decay, but also because of crazy pressure. Why is it hot inside the sun because of crazy pressure? Right, you heat things up when you add pressure to them, and so people wonder, like how hot does it get in there?
You mean when the bubble collapses, because I imagine when the bubble is expanding, it gets sort of like a vacuum. It's super cold, but then when it collapses and compresses this gas, then it gets super hot.
Yeah, and there's one guy with a crazy theory. He thinks that when the bubble expands, the gas freezes and turns into this like weird kind of ice, and then when the bubble collapses, it like cracks that gas, and the electrons are sort of left behind and they're the ones emitting the light.
Wait wait, wait, wait, what do you mean one guy with a crazy theory? Are you talking about a fellow physicist?
I'm talking about a fellow physicist. Because there have been so many crazy theories about what's going on inside of this Because it's been an open puzzle for so long, it's like a playground for people to have crazy, bonkers ideas there. Some people think it's like capturing the vacuum energy of quantum fields. All sorts of other crazy ideas have been battered around these days. The most likely explanations come down to a disagreement about whether when it collapses, does it form a plasma like what's going on inside the sun, or just a very very hot gas that then emits some light.
Interesting because I guess gas by itself can emd light, right like fluorescent lighting. You just have a gas, it glows, right.
I think fluorescent lighting is actually usually creating plasma and that plasma glows. But you're right that hot gas can also emit light, right. You don't have to be a plasma, and there's lots of ways for this to happen if you think about it, like at the particle level. If you do have a plasma, then those things emit light because a plasma, remember, is when things get hot enough that the electrons have so much energy that they're no longer captured by the nucleus. They're flying around free. And if you have an electron flying around free, it's going to get accelerated by all the atoms nearby it that now have a positive charge. And if you accelerate an electron, it will emit radiation and that's photons. Every time an electron changes direction, accelerates, it gives off a photon. So if it's a plasma, that's probably the process as a fancy German word called bremstra lung, which means breaking radiation. So if it's a plasma, probably it's the electrons giving off this light. But other people have ideas that maybe it doesn't get hot enough to create a plasma and it's just like a really hot gas instead.
Oh interesting, But I guess you're pretty sure that it's not like a chemical reaction, you know, like striking a match or something burning or something igniting, or you know, like materials that just kind of flash when you light them up.
We're not sure, actually, because if it's not hot enough to make plasma, there's a whole variety of chemical reactions that can give off this kind of light. For example, it could just be like water disassociation, you know. Either you could just be like pulling water molecules apart and smashing them back together. That's one theory that has this like asymmetric collapse, that these like jets of water are penetrating into the bubble asymmetrically, and when that happens, that's actually called fracto luminescence. This is a commonly known effect in solid state physics. When you're pulling apart and then reuniting things with charges, they can give off basically static electricity little sparks. So that's one possibility.
I mean, like you're pulling the two ageism that o apart and that creates a spark.
Yeah, Or it could be that, you know, water molecules bumping into each other can also give off light, you know, or you could just like excite the water molecule itself make it a little sort of internally hot because water molecules have lots of ways to vibrate and to rotate, and they can absorb that energy and then they can give it off. So water itself can glow in even a liquid form, and so you know, it depends just on the temperature. What's going on inside there?
Interesting because I guess if it is plasma, then the light is more easily explained. Like if you have plasma, it's normal for plasma to just glow.
Right, Plasma's almost always glow. Yes. The trick is, how do you get a plasma? In order for that to happen, you need more than just compression. The calculations people have done suggest that for a plasma happen, what you need is like a supersonic shock wave. You need this bubble to collapse faster than the speed of sound in order to get the gas like compressed enough and hot enough in the short amount of time to become a plasma. That's something like you know what goes on inside of supernova. Right a supernova, you have a gravitational collapse that's racing faster than the speed of sound in that material, and so this shockwave is what gives you this incredible burst of energy from the supernova. So more than just like creating a tiny star inside a water bubble in your garage, you could be making like a tiny supernova in your garage.
I was just sparking my cars, but apparently I've been wasting my garage space on two mundane things.
Yeah, supernova factory right here.
And I think you were saying, there are some clues about what's going on, Like we sort of have a rough idea of the temperature inside of these bubbles.
Well, there is a lot of discussion about that because it's hard to measure it directly, and so what people do instead of, you know, putting a thermometer inside is tiny bubble, what they do instead is they look at the pattern of light that comes out. Because usually the pattern of light, the spectrum of light, like which frequencies are there in this light gives you a clue about the temperature. Just like the fact that I emit infrared radiation tells you that I'm not as hot as the sun, and the fact that the sun emits in the visible tells you it's not as hot as gases swirling around a black hole. So you can sort of invert that and say, what's the frequency of this thing? What temperature of object would give me light at that frequency? And when you do that you get numbers like ten thousand degrees kelvin, which is like crazy hot.
That's hotter than the surface of the sun inside of the little bubble.
Inside in this little bubble in your garage.
Yeah, that's what we think though, right.
That's what some people think. There are other disagreements. Other people measure different spectra that people have different conditions. Some people think that that's not a good model because that assumes that the gas is sort of sitting there and has time to thermalize and equalize, because this is thermal radiation. But this whole thing happens in you know, picoseconds. There's no time for that. So people think it's an inappropriate way to deduce the temperature because you know, what we're doing here is we're like trying to make analogies to what happens with other objects, the Earth, the Sun. But those things are very stable, right, They've been sitting around for a long time. They obey ideal gas laws, for example, whereas this tiny, little dynamic collapsing supernova in your garage, it's not necessarily true that the same rules apply. So you've a bit going out on a limb and making those assumptions.
You're saying, maybe you can't measure temperature because it's not steady or calm.
Yeah, maybe the frequency of light is not just determined by temperature in the same way as it is for other objects. And so some people think it probably might be much colder. Other people think it might be much much hotter. Some people suspect it could even get up to millions of degrees kelvin inside that little bubble.
And you were saying that these pulses, these bubbles last for like picoseconds, which is also sort of a clue about what's going on.
Yeah, one of the recent experimental breakthroughs was improving the timing of measuring of the light, and so we now know that these light pulses can last like fifty to a few hundred piko seconds, depending on you know, what gases you put in there. If you put xenon in there, for example, you get longer pulses. It depends a lot actually on how much xenon and how much are gone you.
Have in there, in dissolved in the water.
Dissolved in the water, because we think the gas in the bubble is evaporating from the surface of the bubble the interior surface. And so it depends on what kind of stuff you have in the water.
Like if you get still water or mineral water, and.
A lot of the instructions for doing this, for example, suggest that you degas your water first as much as possible, and then put in a deliberate bubble, like make one bubble, and that way you'll get a single bubble of suno luminescence instead of like lots of bubbles forming if you want to study in detail. But the clue came from measuring these pulses to be you know, order fifty to one hundred is ish piicoseconds. Because the different theories for how you're getting this predicted different length pulses, and so for example, fracto luminescence, this idea of like asymmetric jets of water forming like these fingers into the bubble when it's collapsing. That would have like shorter pulses, and other theories people have, you know, make longer pulses, and so, you know, the more data we get, the more we can sort of like narrow in on which theories are consistent with what we see.
And you say, I can make this happen with other liquids, like sulfuric acid. But that's very different than water, right, it would be maybe a totally different theory about what's going on.
Yeah, well, some of these theories can be simply extrapolated to sulfuric acid, and other ones not. Some of them are very dependent on the chemistry. But it does happen in sulfuric acid, and actually it's like much brighter if you use sulfuric acid. It's also dependent on the temperature, Like colder water gives like one hundred times brighter pulses than warmer water. Colder colder water, Yeah, exactly.
I guess maybe the water is denser, maybe there's more energy in those waves.
Yeah, so maybe the speed of sound is faster and colder water, right, so the energy is transferred faster, and it depends a lot on the gases you use, so it's really sensitive to a lot of these details, which you know gives you some clues as to what might be going on.
And so what are the current theories about what's going on? Like are there quantum theories like at the particle level about what's going on?
So the two most mainstream theories are either a shockwave model where you have this like supersonic compression into a plasma and then you have electrons radiating in this light.
Meaning like the bubble expands, it fills up with gas, and then the sound wave around it causes it to crunch really fast and that creates a plasma. That's the one theory.
That's one leading theory. The problem is that nobody's ever seen this shockwave or the plasma directly, and the numerical simulations don't necessarily agree perfectly with what we actually see. The second leading theory is sort of a shock free compression model that says, when you take this gas, you squeeze it down, it gets really hot and then it glows, but you don't actually get asthma. But it's not clear that that can generate enough light to explain what we see. So we have sort of two models, which you know, seem kind of reasonable but disagree a little bit in the story of what's going on, neither of which work perfectly. There's like, you know, a lot of holes there. People need to do some development. But then they are the fun models, the crazy model that suggests that something bonkers could be happening.
There's another wild and crazy person out there with ideas.
Yeah, because you know, that's what theorists do. They find things that can't be explained and they say, hmm, maybe this is a clue, Maybe this is the thread that if I pull on, it is going to unravel everything we know about the universe. And you know, kudos to those people for being creative and try to identify things. That's what happened with Einstein, right, He was trying to explain the photoelectric effect, this experiment that nobody else could understand, and he developed quantum theory sort of accidentally along the way. So it's definitely well motivated.
That was an experiment you could do in your garage too, right.
Yeah, exactly. You just you know, shine light on a piece of metal and measure the electrons. So I mean, back then everything was a garage, right, Science was just garage back then.
Well, now the garages have just gotten bigger. Now you can fit one hundred cars in the large hat Tern collider tunnel.
That's right. Welcome to my ten billion dollar garage, Jay Leno, eat your heart out.
Hey yeah, Tony Stark would be proud.
But there's this really fun theory about quantum radiation, and the idea is that maybe somehow this sun iluminescence comes from like the equivalent of Hawking radiation, that you're somehow capturing the vacuum energy from the quantum fields. What remember that space we think is not just emptiness. We think it's this weird quantum fabric that everywhere in space has these quantum fields in it, a field being like the possibility for an electron or a photon to exist here. And you know, you can think of it like parking spaces or something. You know, it's a possibility for something to be there. But the weird thing about quantum fields is that even if there are no cars in the parking lot, there are no particles there, there's still energy there. Quantum fields can never be add zero energy. So even the emptiest space you can imagine has some energy in it, and we talked to the podcast about how maybe to tap into that or identify that, or directly observe it, you know, to show that it's real with this weird experiment called the Casimir effect, where again you create a resonant cavity and what it does is it enhances some of those quantum zero point fields and it suppresses others, and in doing so creates like a pressure differential. So you take these like two very thin plates and put them close together and you feel this weird, mysterious force on them. So people have been wondering maybe the quantum zero point energy is responsible for this, because maybe what's happening when this bubble collapses is that you are suppressing or enhancing various elements of this quantum field. And some guide did a calculation showing that, oh wow, maybe this can actually contribute it and explain it, and so that was kind of exciting.
For a few years, I thought you were going to say that it's when the bubble expands and creates a vacuum that maybe like it pulls energy from the vacuum of the universe.
Well, there is energy in every vacuum, but somehow turning that into real photons is the trick, And so people think that these photons are created when this bubble is collapsing, because it's like enhancing various modes, these very high energy modes of the vacuum inside the bubble.
Like it's such a crazy collapse. It's actually like perturbing the quantum fields of the universe.
Yeah, but then somebody else came along and did another calculation and showed that for that to work, the bubble would have to collapse faster than the speed of light, so not just supersonic, but like super luminal.
Well maybe I don't know, I guess not.
So either you've got to double down and be like yes and I'm overthrowing relativity at the same time, or you're like, hmm, maybe this idea doesn't explain metallity.
Maybe need a better name, Like so no super luminocence. There you go. All right, Well it's still a big mystery. Let's get into what might be some interesting applications of what we might learn inside of these little bubbles. They might help solve our energy needs in the future. But first, let's take another quick break.
When you pop a piece of cheese into your mouth, or enjoy a rich spoonful of Greek yogurt. You're probably not thinking about the environmental impact of each and every bite, but the people in the dairy industry are. US Dairy has set themselves some ambitious sustainability goals, including being greenhouse gas neutral by twenty to fifty. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. Take water, for example, most dairy farms reuse water up to four times the same water cools the milk, cleans equipment, washes the barn, and irrigates the crops. How is US Dairy tackling greenhouse gases. Many farms use anaerobic digestors that turn the methane from maneuver into renewable energy that can power farms, towns, and electric cars. So the next time you grab a slice of pizza or lick an ice cream cone, know that dairy farmers and processors around the country are using the latest practices and innovations to provide the nutrient dense dairy products we love with less of an impact. Visit Usdairy dot com slash Sustainability to learn more.
With the United Explorer Card, earn fifty thousand bonus miles, then head for places unseen and destinations unknown. Wherever your journey takes you, you'll enjoy remarkable rewards, including a free checked bag and two times the miles on every United purchase. You'll also receive two times the miles on dining and at hotels, so every experience is even more rewarding. Plus, when you fly United, you can look forward to United Club Access with two United Club one time passes per year. Become a United Explorer Card member today and take off on more trips so you can take in once in a lifetime experiences everywhere you travel. Visit the Explorer Card dot com to apply today. Cards issued by JP Morgan Chase Bank NA Member FDIC subject to credit approval offer subject to change.
Terms apply.
There are children, friends, and families walking, riding on paths and roads every day. Remember they're real people with loved ones who need them to get home safely. Protect our cyclists and pedestrians because they're people too.
Go safely.
California from the California Office of Traffic Safety and Caltrans.
How to have fun anytime, anywhere. Step one, go to chumbucasino dot com.
Chumbucasino dot com. Got it.
Step two, collect your welcome bonus. Come to Papa welcome bonus. Step three, play hundreds of casino style games for free.
That's a lot of games, all for free.
Step four, unleash your excitement.
Chump.
The casino has been delivering thrills for over a decade, So claim you're free welcome bonus now and live the chamber life. Visit chambucasino dot com. Bwgrouple part necessary. We don't prohibited by lossy terms and conditions. Eating plus.
All right, we're talking about trimple, illuminate, and still which I guess I'm still hung up on because it's sounds tasty.
Well, here's an experiment nobody's ever done. Is take a shrimp, put it inside one of these bubbles, and then put sound on it. See what happens when you collapse the bubble on the shrimp.
Or maybe this light inside of these tiny bubbles is created by tiny little shrimp shrimp patons.
Shrimp photons. Yeah, or maybe we can get sauno shrimp a lessons.
Hmm, yeah, it will be a nice cocktail of physics now. But it's sort of interesting because I'm learning sort of recently that apparently, you know, plasma is this fourth state of matter, and it's kind of straightforward when you think about it, when you hear about it, but actually it's still a big mystery to physicists about what's actually going on and what's happening. And so in this case, maybe that's what's going on inside of these little bubbles, in which case they might teach us a lot about how to make fusion.
Yeah, plasma is super fascinating and it's actually one of the most common states of matter in the universe, right because, like, if you think about the Solar System, the Solar System is mostly the Sun, and the Sun is mostly plasma, So we think about liquid and water in gas because that's what's around us here in our neighborhood. But if you zoom out it just to tiny little bit and include the Sun, then the Solar System is mostly plasma. But plasma is extra tricky to understand because not only is it really hot, so the particles are moving around really fast, which means that every particle is affected by lots of other particles, right, like in a solid, a single atom is mostly affected by its immediate neighbors because nobody's moving very much. But in a plasma, of particles are zooming around really fast, and so they're affected by lots of particles. So if you want to like describe it numerically, do some calculations, then it takes a lot of different interactions to explain. And on top of that, not just are they moving fast, but everything's electrically charged, so you don't just have the speed of these particles and how they're bouncing into each other. You also have all these electric fields which cause magnetic fields, which cause electric fields. It's a real nightmare. It's a whole field called magneto hydrodynamics that tries to deal with this. And as you say, it's not something that we understand aco plasma and you put certain conditions on it, we can't always predict what's going to happen. You just got to go out there and build it and see what happens. Because the universe still has the prices for us.
Yeah, and so what's cool about that is that if we can understand it and kind of control it, then we might be able to do what the Sun does here on Earth, right, we might be able to build fusion reactors that kind of do what the Sun does and gives us energy forever.
It's a long standing goal of physics. It's something that's been like ten years away for about fifty years now, achieving fusion here on Earth. And as you say, this standard approach is to try to replicate what's happening in the Sun, which means get a bunch of hydrogen, heat it up really really hot. The problem is that the Sun is able to hold that together because if it's gravity, it's this huge blob of stuff, it has enough gravity to hold itself together. We don't have that much hydrogen, so we need another way to hold it together. So we use these magnetic bottles, and we talked about on the podcast. Recently there's this program in France called eater Iter, which is aiming to build a fusion react inside a magnetic bottle that might actually create energy, like a first working fusion reactor that could have like commercial prospects. That would be very exciting because you can use fuel like seawater to just get the hydrogen from there and there's no radioactive waste and it's you know essentially renewable and a single gram of fuel as much energy as eighty thousand tons of oil. So it would be really excellent. It would like transform our economy and our way of life. Electricity would be so cheap, it would be almost free.
And we just need to give Eater some shrimp so luminiscence.
But it's difficult, right. Eater is like a thirty forty billion dollar project. Now, it's enormous, it's complicated. It's not easy to contain these things, and so people are always on the lookout for ways to make fusion happen that doesn't require enormous building sized magnetic bottles. So for a while, people thought, hold on a second, if we can create super hot, tiny dots of plasma in our garages, maybe we could just do fusion there. And people have thought for a long time that you don't necessarily need a sustained fusion reaction to make fusion happen. There's this whole other strategy for fusion where people just shoot like lasers at a dot of fuel and try to get it to implode and make fusion happen, like on the spot. So people thought, wait a second, maybe the same strategy will work, except instead of using lasers, we're just using sound waves to make the thing implode and turn into a plasma and fuse.
Wow. Yeah, because you were saying, maybe a theory about what's going on inside of these little bubbles is that there's maybe fusion going on, right like, as the bubble collapses with so much pressure, maybe it's fusing things together. Was that one of the theories.
Well, what happened is people tried to make fusion happen. They're like, well, let's instead of using water, let's use like heavy water that has deuterium in it, because deuterium is a good source of fuel for fusion. So they said, well, let's try to make it happen. And so there were a bunch of guys around fifteen twenty years ago who did a bunch of experiments and they actually claimed that they were achieving fusion. There was this experiment in two thousand and two that used deterium and heavy water and claimed to be generating a bunch of neutrons, which suggests that fusion was happening inside their little bubble. They called this bubble fusion, and that was very exciting because it's cheap, it's not complicated, and like you could build reactors almost trivially if that were true. But unfortunately, and the reason you don't have a sonoluminescence fusion reactor powering your electric car right now is that nobody could repeat that result.
Interesting, so the idea way, the idea is that you would use sound waves to trigger fusion inside of heavy water, like basically the same experiment where you have like a cup of heavy water and then you put speakers and somehow that will you know, create these flashes that then you then capture that energy.
Yeah, and in principle it's not outrageous because really all you need for fusion happen is really really high pressure. Remember, the reason that fusion does just happen all the time is that two hygigen atoms I don't really like each other. You know, they're both protons, and protons are positively charged. So to get them together close enough together for the strong force to fuse them, you have to overcome that kolom repulsion, you know, the two positive charges disliking each other. So really all you need for fusion is take some source of fuel like deterium and compress it enough. And that's what sono aluminescence is doing. It's like extraordinarily effective compression on a very short time scale. So in principle, you know, you might think it would work. The problem is that probably what's going on inside those bubbles gets you to like ten thousand degrees Calvin, but to get to fusion, you really would need millions of degrees Calvin. So it's probably just not quite enough.
Like the effect is enough to compress the heavy water, but it doesn't compress it enough to actually start fusing together.
Yeah, it doesn't actually ignite into fusion. It can make a glow, which is you know, electromagnetism, but to actually get those nuclei together to overcome that repulsion so they fuse and create you know, energy from the strong force, that's a whole other magnitude.
Couldn't you just get bigger speakers, you know what I mean? Like, what's the theoretical limit? Is it just that these bubbles or the physics of the heavy water molecules can't compress that much? Or is it just that we haven't you know, dared to use big enough speakers.
I try it. Nobody's played Metallica loud enough yet. Yeah, that's the reason we haven't solved the energy problem, the.
Whole climate, heavy metal for the heavy water.
No, well, you asked a great question there, what's the theoretical limit. Knowing what the theoretical limit is requires understanding the theory, having a working model for what's going on, and we just don't. So you know, it's possible somebody could cook up a way to make this brighter. And there are people working on ways to make sunoluminescence more intense. That's why they do it with sulphuric acid, or they dissolve xenon it, or they make it cold. But it's an experimental study because we don't have a working model for what's happening. So yes, somebody out there could say, hey, it turns out if you use this sound range, or if you add you know, detergentto your water or something, that it changes the conditions in a dramatic way and boosts you up to levels where you might achieve fusion. That's still a possibility. Nobody's shown that happened yet so far.
Well, it sounds like it's still kind of a big mystery about what's going on inside of these little bubbles, whether it's plasma or just a chemical reaction that's making these bubbles glow. And so I guess the question is, how are we going to figure this out? Daniel? It sounds like it's been a mystery for decades, maybe even as far back as when you were a gratitude. You know, when something like this sticks around in the physics community for so long and it's still a big mystery, like why don't people get on it and try to figure it out?
People are on it, you know, people are studying it, and the way forward is to take better and better measurements so we get more precise details about what is happening, and that will let us resolve our theoretical models. You know, we need like to know what's happening so we can tell a better story about what makes it happen. And so we need, like experimentalists to come up with better ways to measure the temperature inside these bubbles and to take pictures of these collapsing bubbles with better and better resolution so we can just get more information. You know. It's just like when you have a murderer and you haven't solved it, what do you do? You go pound the pavement for more clues, so we need more details which allow us to then weave together a story for what's happening. So it's really exciting because it's the kind of fields where the experiments are leading the way. We see something we don't understand and we want to know more. I'm jealous of that because you know, like in particle physics, we see very little that we don't understand. We're always looking for something we don't understand. It's like decades between glimpses particles that we don't understand. So here's something like very concrete that we don't understand that you don't need a ten billion dollar experiment to recreate. So it's pretty exciting.
Wow. So literally anyone can be in the cutting edge of this physics research.
That's right, Go create supernovas in your garage, folks, but wear eye protection.
Why with theory, Daniel, I think inside of these bubbles are little tiny ardvark sucking up and the particles. And that's my theory.
Yeah, and that's as good as every theory.
Yeah, right, I'm at the I know as much as Stephen Hawking.
Yeah, exactly, You're on the frontier for sure.
But yeah, another a great and awesome example of how there are mysteries even in our everyday lives. Like the next time you take a slip of water, think about the fact that there are mysteries inside of those little bubbles, and that if you hook it up some speakers, you could be doing physics research in your dining table.
And maybe even solve the climate crisis.
All right, well, we hope you enjoyed that. Thanks for joining us, See you next time.
Thanks for listening, and remember that Daniel and Jorge Explain the Universe is a production of iHeart Radio. For more podcasts from iHeart Radio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows. When you pop a piece of cheese into your mouth, you're probably not thinking about the environmental impact. But the people in the dairy industry are. That's why they're working hard every day to find new ways to reduce waste, conserve natural resources, and drive down greenhouse gas emissions. House US dairy tackling greenhouse gases. Many farms use anaerobic digestors to turn the methane from manure into renewable energy that can power farms, towns, and electric cars. Visit you as dairy dot COM's last sustainability To learn more.
There are children, friends, and families, walking, riding, on passing the roads every day. Remember they're real people with loved ones who need them to get home safely. Protect our cyclists and pedestrians because they're people too, Go safely. California From the California Office of Traffic Safety and Caltrans.
We're Paint Care and we're all about keeping it simple. We make recycling leftover paint easy with convenient locations like your local paint store. We have threesome rules for painting smarter and reducing waste. One buy only what you need, two use up what you already have, and three recycle the rest. Visit paintcare dot org slash three simple rules to learn more or find a paint drop off site near you
