Daniel and Kelly’s Extraordinary Universe - How long is a photon?

Episode Date: July 11, 2024

Daniel and Jorge wrestle with the tricky question of the length of a photon, and end up talking about hotdogs and meatballs.See omnystudio.com/listener for privacy information.

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Nobody really knows what a photon is. There's something weird and mysterious we might never fully understand. So you're just going to leave us in the dark? You're not going to shed any light on it? That's as bright as I can be on the topic. Hi, I'm Jorge May Cartoonist and the author of Oliver's Great Big Universe. Hi, I'm Daniel. I'm a particle physicist and a professor at UC Irvine, and I'm still hunting for a brilliant explanation about photons. I thought brilliance was your job description. Isn't it your job to provide that brilliance? My job is to hunt for the brilliance

To try to mine the truth From the firmament of reality We don't always find it I guess it's hard to shine light On some of the corners of the universe That are hard to see We just have to hope somebody out there is bright enough Somebody has a light bulb moment there

But what do you mean? Are you saying photons Depend on where they come from? I'm saying that the language of physics We use to explain things uses as the basic mental building blocks, things we do understand. Waves and bits of sand and tiny little particulate stuff. And none of those things really completely and fully describe the photon. It's those things, but also something else.

I see. It's a language issue. Blame it on the linguist. If we don't understand the universe, it's not the physicist's fault. It also turns out to be fundamental to how we do science. We often tell different stories about the same kind of stuff, depending on the question we are asking. None of our science is totally exact and complete.

It's always approximate and which approximation, which idea we use, which conceptualization is relevant depends on the questions we're asking. Sounds like it's a big relativity problem because it's all relative. It's relatively complicated, yeah. Yeah, indeed. But anyways, welcome to our podcast, Daniel and Jorge, explain the universe, a production of iHeard radio.

In which we take the whole universe as the context for our goal to understand things. We want to understand how droplets form into hurricanes, how tiny little corks make protons, how enormous masses of stuff swirl into black holes. We want answers for everything and we hope one day to be able to stitch those answers together into a single comprehensive, complete understanding of the universe, even though that might actually be impossible. Yeah, we try to track the journey of humanity from the shadow. us into the shining light of understanding and comprehension about this amazing universe we live in, even if it sometimes takes a few stories or different stories along the way.

The history of physics is seeing stuff we don't understand and then coupling together some sort of mathematical explanation for what might be going on. And the bigger picture is to then try to weave those explanations together into a single coherent idea. But that task is still not finished and it leaves us sometimes in an awkward situation of not being able to answer pretty basic questions about what's going on out there. Are you saying physicists can't get their story straight? It's a little suspicious. I'm saying the universe is a little bit like Rushmond, you know.

The story you tell depends on your context. But this is not something that only physicists do. You know, if I ask you how the baseball game went yesterday, you tell me a story about the teams and who was playing well and who is struggling. You put it in context to make it exciting. You don't just give me a dry list of what happened to every single particle in the vicinity. of the stadium that day. But there'd just be one story about who won and who lost.

If you think that's the story, right? Maybe the story is something else. The changing of the hot dogs, how the mustard now tastes, you know, the weather. Everybody might ask different questions about the same sets of events. And then they might need to use different physical concepts, even different mathematical formalisms to get those answers, which makes a very complicated answer, very basic sounding questions. Right, right. Sometimes you need hot dog particles.

Sometimes you need baseball particles. Yeah, exactly. You can build a whole universe on the hot dog theory. Hot dogs are the fundamental component, and what's inside them doesn't really matter. Right, right. Is it the hot dog on or the hot dog gino? The whole brilliance of hot dogs is just enjoying them and not even caring what they're made at. What's the shape of a hot dog on? And how long is it? That depends on which city you're in, you know? Yeah, yeah. Or which country, too. That's right. And your relative velocity, because some of these things can be length contracted.

That's right. If you eat it fast, then it's a lot shorter than it is. If you're at high velocity relative to your hot dog, it will seem shorter. So yes, somebody shoots a high dog into your mouth and near the speed of light, then you're going to have an interesting experience. But then it depends on which direction it is when it's being shot at you, right? If it's being shot at on the side, it's still going to be the same length. Yeah, exactly. It's just going to be thinner. Yeah, let's just spend the rest of the episode talking about hot dog physics. High velocity hot dog physics. Relativistic hot dog physics. A topic nobody has ever explored.

We can be the first to write a paper in the journal of hot dog physics. Well, I think we're definitely the first to ever talk about it in a physics podcast. I'm thinking, I don't know, I haven't done the exhaustive literature search. Somebody out there let us know if we need to cite you on this. Yeah, somebody else do the research for us. But anyways, it is interesting to talk about how long things are, you know, basic questions like that about everyday objects. we see every day. It is often a really fruitful but sometimes frustrating

to ask intuitive, natural questions about the kind of things we think the universe is made out of. We think everything out there has certain properties. It has a size, the length, the mass, etc. And so we try to apply those concepts these things we're familiar with from the kind of stuff we're used to interacting with and apply that to quantum objects,

but it doesn't always quite work. Yes, we found out the quantum world is very strange, very mysterious, very uncertain, and very hard. for our simple brain sometimes to understand and capture and to get an intuitive understanding of it. But that doesn't mean it's impossible and that doesn't mean it's not useful. In fact, it's very helpful for shining a light onto what we do understand and what we don't understand. And it can help you make a better mental picture for what's going on at the quantum level. Right, but the question is, can we shine a light on light itself?

And so today on the podcast, we'll be tackling the question. How long is a photon? Now, is this a photon coming off of a hot dog, or does it matter where it's bouncing off of? A hot dog colored photon? Wow, what is the color of a hot dog? What is the color of a hot dog? Sounds like the topic of a philosophy class here. If you eat your hot dog with eyes closed, does it have a color or not?

I wonder if there's a paint shade out there that's called hot dog. I think people usually avoid having the runes painted hot dog There's probably more adjectives to it like bright summer hot dog or something Summer baseball hot dog Home run hot dog misty hot dog Hot dog vapor Wild Mountain hot dog There's so many shades to a hot dog isn't there

But we're not here to talk about hot dogs though it seems like we're gonna We're here to try our best to answer a very simple but very hard question about the nature of light now how long is a photon is that a question about its length or like how long it lasts oh i interpreted it as a question about its length like its physical extent photons can last forever you know their lifetime is potentially infinite you shoot a photon into empty space it'll just keep going forever but you can kill a photon can't you can kill a photon yes absolutely you can absorb it you can interact with it but a photon on its own will not like necessarily decay.

Can it ever, like, is there a possibility for it to, you know, have its energy convert into something else? Absolutely. A photon flying through space can just fly through space, but it can also turn into an electron and positron and then back into a photon or into a muon or an anti-muon and then back into a photon or all sorts of other stuff. So there's lots of quantum possibilities constantly for photons. Can it turn into a hot dog, technically?

Like, you know, in the infinity of infinities, is there a slight change? it can turn suddenly into a hot dog. Yes, there's a slight chance a very high energy photon could turn into a neutrally charged hot dog momentarily. Hopefully it doesn't turn into a hot dog inside your eye. And that tells me exactly what I want to paint my room next year, which is quantum hot dog.

Oh boy. It's like it's different shades at the same time. Exactly. Schrodinger's hot dog. It's like yellow mustard, red ketchup. But it depends on how you look at it, Kind of like the dress. Anyways, that's a very spicy idea. All right, let's talk about this question. But first, we were wondering how many people out there

had thought about the length of a photon or even if photons have length. Thanks very much to everybody who answered this question. I only got one response online. So I walked around campus at UC Irvine last week and I asked a bunch of psych majors and other random people about photons. All right. Well, if you spot a physicist with a microphone on the UC Irvine campus,

make sure to, I don't know, run away or approach. If you think you can answer physics questions on the spot. Or even if you don't, I'd love to hear your thoughts. All right, so think about it for a second. How long do you think a photon is? Here's what people had to say. I don't think we can know about that yet because of the mathematics going weird

since the photon is traveling in speed of the light. So it's my guess. Oh, my gosh. I don't know. I'm going to say, like, 10 to the power of negative 20 centimeters, let's say. I guess photons, they don't have a mass, but they have a momentum, right? So it depend on the wavelength of light. No, I wouldn't even have, like, a guess of length?

Yeah. How long? In size. Yeah. I don't even know what a photon is. I remember it from biochem. Okay. Like maybe inches?

Okay. Yeah, I wouldn't even know. Photons. When I think of physics, I think of, like, small particles. Yeah, so then I'm thinking like centimeters in my new designs. Two millimeters. Two millimeters. I don't know.

Thank you. I don't even know what a photon is. Okay. I majored in criminal justice, so completely outside of my major. Is a photon of particle light? Yes. How long is it? I'm going to say 0.0001 light years.

I don't know, like somewhere in maybe like 0.1 microns, I don't know. All right. Some pretty good answers. Some of them are very specific. 0.1 microns. 10 to the power of negative 20 centimeters. There's a huge, huge range. range of answers here. I think the biggest one is probably 0.001 light years. That turns out to be

a very big number. Well, I'm impressed that they even stuck to the metric system. I mean, everyone, nobody switched to inches or miles. You think photons are metric? I don't know. You don't believe in imperial photons? I believe photons are king, but, you know, I think they should stick to the more reasonable metric system. That's why Darth Vader is all black, because there are no Imperial photons. Wow. That was a big reach there. It took me three seconds there.

Wait, oh, Imperial, yes. Yes, that was a very dark joke. I thought you were going to go with a lightsaber response. I totally set you up for that. What would be the lightsaber joke? Lightsabers only cut things in metric units. I don't know. Lightsayers are about a meter long.

There you go. All right, well, interesting answers. So Daniel, let's dig into it. Well, first of all, what is a photon? How do we define a photon? So a photon is like the minimum packet of light. If you take a really bright source of light, you might imagine it's just shooting out huge amounts of light. As you dial it down, it'll get dimmer and dimmer and dimmer, but it can't get infinitely dimmed.

As you dial that light source down, eventually you'll notice that the light is actually discreet, that it comes out in little packets rather than just being dimmer and dimmer waves. So photons are like the minimum unit of light. But wait, are you saying that photons don't have a minimum energy? Photons do not have a minimum energy, that's true. But photons of a specific frequency have a fixed energy. And if you have, for example, a laser at its very specific wavelength and you dial it down. So it's dimmer and dimmer and eventually you're going to notice that beam gets broken up.

And it comes out in pieces. Like you lower the power to the laser and eventually you'll see it go down in steps. Yeah, exactly. It's just like everything else in our quantum world. Matter is not continuous. You can't zoom in forever on matter and have it always look the same way. As you zoom in on matter, you notice that it has a particular scale, that at some point it breaks up into discrete bits out of which everything is built, just like the resolution on your screen. So light itself has a resolution. It's made out of these little quantum bits, these discrete building blocks. It's thought perfectly smooth. And what is that smallest bit? For light, it's a photon. That's what we call the photon. It's the smallest bit of light. Like if I'm shooting light at a certain frequency, the little steps that I see as I dial down the power to it, that's what you would call a photon. Exactly. Those are photons. And so if you have a bunch of light, you can always ask how many photons are there. There's a specific number. It has to be an integer number of photons. You don't usually notice this because the number of photons usually around hitting your eyeball is enormous.

It doesn't really matter that they're countable. But as things get very, very, very small, then you can notice that you can have zero or one or two photons. You can't have 1.7 photons. Now, how do we think about light? Is it like a, you say it's like a packet, like it's a discrete little object? Yeah, so this really gets at the heart of the question because how you describe this object helps you answer the question, how big is it? And the answer is that we think about light in lots of different contradictory ways

depending on the context. Sometimes we think about light as like a tiny little object, but we, We think about it like a particle, which has no extent, just like a zero volume particle. Sometimes we ignore the quantum nature of it because it doesn't matter. We're thinking about really bright sources where the quantum nature is irrelevant. So we just think about it as classical waves of electromagnetism, the way people did 200 years ago. And sometimes we think about light interacting with quantum particles like light hitting an electron, and then we think about it as a little quantum packet and excitation in the electromagnetic field.

So we have lots of different pictures. of what a photon is and the one that we use depends kind of on the question we're asking. Well, so do you want to then tackle each one of these different ways to look at it at a time? Yeah, sure. I think probably the most relevant in this case is the quantum field theory one, the last one we talked about, but each one gives you a different answer. All right, well then let's maybe tackle each one of these. What does quantum field theory say about the nature of light? Quantum field theory is an updated version of classical field theory, which sounds fancy,

But it just says light is a wave in the electromagnetic field. That's what Faraday and Maxwell and those guys figured out a couple of hundred years ago, that the universe is filled with this electromagnetic field and that waves in it are what we call light. And so you can shoot light from one planet to another and the medium for that is the electromagnetic field. Even though space is empty, it has these fields in it. So light is a ripple in those fields. And we talk about that all the time on the podcast and you have electric fields and magnetic fields and they're at 90 degrees from each other and they're oscillating.

And that's what light is from a classical point of view. That's a traditional classical field theory. The quantum field theory version of that is the same. It just says that there's a minimum to how much it can oscillate. So that as you turn it down, you discover that you can't turn it to any intensity. There are certain steps. So the quantum field theory version says the universe is filled with this electromagnetic field, which has certain steps in energy that it can take.

Well, I guess, first of all, I wonder if listeners, sometimes get confused. used by this like I do, which is that you say light is a wave, but like if I think that's rippling through a field, but if I think of a wave like rippling through a lake or a, you know, my bathtub, it's something that ripples outwards in all directions. Or if I think of like a wave in the ocean, it's like this broad thing that's moving and undulating across kind of a wide area. But in terms of light, it's not that, right? It's not spreading in all directions and it's not broad like that. It can be, though. I mean, think about a star. a star is emitting light and it's emitting light in all directions and before you think about the quantum nature of it it is in fact spreading out and that's why stars seem more dim the further you are away from them right because the intensity of the light drops with the distance squared and so you have light waves which start out very intense and then they spread out and so they get dimmer and dimmer the quantum version of that is the same except that now you have individual photons being sent out and close to the star you have a high intensity and

intensity of those photons and further away, you have a smaller intensity of those photons. And you can understand why the intensity of the photon drops as you get further away because the space they're feeling is getting bigger and bigger. And so if you have like the same size eyeball, you're going to have fewer number of photons hit your eyeball when you're further away than when you are close up to the star. Right. You can sort of think about it that way. But I guess what do you call the photon then is the photon, the ripple that's shooting in all

directions or just if you catch that ripple in a particular spot. You know what I mean? Like you can imagine a star and it's rippling light out. Is a photon that a ring that emanates from the star or what? Yeah, great question. Say you slow the star down so it's only emitting one photon at a time somehow, right? Like a single photon star. Basically, we're just putting a laser out there in space.

But it's interesting to think about how it could go in any direction. So then any individual photon has the same probability to go in any direction from the star if it's totally symmetric. And so an individual photon has a ring of probability around the star where it can go. And then when it actually hits something, then the universe decides, okay, this one's over here or this one's over there. It's just like when you shoot photons at a screen, they have a range of possible locations where they can land. And then when the photon actually hits, that's when the universe decides this photon's over here and this photon's over there. So yeah, individual photons come out in only one direction, but they have a probability to come out in any direction.

There's a bit of a quantum wrinkle there. So it's a little bit like the Schrodinger's cat. I know you don't always like this analogy, but it's sort of like the photon as it comes out of the sun or the star, it's in all directions at the same time. It has the possibility, the probabilities to be in all directions at the same time. You can only ever observe it in one. So it depends what you mean by like it is in those places at the same time.

it has the possibility to be there can never be seen to be in more than one place at once so like it emanates like a bubble basically out of the star that ripple that's the photon technically right until something hits it or until it hits something it might roll the die and say okay yeah that's where I was at yeah that's right

so then these ripples these bubble ripples have a wavelength yeah exactly so these bubble ripples have a wavelength right high energy photons have a very short wavelength, like blue photons have a shorter wavelength, a higher frequency, than red photons, which have a longer wavelength and a shorter frequency. And so that immediately feels like, ooh, that might be part of the answer that tells us about the length of these photons because red photons have a longer wiggle than blue photons, which have a shorter wiggle. And the answer is sort of in that direction, but it's not the answer. A red photon with a very

specific energy, it's the length of the photon is not the wavelength of that ripple. Well, let's talk a little bit about this wavelength. How do you measure this wavelength? Like it's the distance at which the ripple repeats itself? Yeah, remember we're talking about a ripple in the electromagnetic field? What is the electromagnetic field? It's a vector in space, which means every point in space has an arrow with a direction in it.

That's confusing to you. You can just pretend it's just a number. Don't worry about the vector. And the wavelength tells you when the electromagnetic field returns to its original value. right so the electromagnetic field is pointing up and then it oscillates down and then it oscillates back up again and this is just like the direction of the electric field meaning like it increases in value like if I put my finger in front of me that's a point in space and that point in space has an electromagnet field going through it and that field can suddenly have a value where I'm pointing my finger the electromagnetic field has a value at every point in space yes

it has a vector value which means it has a direction and a length right but we're just talking about value And so like where I'm pointing my finger can suddenly go up in value. Like it can be zero right now, zero, zero, but suddenly it can go up to 10. Yeah, exactly. You can change with time. And then it can go back down to zero

and that's a ripple. And if you want to think about the wavelength, you know, you have your finger at one point and the electromagnetic field has a value there. If there's a photon moving through space there, then if you could put another finger somewhere else, you can ask where do I have to put my other finger so it has the same value as my first finger.

And that's what the wave. length is telling us because the wavelength tells us the electromagnetic field goes up and then down, where does it come back to its original value? That's the wavelength. For blue photons, your two fingers would be closer together and for red photons, your fingers would be further apart. And so light is like the value going up in one of my fingers and down and then going up and down in my other finger, but it only happens once for each photon.

Like a photon passing through is just a one wave, right? I understand why that's confusing, but that's not actually what one photon is. And this is going to sound like nonsense, but a single photon of specific energy, like if you say exactly what the wavelength is, that photon actually has an infinite size in space. Like that photon exists everywhere in the universe. I told you it was going to sound like nonsense. I tried to warn you.

Well, it sounds like we're going to get a pretty deep into this. So why don't we take a quick break? And then when we come back, we'll dig into what it means for light to be everywhere. all at once. So let's do that. But first, let's take a quick break. December 29th, 1975, LaGuardia Airport. The holiday rush, parents hauling luggage, kids gripping their new Christmas toys. Then, at 6.33 p.m., everything changed. There's been a bombing at the TWA terminal.

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That sounds totally inappropriate. Well, according to this person, this is her boyfriend's former professor and they're the same age. And it's even more likely that they're cheating. He insists there's nothing between them. I mean, do you believe him? Well, he's certainly trying to get this person to believe him because he now wants them both to meet. So, do we find out if this person's boyfriend really cheated with his professor or not? To hear the explosive finale, listen to the OK Storytime podcast on the IHeart Radio app.

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impacting your very legacy. Hi, I'm Danny Shapiro. And these are just a few of the profound and powerful stories I'll be mining on our 12th season of Family Secrets. With over 37 million downloads, we continue to be moved and inspired by our guests and their courageously told stories. I can't wait to share 10 powerful new episodes with you, stories of tangled up identities, concealed truths,

and the way in which family secrets almost always need to be told. I hope you'll join me and my extraordinary guests for this new season of Family Secrets. Listen to Family Secrets Season 12 on the IHeart Radio app, Apple Podcasts, or wherever you get your podcast. All right. All right. We're talking about light and how long light is. And Daniel, you just kind of blew our minds here and said that light can be everywhere all at once, which is the name of a great movie, which coincidentally involved hot dog fingers. That's true. Not coincidentally, man. That was the long term plan for this whole. joke. I was going to bring them back together. Yes. It was just a giant plug for a movie.

824, send us some free passes. Yeah, there you go. So we're talking about like a photon is a giant bubble that emanates from a light source. It's everywhere all at once in all directions until something hits it. But then if I'm the person that it hits, you're saying it's not something that just washes over me.

Yeah, so if we're going to talk about the length of a photon, then we have to know something about the energy of the photon and you might think hold on isn't he changing the subject remember that for quantum objects their location and the uncertainty in their location how well you can pin that down is intimately connected with their energy the Heisenberg uncertainty principle tells us that you can't know perfectly well the energy of an object or its momentum nearly equivalently and its location and so for a photon if you know exactly its energy if i have a laser for example which always puts out photons at one wavelength.

And I know it exactly. Those photons, because we specify their energy precisely, that means we can't know anything about their location. And so like the quantum field theory version says that the whole universe, the electromagnetic fields of the whole universe, has that photon in it. It's oscillating simultaneously everywhere.

And now I guess it's getting kind of hairy because we just talked about how like a photon is a ripple, like a bubble that emanates from a star or a light source, right? And so that bubble is getting bigger and bigger until it hits something. But that bubble kind of has a location, right? It's on the surface of that bubble. So how can it be on the surface of that bubble and also everywhere all at once? Yeah, great question.

The answer is in the uncertainty of its energy. If a star really could produce photons of exactly one energy, then they would be everywhere all at once. But that's totally unphysical. You can't have something which is everywhere in the universe all at once, right? that violates all sorts of principles of relativity. Quantum mechanics and relativity sometimes take a little bit of conceptual glue to stick together.

The way to resolve it is to realize, well, there are no such photons in the universe. Nothing is actually made with that exact super specific energy. In reality, photons always have an uncertainty in their energy. A star is never making exact energy photons. There's always a spread. Even lasers that you think of as having one specific energy, there's always an uncertainty.

Even atoms, when they're emitting photons between energy levels, there's always a little bit of fuzziness there. So there's an uncertainty in the photon's energy. And the more uncertainty in the energy, the more constrained the photon can be in space. So what's coming out of the star is a ripple and it's localized in space because there's an uncertainty in its energy. Is the time at which it gets made also uncertain? Or is that something we're allowed to know for sure?

Because then, you know, we know exactly when it was emanated and we know the speed of light never changes. then we know sort of exactly where that bubble is. Yeah, there's a Heisenberg uncertainty relationship between uncertainty in energy and uncertainty in time. So no, you can't know that exactly either. Either? No.

So there's three things or they're all tied together? They're all tied together. There's location and momentum. And then there's energy and time. Those are two separate Heisenberg uncertainty relationships. But for a photon, momentum and energy are the same thing. They're only different for massive particles. And so they really are all three things tied together by this fuzziness.

And so it's the uncertainty, the fact that we can never have pure single energy photons means we always get these packets, these blobs, there's like, well, maybe this photon is this energy, maybe it has that energy, maybe it has this other energy, and that's what defines the length of a photon. It's really a packet of this uncertainty, and the amount of energy uncertainty in that packet gives us the length of the uncertainty in its location. Meaning like the bubble that emanates from the star or light source is not like a hard bubble, like a real soap bubble,

but it's actually more like a expanding fuzzy cloud. The way I think about it is sort of like a little wave packet. You got lots of frequencies together. They add and subtracted. They interfere positively and negatively to give you this wave packet that's moving through space. For those of you out there who know like signal analysis or Fourier analysis,

you know that like a single momentum corresponds to an infinite extent in space. But if you add up a bunch of different momentum and different frequencies, you can make any sort of shape you want in space. Right. But then I feel like this, This uncertainty comes from the fact that we don't know when it was made this photon. We don't know how it was made.

We don't know how energy it had when it was made. But once we detect it, we sort of do know all these things, right? Well, we never measure an energy of a photon exactly, right? You can never precisely measure the energy of a photon. How do you measure it anyway? You have an impact some device, and that device has some mechanism inside of it. And you read that number off. There's always uncertainty, not just because the mechanism is something cheap you bought off Amazon,

but because there is an inherent quantum uncertainty. in the measurement itself. There's a little bit of uncertainty, sure, but like when I'm looking at a hot dog, it doesn't suddenly turn yellow or purple or hopefully it doesn't turn yellow and purple as I look at it. The hot dog is not a laser

and it's not an idealized laser. It's emitting a spread of colors. And so every photon that comes out of that hot dog has the possibility to be a little greener or a little redder or a little bluer. There's the fuzziness in every single photon that comes out of the hot dog. But once I measure,

don't I know exactly what frequency it had? There's still an uncertainty when you measure it, but yeah, it does collapse some of that uncertainty. I mean, you see a blue photon or you see a red photon or you see a green photon, but again, still never super precisely. What if we had a perfect measurement device and we can collapse it perfectly? Would we know its exact frequency? I think such a device would have to be the size of the universe, and so then you would know nothing about where it was. Can you explain that? First of all, a device that measures anything exactly is just impossible, right?

You can take the limit of something. You can start with like what's the most precise measurement device I can have and then try to think about taking the limit of it to perfect precision. In order to measure something very precisely that has a lot of energy, you need to have an object which can interact with photons of very different wavelengths, right? Wavings can be very, very short for very high energy or very, very large for very low energy. And so measuring things that are very, very large requires large objects. Like you want to receive radio waves, you need a very big antenna.

You want to receive microwaves. you need very small antennas. So you want to measure something super precisely that can be of any wavelength. You're going to need essentially an antenna of the size of the universe. Oh boy. That said, that would be a very big hot dog.

It would cost more than a hot dog. But maybe let's give up on perfection and say that, you know, I measure a photon coming from my hot dog and I see that it's red plus or minus 0.1 hertz. That's a pretty good measurement of its wavelength. No? We can get to that point, right?

Yeah, you can make fairly precise measurements of individual photons, yes. We can also produce sources of photons that are fairly pure, that are very tight bands of energy ranges, yeah. So then if I know the wavelength of the photon, doesn't that give me a sense of how long it is? If you know the wavelength of the photon and you know the uncertainty in that wavelength, then yes, that defines the length of this wave packet, all these possible photons that

are flying through space together. It's a little unsatisfying as an answer because it's not something inherent to the photon. it's like you've got a bunch of these blobs all moving together through the universe. The answer, how long is the photon depends sort of like on your uncertainty in your knowledge of its energy. So I think it's accurate from a quantum mechanical point of view, but it's very unsatisfying from a philosophical point of view because it feels like the photon should have a length that's just inherent to it. It shouldn't depend on like your measurement of it or your knowledge of it. But it doesn't sort of depend on my knowledge or measurement of it, right?

Like if I measure it and I measure it be red plus or minus 0.1 hertz and somebody else measured would have measured it. They would have probably gotten the same result, right? Yeah, it doesn't depend on your particular knowledge of it. There is an inherent uncertainty in it because it's a quantum state. And to me, that's a little bit unsatisfying. The idea that it doesn't have a fixed length or that its length somehow depends on that uncertainty. To answer your specific question, if there's uncertainty, it means that no two people would make exactly the same measurement. They'd be probably consistent, you know, within the uncertainties, but they wouldn't get,

exactly the same answer. Right, right. We would all see it as vapor hot dog. Right? And so couldn't you, I mean, I know we're not, we can't ever get super precise, but we can probably say you and I can both agree that, yeah, that's vapor hot dog and not misty hot dog. Yeah, and I'm not saying photons don't have a length. I'm just saying that the length depends not just on the wavelength of light, but on the uncertainty on the wavelength, because in the end, they're quantum objects. Right. So then can we answer the question of how long a photon is or was, or is it that we can, that we can only answered what the length of a photon was. We can answer the question if you know the energy and the uncertainty on that energy.

That determines the length of the photon in this sense of length. So that's good, right? It's possible. Yeah. Are you saying it's impossible? No, no, I'm saying it's possible. All right, so then that's the quantum field theory version of a photon. You said that how long a photon is.

It depends on how you look at it. So then if we assume light is a particle, can we measure the length of that particle? Yeah, the answer does depend a little bit on how you look at it, because in some cases, you don't care about the length of a photon, you don't care about these details, and you don't care about the size of anything that's really, really small. So you could just treat them as zero point particles. And we talk on the podcast a lot about how like electrons have no size and corks have no size. And the answer to that really is they have no size that we measure or in some cases that we care about. And so we can treat them as if they're zero point particles with no length to them for some problems where it doesn't really matter if they have length. You know, like when they're hitting a screen, we don't really care how long it took to hit the screen

or what their extent was as they were flying through space. We can just treat them as if they were tiny zero point particles. And so that picture is useful for answering some kinds of questions. Just the same way we can think about classical waves moving through space. Well, I feel like it's sort of useful. Maybe I wonder in some applications. Like, for example, let's say photons are super duper long. They're the size of a planet-sized huddle.

Then when that photon hits me, it's going to take a long time, you know, minute for me to feel the photon all the way. As opposed to if a photon is just an infinitely small point particle, then I'm going to feel the photon instantly. So is there sort of a time at which I get to feel photons or is that relevant or what are the hot dog dynamics here? Yeah, so that's a great question. And to answer that question, you definitely need to use the quantum field theory version of a hot dog. You need to think about the probability of photon having various wavelengths and those wavelengths over the wavelength. with you, when that probability wave packet overlaps with you and when it doesn't overlap with you.

When it does collapse, though, it collapses instantly across the entire photon. You can't feel like part of a photon. There is no part of a photon, right? Photons are quantized. Like when I feel a photon, it's instantaneous, is what you're saying. Yeah, you feel the whole photon or no photons, exactly, or seven photons. What if it has like super duper big waves? Like we've talked about light waves having a wavelength the size of a galaxy, for example.

like we feel those instantly, or do we need to wait a long time to feel them? Yeah, you either feel them or you don't, right? There's no time at which you're like accruing a photon. Right, but the ripple of it, isn't the ripple of it in space long to or what? Yeah, so photons could be really, really long, right? If you have a photon with really long wavelengths and really large uncertainty, those photons could be the size of a galaxy, absolutely. And that photon could interact with something within the galaxy, right?

but then the whole photon collapses all at once. Just the same way that a pair of entangled particles, you shoot off in opposite directions, they're really still part of one big quantum state. You measure one on one side of the galaxy, the whole quantum state collapses at once because it's really just one quantum state. Same way for this galaxy size, hot dog size photon,

if it's really as big as the galaxy, if it interacts anywhere, then the whole quantum state collapses at once. So like you can think of it as having a giant photon, the size of a galaxy, but once I catch it, it's really just a little tiny point particle. Yeah, exactly. It interacts in that one spot. You might think, hold on a second, doesn't this violate special relativity? And it feels like, you know, that might allow you to send messages faster than time. And there is a real subtlety there with how quantum theory and

relativity interact. We talked about in the podcast, it's the reason why we have antiparticles. Antiparticles patch all this up with all these negative probabilities and make sure that everything is following all the rules. Check out our episode. on why quantum mechanics and special relativity require antiparticles. Well, I feel like you're kind of making a judgment on the particle view of light. You're saying it's not really a particle. Or you ultimately have to kind of go back to quantum theory to talk about light. We can't stay in the particle view it for very long.

I'm definitely using this field picture here, thinking about light as ripples in an electromagnetic field. And that I think is the most mainstream view. but there's definitely a chunk of particle theorist who think in the particle picture, and you absolutely can. You can replace the field with an infinite number of virtual particles and do all the same calculations, and it all works. So what I've described is the field picture of light as a ripple in this electromagnetic field. You can also think about these probabilities in terms of like these virtual particles, which are conceptually kind of slippery because they're not really particles or really just probabilities. But you can think about all these kind of interactions and these transmissions in terms of an

infinite number of virtual particles if you like though I think it's a lot more awkward especially in this case well awkward is a relative turn Daniel they might say the same thing about you yeah absolutely and it's a little bit subjective mathematically both pictures work so I'm trying not to make a judgment on what is the best picture of the quantum universe there's a particle people and the fields people and both of them have strong cases conceptually for me the field picture is more intuitive though that doesn't mean that it's right right so then let's say we replace you Daniel we call this podcast, Mark and Jorge explained the universe, and Mark happens to be a particle person that sees

the world as particles, how would they answer the question? How long is a particle? Even in the particle picture of the universe where there are no fields, there's just an infinite number of real particles and an infinite number of virtual particles communicating between them, there are still probabilities. You still have wave functions about where these particles are and uncertainties on where the particles are and how much energy they have. So in the end, the answer is very much the same, right? A photon, even if you think about it as a particle, has an uncertainty in its location. A photon that's infinitely well known would still have an infinite uncertainty in its location. And so even if you think about it in terms of particles, you get the same

answer. It's either a packet of waves moving through the universe with a range of frequencies or it's a packet of possible particles moving through the universe with a range of possible energies. All right. Thank you, Mary, for answering that question. Now, I think what you're saying is that even if you look at light as particles, a particle is a point particle. So itself, it doesn't have any length. It kind of doesn't make sense to talk about the length of a photon. But these point particles have a certain fuzziness

about where they can be in the universe. And maybe you can talk about the length of that fuzzy cloud of where it could be. But ultimately, you can have to make a call about where you draw those boundaries. Like these fuzzy clouds don't have a hard edge to them. they kind of fuzzle out to infinity. And so it's up to you to say, this is what I would call the photon.

This is what it would not call the photon. Exactly. And the pure concept of a single photon isn't really helpful. Number one, because they never exist in the universe. And number two, because they have infinite uncertainty in their location. And so they're sort of everywhere. Cool. Well, I like this new podcast host, Mary.

Does Mary like white chocolate then? Because she's the opposite of you. No, she agrees with me and everything else. Right. All right. Well, let's talk about how you might actually measure what you might call the length of a photon or not measure it or maybe it's impossible. So let's dig into that question. But first, let's take one more break. December 29th, 1975, LaGuardia Airport. The holiday rush. Parents hauling luggage. Kids gripping their new Christmas.

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and the way in which family secrets almost always need to be told. I hope you'll join me and my extraordinary guests for this new season of Family Secrets. Listen to Family Secrets Season 12 on the IHeart Radio app, Apple Podcasts, or wherever you get your podcasts. All right, we're talking about the length of a photon, and now, is it Daniel? Daniel's back, or is it still Mary? Let's go back to Daniel. All right, Daniel. We've sort of concluded that, you know, light is a fuzzy quantum thing. So to talk about its length kind of doesn't make sense.

But there's sort of the other aspect of which is what I was trying to get at, which is like when you measure a photon, maybe you can measure its length, sort of, because maybe it depends on how big your eyeball is or how, you know, how long you're there waiting for the hot dog to hit you. So let's talk about measuring. How do you measure a photon? And how does it change the length of it? Yeah, this is really fun.

I spent some time thinking about this and starting with how you measure the size of other particles. It's a little bit easier to think about like measuring the size of a proton because we've done that or try to measure the size of the electron because we've tried to do that. But we have measured the length of a proton? We have measured the width of a proton. Yes, absolutely. We know something about the size of a proton. Wait, wait.

I thought I thought we just concluded that you can't do that with quantum particles. We decided you can, but protons are not like fundamental objects in the universe, right? So really we're talking about like a bound state of quarks and how close do they stay to each other. But even that has a sort of uncertainty that spills out to infinity, doesn't it? So where do you define the bounds of a proton? Yeah, it's a little bit fuzzy and you have to do a little bit of mental gymnastics and come up with a concept of size that makes sense for these particles. You have to think about like what can I actually measure and what number does that give me? And is that really measuring the size of the object?

All right. Let me do some mental stretching here before I do some mental gymnastics. What do you mean? So when you say the size, because you just said the size of a proton pretty decisively, then as a particle physicist, what do you define as the edge of a proton? Yeah, so I will be totally up front here that physics has redefined size and then answered the question. What we really mean is that we do a specific kind of experiment where we bounce stuff off the proton and we notice how that changes as we scan across a proton.

So, for example, you shoot electrons at the proton and they mostly go through and then you shoot them a little bit to the right and oops, and now they're bouncing back or now they're exploding the proton. And as you keep going, you discover that as you sweep your beam over past the other side of the proton, then now it's missing the proton again. So there's like a size of the proton there in the sense of like how it reacts to the beam of electrons that you're sweeping over it. It's sort of like searching for a stud on your wall, right? Yeah, exactly. And it's a little bit philosophical to interpret this as size because what do you mean anyway by the size for proton? A proton is an easier thing to talk about than a photon because at least a proton has mass. You can like hold one.

You can capture one. You can say this is the one I'm talking about. Photons are much harder and we'll talk in a minute about how you might be able to measure their size. But this is the kind of thing we do for a proton. And this is one way, for example, that we discovered that the atom had a proton inside of it, right? Rutherford's original experiment was basically this. He shot alpha particles at gold foil. and notice that they bounce back sometimes and not other times.

And he used this to see like, oh, there's like hard little nuggets inside the gold foil. And those were the nuclei. And you can do the same kind of thing to see the size of a proton. You can also do the same kind of thing to see inside a proton to see like how often is it bouncing off of a quark that's inside the proton. Right, right. But like you said, it's sort of a fuzzy boundary, isn't it? Like as you're scanning where the proton is by shooting electrons at it, at some point, like sometimes it'll hit, sometimes it won't, even though you're shooting in the same exact direction.

And as you scan to the right, for example, the frequency at which it might glance off of the proton changes. So there's a bit of fuzziness of when do you make the call like, okay, that's the edge of the proton. Or do you? No, you're exactly right. There's a little bit of fuzziness there. Like if you did this experiment with billiard balls, right?

There'd be a moment when they come into contact and then a moment when they don't. And there's a precision there. And we don't have the same thing with protons. There's some point at which you shoot the electron and sometimes it bounces back and sometimes it passes through. And so like, is that the air? of the proton. And so we just make a sort of mathematical definition. We define the width of this

distribution and we say the width of this distribution tells us the size of the proton. Meaning like the width of a proton is the width at which if you aim at electron at it beyond that, then only, you know, 10% of them will hit it. Exactly. Like if you know a Gaussian distribution, you can characterize the width of it. It doesn't capture the whole distribution. It's just like a characteristic number that tells you roughly how wide it is. And there's a possibility you go past. that with and you still interact with the proton. And there's a possibility you go below that width and you don't interact with a proton. So it's a quantum fuzzy definition of size. That's fuzzy in another way too because it depends on the thing you're touching it with. Like protons will react

to electrons differently than they'll react to muons or react to neutrinos. So the whole concept of size is really about the interaction of two things. It's not inherent property of the object anyway, at least this quantum definition of size. I see. Like it depends on experiment the width of a proton you can't talk about the width of a proton you have to say what's the width of a proton when it's interacting with electrons or what's the width of a proton when it's interacting with a hot dog he knows even then it's fuzzy and you kind of have to make a call and say well it's uh you know it's about here that it starts to taper off yeah exactly all right so then let now switch to photons does the same thing apply to photons like does it depend on how

we measure it so this is tricky because photons don't like to interact with each other you can't just like shoot one photon at another and say like often are they going to touch each other this kind of stuff remember photons only interact with things that have electric charge so you can shoot photons at electrons but you can't shoot photons at photons and see them interact very often when they do it's because they've actually spontaneously transformed into electrons and positrons and then interacted so I was thinking about it and there's another way you might be able to get a sense for the length of a photon because photons don't interact with each other the same way particles do but they can interfere with each other. If photons are at the same place at the same time, they will interfere. Like the way we have interferometers, you know, we're talking about interference. You get like light patches and dark patches. Wait, wait, let's maybe take a step back. What is it that you're trying to do?

You're trying to measure the size of this wave packet or the size of the fuzziness of an electron. Is that kind of what you're trying to do? I'm thinking about how to measure the length of that wave packet of a photon. And I was thinking about if you sent two photons through an interference experiment, like do they interfere with each other, they will if they're right on top of each other. They won't if they're really separated. Like if you wait 10 seconds between shooting photons, they won't interfere with each other. There's some point at which if you send two photons through the experiment close enough together in time that their wave packets are overlapping, that they will interfere with

each other. And so I'm thinking that's like one way to define the width of the wave packet of each photon is like how close they have to be to each other in time, which then gets translated to distance so that they start interfering with each other. Doesn't light interact with electrons, for example? So, like we use electrons, like you just said, to measure the width of a proton. Couldn't we kind of flip it and use an electron to measure the width of a light particle? Like, what if I sit an electron there in a table and I just shoot photons at it? Wouldn't this sort of tell me how wide my photon is?

Yeah, but are we talking about the length of a photon or the width of a photon? Wait, wait, meaning like, is it light shaped like a hot dog? Let's assume it's shade like a meatball. Wouldn't the length also tell you the width? The length or the width depends on the uncertainty of its production, right? The entire length of the photon comes from the uncertainty you have in how it was produced. It's either infinitely long, if it's perfectly well measured, or it's very, very tight if it's very uncertain in its energy. So the width might come from a different uncertainty.

So, yeah, if you want to talk about the width of the photon, like which direction does it come out of the laser, this uncertainty there in the photon's width as well. is in its length. That could be a different number. But I feel like when you were talking about the proton, you were using the word length to mean its width. Yeah, for a proton, we really are measuring its width in that case. You're right. So you're assuming protons are meatball shape. Well, I mean, I think this is important, right? No, you're right. Yeah, you're right. So you're assuming protons are meatball shapes, but you're not assuming that light is meatball shape. You're assuming it might be hot dog shape or not. I don't know.

Yeah, absolutely. I'm using the meatball model of a proton. and the hot dog model of a photon. And somebody else might have a different, you know, maybe a French version of it, right? With there's a pastry version. A donut, a French fry version, the Palmfleet model. Yeah, so to measure the width of a photon, you could scan a beam across a bunch of electrons

and see when they interact. And then we'll give you a sense for like the width of your beam. And if you slow it down to individual photons, you go a sense of the width of the wave packet of the photon. I think to get a sense of the length of a photon, you might want to see how the photons overlap in an individual. experiments, see when they start interfering. That probes something we call coherence length of the photon.

I wonder if you can measure the length of a hot dog photon by measuring, by using time. Like if there's more uncertainty in when you receive the photon, would that tell you that it's a really long, it's a foot long hot dog? Whereas suppose if the uncertainty when you receive the photon is very short, it's like, oh, it's a Vienna hot dog. Yeah, in principle, if you know the energy and uncertainty, you can just define the length. I was trying to think about a way to like experimentally measure another sense of the length in terms of like when two photons overlap with each other rather than just thinking about the length of an individual photon theoretically. But yeah, you can definitely define the length of an individual photon theoretically from

its energy and the uncertainty, which again is coupled to the uncertainty in its time measurement. So I feel like maybe the headline from this podcast episode is a physicist claim light is shaped like a hot dog. You know, one thing I love about this podcast is I've never have any idea where it's going to end up going. There's no way to prepare for this. There's an uncertainty about its length also. The topic, the concept, the analogies we end up using.

This is proof that this podcast is unscripted because nobody could write this stuff. Well, we are. We're writing it right now, Daniel. It's happening. It's happening. We're living it, man. Well, I mean, I feel that that's a big. thing that I'm getting out of this is that, you know, in your thought point of view, a photon is not

spherical. It maybe has different dimensions to it. Yeah, I hadn't thought about the width of a photon, but you're right. It has all the same theoretical questions to it and experimental trickery to measure the width of it. But the width and the length of a photon could be very different. You could have a source of photons that's very uncertain in length and very certain in width. I think that, you know, as you gave a proton of definite size, right? Like in physics, you have a size with plus or minus a certain amount of uncertainty. If you had to do that for a light, for a photon, like maybe an everyday photon that we see every day, what would you say is its length?

Yeah, that's a great question. You know, a typical photon that's like coming out of the light that's made from a light bulb in your house. That's a glow of like a little piece of metal. So there's a very widespread in the uncertainty of those photons. Oh, cool. Now, how would you say it compares to its width? Like, are photons hot?

Like the everyday photons we see hot dog shaped or are they football shaped or are they more spherically shaped? Like what kind of bun? What kind of bun should I get to eat of? I think it's probably curved. So you should get a croissant. Oh, no. I don't know the answer to that. It depends a lot on the source for a typical filament from like an incandescent bulb.

There's again going to be a lot of uncertainty in the direction. So these things are going to be pretty fat. Maybe there's sausage patties after all. Oh, yeah. Oh, man. I hadn't even thought about that snack. Like, they could be like pancakes flying at you face forward. Yeah, more sideways.

Yeah, interesting. All right. So I guess we sort of answered the question, how long a photon is. We know that these things are really hard to think about and that the answer depends a little bit on the question you're asking and exactly how you want answered. And along the way, you often have to redefine what you mean by your question in order to get a specific unsatisfying answer.

Yeah, and in the end, I guess it's all a little bit fuzzy due to the fuzzy nature. of the universe. But put enough mustard on it, it'll be delicious. Yeah. It's a little fuzzy, though. The fuzzy hot dog podcast. All right. Well, another interesting dive into the quantum nature of the universe and how even

simple questions like how big is a photon or what shape it has requires a whole conversation about the nature of a length and what even means to be something in the universe. That's right. The most basic questions are the hardest to end. answer. All right. Well, we hope you enjoyed that. Thanks for joining us. See you next time. For more science and curiosity, come find us on social media where we answer questions and post videos. We're on Twitter, Discord, Insta, and now TikTok. Thanks for listening and remember that Daniel and Jorge Explain the Universe is a production of IHeartRadio. For more podcasts from IHeart

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