How did Max Planck accidentally discover quantum mechanics? Why is his constant so special? What happens at the quantum level? I discuss these questions and more in today’s Ask a Spaceman!
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EPISODE TRANSCRIPTION (AUTO-GENERATED)
Have you ever needed to make a quick hack to get something to work? As in, like, you you needed to fix something or figure out a solution, and you just totally MacGyvered it. You took the nearest random objects like a piece of bubble gum and a rusty razor and a deflated balloon, and you strung them together and you turned them into an airplane or something, and you just hoped for the best. We've all done it. Right?
Did it work? Did it work for a really long time? Did it work so well that your ugly, quick, last minute hack that was mostly based on hopes and wishes and prayers became the standard way of doing things? Did it work so well that other people started doing the exact same thing? Did it work so well that generations later, your way of doing it, your hack was taught in schools?
Did it work so well that you won a Nobel Prize for it? Well, welcome to the wonderful world of quantum mechanics, which was born in 1900 with an ugly, ugly, ugly hack that worked and stuck. And to kick things off, I need to start with blackbody radiation. Yes. Here we go again.
I think I've only mentioned blackbody radiation about 47 times on this show, so you already know it's kind of a big deal. And in case you forgot, and or for the new folks at the table, black body radiation is a horrible name for a very cool thing. It's the radiation given off by hot stuff, by you, by the sun, by the table in front of you, by the road, by the Earth. Like, if you have a big thing made of lots of particles and molecules and they're all jiggling and wiggling around all over the place, they will emit radiation, and they will emit a very specific kind of radiation called black body radiation for various historical reasons that don't make sense anymore, but the name is stuck. And one of the most important things about blackbody radiation is that the the radiation given off by a hot thing is not one specific frequency or one specific wavelength of light.
It's a lot of wavelengths of light. It gives off lots of different colors, lots of different wavelengths, and there'll be a peak. Like, there'll be one or a few wavelengths that it will emit the most, and then there'd be other stuff along with it. So why is block body radiation so important in the story of quantum mechanics? Because it doesn't make any sense.
If you make a thing hotter, you give it more energy, which means you get brighter light. That's no duh. But also if you make a thing hotter and you give it more energy, you get bluer light. Now that's a little bit puzzling. If I if I cool something off, then the black body radiation that it gives will be mostly redder, maybe even infrared or microwave.
And if I heat something up, then it will tend to be bluer light or ultraviolet or x-ray. Interesting. Well, if if you make something hotter, then there's a lot more energy inside of it, and that means there's a lot more energy to go into making light. Duh. But how does the energy get divided up into all the different kinds of wavelengths?
You know, black body radiation emits all sorts of different wavelengths. There might be a peak, a particular color that is emphasized, but it still gives off a lot of other wavelengths. Who decides how much of this wavelength over here or that wavelength over there should there be? Where does the who decides where the energy goes? If you dump energy into a thing to give it a lot of heat and it starts glowing with black body radiation and you dump even more, who decides where the energy should go?
Who decides which wavelengths become most important? Is it even? Does does every wavelength get a little bit a little slice of the energy pie? This was the thinking in the late eighteen hundreds when people were doing black body experiments. It's like, okay.
We got we got a whole bunch of energy that we gotta spend. Let's look at all the wavelengths of light, you know, all the way from radio to microwave and infrared and reds and blues and ultraviolet, the x rays get the whole deal, and everyone gets a little bit of energy. So a little bit of energy goes into red, a little bit goes into blue, a little bit into ultraviolet, a little bit into microwaves. It's very democratic. It's very democratic.
Just everyone gets a little piece, but this doesn't work. Because according to this picture, if you have a hot cup of coffee, then a little bit of its energy should be getting dumped into, I don't know, X rays, and you should be getting, you know, you should be getting an x-ray scan from your cup of coffee, and that's like not how it works, thankfully. And in fact, in general, it seems very, very hard to emit high energy radiation. What's preventing it? Why is it so hard?
Why do you have to really heat something up if you want to generate high energy radiation? Enter Max Planck, a dude, a physicist, in his ugly, dirty, quick hack to just make the math work to explain some confusing experimental results. In his ugly hack is this, a constant, A tiny little number. A single number. A constant.
And once you introduce a constant, like Max Planck did to explain back blackbody radiation, instead of all the energy getting divided up equally amongst all the possible wavelengths that could be emitted, all the possible colors, no. No. No. No. No.
No. No. To make light, you gotta pay to play. To make some light of a given wavelength, you have to pay a price. You have to chip in.
You have to contribute to, and I'm avoiding the obvious Patreon pitch here just to keep you on your toes. You have to chip in. How much you chip in to make some light depends on the wavelength. Long wavelength light, like really stretchy stuff like in red or infrared or radio, are cheap. You don't have to pay a lot to make long wavelength stuff.
Short wavelength stuff with a really high energy light like blue or ultraviolet or X rays, those are more expensive. So that's fine. Okay. It costs more energy to make short wavelength light than it does long wavelength light. But how just how cheap is the long stuff and just how expensive is the short stuff?
Like, you know, what's what's some actual numbers to put on it? Well, that's where Planck's ugly little hat comes in. That's his constant. His constant, a single solitary number tells you how expensive it is to make a certain wavelength of light. It tells you that short wavelength light is gonna be yay expensive, and there's a number, a price tag on it.
And that long wavelength stretchy stuff, red infrared, that has a different price tag on it. Planck's constant gives you the price tag. According to Planck himself, he was just really, really, really, really, really obsessed with this whole black body problem and and obsessed with the fact that no one had been able to crack it, and he was just trying anything to find a solution. And this idea of a constant was his absolute last resort, and it was this just this lame idea. They was like, fine.
Fine. I guess I'll try this because I've tried everything else of adding a constant so that there was a minimum amount of energy needed to make a bit of light. You had to pay the price tag. You couldn't pay half of it. You couldn't pay a quarter of it.
If you wanted to make light of a specific wavelength of a specific color, you had to pay a very specific price. He didn't know how it worked. He didn't really think it was important. He didn't know how it might be connected to light itself or molecules themselves. It was just an ugly math hack, and it kinda sorta worked.
And just like that, in 1900, Max Planck accidentally invented quantum mechanics. The constant that he put in, which we now call Planck's constant, in his dubious honor, He also, by the way, won the Nobel Prize in 1918 for this work. It's the minimum of energy needed to make some light. It's a chunk. It's a byte.
It's a fundamental bit. It's a unit that cannot be divided into anything smaller. We have a word for that. For things that cannot be divided into anything smaller, we call them a quantum. Planck's constant is a quantum number.
But a quantum of what? Well, Planck's constant tells us how much energy you need to make light, but the constant is not a quantum of energy. It's it's like a conversion factor. You know, it's like of this wavelength, how much energy to make that wavelength. So it's it's it's a little bit different.
Instead, it's even more fundamental than that. It's a quantum of Patreon. Now I got you suckers. Go to patreon.com/pmstarter to learn how you can keep this show going. It is your contributions that keep it on the air.
It is your contributions that support me doing all my science outreach and communication. I sincerely appreciate it. Patreon.com/pmsudder. Planck's constant is not a quantum of energy. It's a quantum of action.
Yeah. Action. Action. I know it sounds simple and kinda weird, but I swear this is like the most fundamental concept in all of physics, which is strange because it's not taught to anybody except physicists, so maybe I'm breaking some secret code here. So if this is the last episode ever of Ask a Spaceman, you know why.
Action. Action. It is it's a little bit hard to describe. It's something we have intuitive sense. Like, if you think of where you gonna watch where you gonna watch tonight, where we're gonna watch an action movie.
What does that mean? There's gonna be a lot of intention. There's gonna be a lot of movement. There's gonna be a lot of stuff happening. The word action in physics is movement along a path, momentum along a path.
So not just your momentum in this instant. Like, if you start running, you have some momentum and you can take a snapshot, like, there's your momentum. But if you follow that momentum along, if you actually run the race and you play that movie, that becomes action. Or it's like a dance. You can be you can be in the middle of a movement and dance like, and you have that frozen motion.
You have momentum and angular momentum, and that's great. But if you actually follow the movie of that motion, that becomes this physical concept of action As particular units, you know, like, you know, everything is units, like length, time, all that. The the units of action are either energy times time, so energy applied over time, or it can be momentum times length. It ends up being the exact same thing, like intention, momentum applied over a path over a distance. And what it means for action to be quantized, for there to be a quantum of action, is that if you're watching your action movie you know your action movie?
These aren't real people actually, you know, running around and jumping and blowing things up right in front of your face. It's about your frames stitched together to give the illusion of motion. For action to be quantized means that all action, real life action is like frames in a movie. It's like stop motion animation. That if I throw a ball and the ball follows has its momentum and follows a path, follows a trajectory, that action is quantized.
There is a minimum amount of action that can be applied in this universe, and the value of that amount is Planck's constant, the quantum of action. That's all well and good and and very, very seriously important, I'm sure. But in 1900, it was just an ugly hack without any any weight, any significance, any deeper meaning. It was it was just proposed to solve this one little black body problem, and that was pretty much it. And it stayed that way for, like, a decade.
This idea, though, needed weight and leave it to Einstein to give an idea weight. He was interested in a totally different problem, something called the photoelectric effect, which was this very basic experimental setup where if you shine a flashlight on a chunk of metal, then electrons will pop off the metal. Hooray. And I want you to imagine pouring, like, a bucket of light into the metal, like you're shining your flashlight and and electrons start popping off. What do you expect?
What do you naively expect the electrons to do? Well, you would expect that if the light was more intense, like if you got a brighter flashlight, then the electrons would get more energy and they would shoot off faster. And you'd also expect if you had really, really, really dim light, then it might take a while to to build up enough energy to finally kick an electron off. Like, they were like, okay. Soaking it up, soaking up, soaking it.
Okay. Now I'm gone. But neither of those is right. Big surprise. Instead, no.
Zero electrons pop off the metal until you reach a certain high enough energy of light. And that's not brighter light, that's higher frequency light. That's shorter wavelength light. That's higher energy light, not the brightness, but the wavelength, the color. And if you crank it up to be a brighter light, if you get a bigger flashlight of that color, that doesn't lead to faster electrons.
But, again, more energetic light does. So it's not the volume of light that matters for this thing called the photoelectric effect. It's the color that matters. And this was puzzling, and Einstein liked puzzles. And to find a solution, he eventually turned to, well, an ugly hack, which at this time, the hack was, like I said, about a decade old, and it was pretty well known.
It was Max's hack. It was the Planck constant. And here, Einstein added his own little twist to it because he's Einstein. And the hack that Einstein added, the twist he added to it was way different than the twist in the intention that Max Planck put to this constant. Planck originally proposed this constant to explain the emission of light.
Like, he's like, okay. I don't know how it works, but something's gotta make the light go. Something's gotta decide where the energy goes. I'll just put in this constant. I don't understand the physics.
I just know the math and the experiments. Okay? Einstein kicked it up a notch. He said, oh, it's not just action that's quantized. It's light itself.
Light comes in tiny little bits. Light has a fundamental indivisible quantum unit, something we call the photon. Our understanding of the photon as the smallest bit of light possible has its origins in Max's ugly hack designed to explain some random experiment. So it was through Einstein that Max's ugly hack became kind of important. But remember what his hack is, a constant.
It's a number, a single number derived from experiment. Planck's constant does not emerge from theory. It is not born from a desire to understand nature with beautiful mathematical form. Nothing like that. It wasn't some crazy idea cooked up in a basement.
It was forced upon us from brutal experiments. Nature was shoving this concept in our faces in the late eighteen hundreds through the black body experiments, and the only way to explain it was this ugly hack. It was our only answer, and it is the only answer that action is quantized, that light is quantized, that we live in a quantum world. And the value of that number, Planck's constant, 6.626 and so on. There's a bunch of digits.
6.626 times 10 to the minus 34 joule seconds. Don't worry too much about the units. That's just the units of action. 6.62 times 10 to the minus 34, that's small, that's tiny. That explains why it took until the late 1800s before we noticed that we lived in a quantum world.
That this stop motion effect in action happens only at really, really, really, really, really tiny scales. Up here in the macroscopic world, you move your arm, you're blowing through so many quanta of actions. You're so, so much more overwhelmingly active than the quantum of action that you don't notice the the herky jerky stop motion, you know, frame by frame thing that is reality. You just don't notice it. You have to get really small and you have to get really careful and you have to get really detailed like running a blackbody experiment before you start to notice this kind of stuff.
But Planck's constant, 6.62 times 10 to the minus 34, tells us about, those tiny scales, doesn't it? That if you start getting actions that are of that same, you know, order of magnitude, that you've entered the quantum world. This is the gateway. This is the the signpost that you're now must care about quantum mechanics when you reach Planck's constant. But action isn't the only thing in our universe.
It's not the most useful gauge of deciding when you've entered the quantum world, but we can combine Planck's constant with other constants to find some, some interesting things. You know, there are a lot of constants out in nature out there. They're not just Planck's. There's the speed of light. There's Newton's g.
There's the Coulomb constant, the Boltzmann constant. You know, there there's lots of constants out there. Each of these constants, each of these numbers act as little little bosses of their respective domains, like mafiodons. You know, Planck is in charge of the quantum. Newton's g is in charge of how strong gravity is.
The speed of light is in charge of of how quickly light moves. These are little slices of physics across the universe. Right? Yeah. I wanna know how well I'll respond to an electric field.
I wanna know fundamentally how strong gravity is. I wanna know what is the scale of quantum mechanics. That's what the that's exactly what these constants tell us. We don't understand the origins of the constants. That's another show.
Feel free to ask. And we think they have been constant throughout space in all time. That's another show. So feel free to ask about constants of nature if you want. Just for the sake of our discussion here, they just exist.
Gravity is yay strong. The speed of light is yay fast. Electricity is is yay permeable, and the quantum scale is yay big. And when we combine these constants, we see where physics overlaps. And we're very, very interested at the points where other physics meet quantum mechanics, meet Planck's constant because we're very, very interested in quantum mechanics itself.
Quantum mechanics is pretty fundamental, and Planck's constant is, you know, accidentally, not intentionally, in charge of quantum mechanics. So we combine Planck's constant with the other constants to get some interesting numbers. Like, you can combine Planck's constant with Newton's g and the speed of light, and you get something we call the Planck length, which is, 1.6 times 10 to the minus 35 meters, very, very small. Or you can combine it in a different way with the speed of light in Newton's g, and you get something called the Planck mass, which is, two times 10 to the minus eight kilograms. You can make a Planck time, which is 10 to the minus forty four seconds.
You can make a Planck charge. You can make a Planck temperature, which is 10 to the 32 Kelvin. So you get all these numbers popping out, these length scales, these mass scales, these time scales, these temperature scales. And it's interesting what you're combining. You're combining Planck's constant.
You're combining Newton's gravitational constant. You're combining the speed of light. This is telling you something. These numbers are telling you something. These are telling you where, say, gravity represented by Newton's g, gravitational constant, meets the quantum world where it meets Planck's constant.
It's at this length scale or this mass scale or this temperature scale. That's where gravity and quantum mechanics are on equal footing, and we don't understand how gravity and quantum mechanics behave together. That's a fundamental issue in modern physics. We don't have a quantum description of gravity. And this is why we're so interested in these Planck scales and these kind of lengths, distances, and times, and temperatures represented by combinations of Planck's constant and Newton's gravitational constant.
Because once you get smaller than the Planck length or hotter than the Planck temperature, you are outside of known physics. It's not a hard and fast rule, of course, but it's a sign. It's a sign that the physics you know and love may not be able to take you where you want it to go. And this is why we talk about things like the early universe or the center of a black hole, you know, the singularity events with such reverence because these are places. These are known places in the universe that are smaller than the Planck length, hotter than the Planck temperature, shorter than the Planck time.
And it's telling us, ah, the Planck constant representing the quantum world meets the gravitational constant representing the gravitational world. This is where they meet. This is where they're both have an equal voice, and you can't ignore one in favor of the other. You have to treat them equally, and that is something we don't understand. So Max may have intended his little constant as an ugly hack in 1900, but it ended up being the key to brand new physics both then and now.
Thank you so much for listening, especially Nirben z on email, Brent r on email, Frankie c on YouTube, Vicki k on email, Dialogical on email, Katya n on email, and at Felebair on Twitter for asking the questions that led to today's episode. And, of course, go to astrotours.co. We've got a brand new tour coming up. We're doing an all stars party in Joshua Tree National Park that's outside of LA. Beautiful stargazing.
It is really gorgeous skies out there. Gorgeous skies every night. I'm not alone. There's gonna be Fraser Cain, Pamela Gay, Skylius, John Michael Godier having tons of fun during the day and then stargazing every night. We're gonna have telescope.
It's gonna be a party, a serious party. Go to astrotours.co for more info. Of course, go to patreon.com/pm. So to learn how you can contribute to the show. I'd like to thank my top Patreon contributors this month.
We got Robert r, Dan m, Evan t, Matthew k, Helga b, Justin, Matt w, Justin g, Kevin o, Duncan m, Corey d, Kirk b, Barbara k, and Chris c, and of course, many, many, many, many others. Go to askaspaceman.com to see show notes. You can ask questions at askaspaceman@gmail.com, hashtag askaspaceman. You know what to do. Leave an iTunes review.
Go buy my book if you haven't already bought it, Your Place in the Universe. And I'll see you next time for more complete knowledge of time and space.