What does it mean for an electron to spin? Why do we have such a hard time measuring it? And why doesn’t Paul Dirac get any attention anymore, anyway? I discuss these questions and more in today’s Ask a Spaceman!
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Hosted by Paul M. Sutter, astrophysicist at The Ohio State University, Chief Scientist at COSI Science Center, and the one and only Agent to the Stars (http://www.pmsutter.com).
EPISODE TRANSCRIPTION (AUTO-GENERATED)
You know what time it is. It's time for Ask a Spaceman. I'm your host, Paul Sutter. You've got questions and I've got answers. You know how the show works, but let's take it for another spin. You go online, Twitter, Facebook, use the hashtag AskASpaceman. Send me some questions and I will pick a small subset of them to answer on this show only because there's a lot of questions and not a lot of shows. I got to work on that. You can also email me directly at AskASpaceman at gmail.com. You can also go to AskASpaceman.com. or youtube.com slash paul m sutter to check out the videos all those places can accept questions how awesome is that we have one simple goal with this show complete knowledge of time and space and on the road to complete knowledge of time and space we have today's questions from so many people asking the same question this is fantastic we've got dean b via email what is fundamental spin we've got p e via email how does an electron have quote unquote spin we've got at n-i-r-b-n-z on twitter could you explain once and for all what does the spin property mean in quantum mechanics We've got Kerry Kael via email.
Why are so many things spinning? Where does that energy come from? We've got at Sojournal via Twitter, 10 bucks. If you can explain the spin of the electron. Now, I don't often take bets. But you know what? At Sojournal, as you're listening to me, prepare an envelope. I want you to put on that envelope the address Paul M. Sutter, P.O. Box 3322, Columbus, Ohio, 43210-3322. You can put that $10 in that envelope because I think... At the end of today, you're going to owe me 10 bucks. I think we're going to do it. We're going to do quantum spin to your satisfaction. I'm laying it out there. I'm laying it out there. I haven't even recorded. I don't know how well this is going to turn out, but I've got a good feeling about this. Now, since I don't often take bets, I don't want to just take your money and do something frivolous with it. I want you, this is going to be a game. I want you to choose a cheese. That's right, a cheese, and I will buy that cheese and eat it with your $10, and I'll put the picture on Twitter.
I know you're thinking this is a little out of left field. It's just never come up before. I love cheese. I like cheese. In fact, if you just want to mail me cheese directly instead of contributing to Patreon, that's P.O. Box 3322, Columbus, Ohio, 43210-3322. I'm a big fan of cheese, and I can't believe in the years that this podcast has gone on, it's never come up. But there it is. I believe 90% of my diet is cheese. But seriously, you know what? If I've successfully explained spin, I want to reward myself. You know, I want to congratulate myself. I don't often congratulate myself. And what better way? than with a good cheese. Now, first things again to everyone for all the amazing and thought provoking questions you've asked all these years. I can't thank you enough. This show drives on your questions and you are all definitely curious about more than I thought you would be like spin. good old spin, quantum spin. When I started this show, I never thought I'd get questions about spin, but here I am.
And you know what? I'm pretty happy for it. I love talking about astronomy, astrophysics, and quantum mechanics. But as you know, quantum mechanics is such a thick, rich, dense soup of a topic. It is, after all, an entirely field of physics. It's hard for me to find entry points, little dabbles here in quantum mechanics, but spin, in my opinion, is the classic, that's not the right word, the prototypical quantum mechanical subject. And it's a great way to start entering into this quantum world and working it into the show is through spin. And yes, there's all the sexy quantum mechanics stuff like superposition and probabilities and entanglement and teleportation and spooky action at a distance. And that's all great. That's all cool stuff. And historically speaking, if I wanted to follow a narrative of our development of quantum mechanics, we started figuring out all that stuff before we figured out spin. But you know what? That stuff and don't worry, I'm sure eventually I'll get to do shows about all that stuff.
A lot of that knowledge, a lot of that language, the perspective of looking at quantum mechanics is due to a particular physicist by the name of Erwin Schrodinger. And you may have heard of Schrodinger's equation or Schrodinger's cat. That's a long story on the cat thing. So feel free to ask. But all that stuff. All that good stuff, superposition, the uncertainty principle, things like that, that's just waves. The Schrodinger equation, the mathematics that's used to describe a lot of quantum mechanics, is a wave equation. It's an equation that describes the behavior of waves. So superposition, uncertainty principle, normal waves do that too. It's just in quantum mechanics, they acquire this new interpretation. But there's a lot of analogies that we can use in the macroscopic world where we can take things that we're already familiar with. And because the equations are exactly the same, they're just applied in a new scenario. We can build some mental models. We can make some analogies. And that's all great, except for spin.
There's nothing quite like spin. And as I'm about to tell you, I think spin is a purely quantum mechanical thing, despite its name. And I'll get to the whole name thing. There's nothing quite like it in the macroscopic world. And so what's the big deal? What's the big deal? Let's start with an electron. How many numbers do you need to totally describe an electron? Well, an electron has mass. There's one. It has charge. There's two. So at least two numbers you need to describe any electron in the universe. But some experiments in 1922 found something funny. These two physicists, Otto Stern and Walter Gerlach, shot some silver atoms through a magnetic field. And apparently, no, no, no, shot some silver atoms through a magnetic field. And apparently they had some motivation for doing this and they weren't just bored. They were intent on looking at this. And as the atoms passed through the magnetic field, they got deflected. Their paths got bent away from a straight line. Hmm, that's interesting.
Not totally unexpected, but that's pretty cool. Okay. Shooting these silver atoms through the magnetic field and their paths get curved. But they got curved in two directions. The beam of atoms was split. Some atoms would curve up and some atoms would curve down. down and it's at this point in the life of a scientist where you go from okay okay pretty cool result that's nice to uh stern and gerlach pretty much had no idea what was going on And remember, the magnetic field in their apparatus, in their experiment, isn't changing. It's just staying there. Nothing's changing about the beam of silver atoms being shot through the magnetic field. They just turn it on and go. But something, somewhere, somehow is making a decision. Each silver atom chooses, for lack of a better word, to go up or down as it gets shot through this magnetic field. How do we even begin to explain this? Presumably, that's what Stern and Gerlach said, but in German. And seriously, until 1922, nothing like this had been encountered before.
Nothing. This was a very unique thing. This was a very, very special thing. If you pretend... You know nothing about electrons and atoms or quantum mechanics. We do know about how charged objects operate in magnetic fields. We do know that if you have a metal ball, let's just say you got a metal ball and it has an electric charge. It can interact with a magnetic field. It can spin in the same direction as the magnetic field. So the magnetic field is pointing in one direction and then the axis of this spinning ball can point in the same direction or it can point in an opposite direction. It can point in any direction you want. And if it's not pointed in the same direction as the magnetic field, then the magnetic field can push on that charged metal ball to rotate it. This is very simple, James Clerk Maxwell, electrodynamics, seriously kindergarten level physics. I mean, learned this decades ago. And if you take these spinning charged metal balls and shoot them through a magnetic field, they'll get deflected.
So it's that easy, right? Like if we're performing this experiment with not silver atoms, but with giant metal balls, it would be very, very simple to interpret. We would get a very, very simple result, which would be, yes, the paths of these charged metal spinning balls would get deflected. They would end up on the opposite side. And so the natural intuitive, the first thing a physicist's mind goes to when you see this result of the silver atoms and then very, very quickly we realized it wasn't the silver atoms doing the work, but the electrons themselves. The first step, the first thing you think of is, oh, electrons have an extra property. They don't just have mass. They don't just have charge. They also have this property, and we're going to call it spin because it seems to act like an electron is a tiny spinning metal charged ball because that's what would happen if we were to run this experiment in 1850 or whatever. That's what would happen to the spinning charged metal balls. So this is, the electrons are doing pretty much the same thing.
And so they have an extra property. We'll call it spin because that seems to work well. So we can think of electrons as tiny little charged metallic balls and they're spinning really, really fast. And then when you shoot the electrons through a magnetic field, some will randomly be pointing up, some will randomly be pointing down, and that's how you get your split. Now, I want you to take that nice, neat, tidy, cozy little explanation, that understanding you have in your head of how an electron works like a spinning metal ball when we shoot it through a magnetic field. I want you to take that notion and put it in a box. I want you to lock that box. I want you to throw away the key. I want you to light that box on fire. I want you to take those ashes and put them in another box. And lock that box and throw away that key. And then I want you to attach that box to NASA's Parker Solar Probe as it crashes into the sun. I want you to never think of an electron like a spinning metal ball. Ever again.
And I mean it. Why? Because it's wrong. And this was realized right away. For one, we can calculate. given simple electromagnetism, how much the electron should respond to the magnetic field. This is a quantity called the magnetic moment of the electron for the curious. And if you have a spinning charged metal ball, you can calculate for how fast it's spinning, how much is charged, how massive it is, how much it ought to react to a magnetic field. And you apply those numbers to what we know, the mass and charge of an electron, and you get the wrong answer. And we know that electrons are really, really, really small. In fact, they may be infinitely small. That's another episode. And if they're just the size of our current detection limit, if they're just below that, if we think they're a certain size, that means to get that kind of a magnetic moment, the one we actually measure, that kind of reaction to a magnetic field that we actually measure, it means they're spinning faster than the speed of light, which is kind of wrong.
And if all the electrons being shot through this magnetic field had random spin directions, if they moved all over the place, if you imagine like these little arrows attached to the electrons, then some will already be pointing in the same direction as the magnetic field. Some will be a little bit off. Some will be way off. They should get tossed around randomly. If they have random spin directions, they should get spread out randomly and evenly on the opposite side. Because some will react strongly based on their spin and some will react weakly. Some will get deflected a little bit. Some will get deflected a lot. So it should be spread out evenly. Instead, they separate into two and only two camps. And this is the real kicker. Because no matter how we measure it, we always only ever get two answers for how much the electron is spinning. It's always either up or down. And the amount of upness and the amount of downness is always the same. We don't see any intermediate values. We don't see this nice continuous spread on the opposite side of the instrument.
We only see two clumps. And that is something that normal spinning metal balls simply wouldn't do. To sort this out, to really put us in the right perspective, we have to go in a fully quantum mechanical state of mind. We need to put blinders on either side of our eyes so we resist the temptation to apply our normal everyday macroscopic experiences and expectations of the world to the subatomic realm. Down there, things are simply different and it's not going to make intuitive sense. But nature doesn't care if nature makes intuitive sense. She doesn't care. Nature is nature. Electrons are going to do what they're going to do. And we have to, we absolutely have to discard. our classical worldview. Just like we do for relativity, we have to do it for quantum mechanics. The rules are simply different down there. So now we must go down that quantum road, full speed ahead, unwavering, unflinchingly, no stopping, except for one pit stop for Patreon. Patreon.com slash PM Sutter is how you can support this show and keep all the episodes going.
And the YouTube show, like every education outreach thing I do, it's supported all by contributions like yours at patreon.com. I can't thank you enough. And if you can't, I know I tease you that you ought to contribute even if you can't. Believe me, that is just a joke. If you can't contribute, I still appreciate you just listening to the show. If you can tell someone, if you arrive you on iTunes or Google or on the website or tell people on the internets, I really appreciate that too. Thank you so much. Now that we've had that appropriate stop, we can continue down the quantum road. In the early days of quantum mechanics, I mean, wait, like 1910s, 1920s, physicists really around the world were coming up with all sorts of rules to explain the subatomic world. There were all these experiments going on, you know, revealing what's happening to atoms and particles. And the physicists, the theorists were really trying to catch up, like piece it all together, put it into some coherent framework.
And they did. They had things pretty much sewn up tight in a compact set of mathematical descriptions, which is another episode, except for spin. So they were able to explain all these interesting, complicated phenomena, except for spin. And spin was just kind of tacked on. So they said, like, here's a self-consistent, elegant, beautiful description of the microscopic world. And then here's some stuff on spin. And of course, as the rules were developed, as we learn more about what quantum spin is really like, shorthand and notations were developed. And they seem, when you first encounter these shorthands and notations, they seem non-intuitive and awkward. And that's because they're non-intuitive and awkward. So what are some of the rules of quantum spin? Well, first it's, you guessed it, it's quantized. What does quantized mean? It means it comes in little packets or steps. The difference between the classical and the quantum world is the difference between a nice gentle slope in a staircase.
A nice gentle slope, I can choose to be anywhere I want on that slope. I can just be a little tiny bit. I can be a lot. I can step down just a little bit. I can go half a step, a quarter step, an eighth of a step. It doesn't matter. The slope lets me be anywhere. But on a staircase, I can only be on one step at a time. If I try to walk in half steps, I'm going to fall over. I can't do it. I can only go on this step, the number two step, number three step, number four step, number five step. And that's it. That's what the quantum world means. Things like angular momentum, things like energy only come in little packets, only come in steps. You can't have anything you want. And this is showcased really, really well with spin. When it comes to spin, an electron can only be measured to have, and here's a notation, here's a definition, either plus a half or negative a half spin. That's it. If you go to measure the spin of an electron, like, hey, how much is that electron spinning? You'll only measure one of two numbers, plus one half or minus one half.
And the one half, again, that's just a notation, a definition, a way to kind of untangle this mess. There are other kinds of particles than electrons, of course. Some kinds of particles can have three values of spin. They can have one. They can have zero. Or they can have minus one. Some other kinds of particles can have four measurements of spin. You can get plus three halves, plus one half, minus one half, or minus three halves. Even others can have five measurements of spin. Two, one, zero, minus one, or two. There are two kinds of spin. And all particles in the universe are either halfers, spin one half, or they're holers, spin one or spin two or spin three. And we've encountered this before. These kinds of particles have names. The fermions are the halfers in the universe. They are the ones with spin half or spin three halves or five halves. And the bosons are the holers. These are the spin zero, the spin one, the spin two. And I need to do a whole other episode on how this spinniness, that's my name, by the way, determines what kind of particle is and what are the implications.
That's a whole other episode, super fun, but not the subject of today. So an electron, let's go back to electrons. You can only see, you can only measure the spin of electron. You only have two values that will come out of your experiment, either plus a half or minus half. And I need to talk a moment about this concept of measurement. Because a lot of times you'll read or even I'll say like, oh, the electron has spin plus one half. I'm actually being a little bit lazy when I say that. And this is a very subtle point, but I think it needs to be made because this cuts right to the heart of quantum mechanics. Let's say I have a box of electrons, a big old box, lots of electrons. They can have any spin direction they want. Like the analogy I used before, imagine a bunch of little arrows, right? painted on all these electrons. And that arrow represents their spin direction. They all have the same magnitude of spin. So they're all spinning at the same rate, but they can be oriented any way they want.
All the electrons are jumbled up, so the arrows point all over the place. Then I start throwing them through the magnetic field. The magnetic field has a direction to it. It has an up and a down sense to it. For each individual electron, it has a little arrow being shot through this apparatus. That arrow will be maybe it's pointing up and a little bit sideways. Maybe it's pointing mostly sideways and just a little bit up. Maybe it's almost exactly split at a diagonal halfway between sideways and up. It doesn't matter though. It doesn't matter what that orientation of the spin is. I will only ever measure the arrows pointing straight up or straight down. I don't get to learn about how much the arrows are pointed left or right. This is a fundamental limit to measurements in the quantum world, and it's kind of a big deal. Imagine, imagine, imagine you bought your new smartphone. It has GPS, it has maps in it, turn-by-turn navigation. You're super excited. You plug it into your car and you say, hey, I want to go to that restaurant.
And instead of giving you accurate directions like, oh, you need to travel north-northeast for one mile, then turn left, you know, all the instructions. What if instead there's only two lights, right? And lights tell you north or south. And that's it. So let's say, well, if you say, oh, how far to that restaurant? Oh, it's two miles north. And then you travel two miles north. And then you ask again, hey, where's the restaurant? Oh, it's two miles south. So you travel two miles south. Okay, now where's the restaurant? It's two miles north. No, no, no, it's two miles south. No, no, no, it's two miles north. And that's the only ever answer you can get out of your GPS. You would immediately throw it in the trash. Unfortunately, we can't throw nature in the trash. We're stuck with it. This is a fundamental limit of measurement. The electrons can have whatever spin they want. If they're pointing just a little bit up, just a hair up, we will measure it as all the way up, spin plus half. If they're pointing just a little bit down, Just a tiny, tiny, tiny bit down as they're thrown through this magnetic field.
We'll measure them as negative one half. And that's it. That's all we will ever measure. Ever. We don't get to learn how much left or right. We don't get to learn how much up or down. Just if it's any bit up, it gets counted as up. And any bit down, it gets counted as down. Now, if I repeated my... Magnetic field Stern-Gerlach experiment apparatus. Instead of having an up-down magnetic field, I rotated it so it was a left-right magnetic field and repeated the experiment. Then I would get to learn about the electrons left-right. Are they pointing left? Are they pointing right? But I don't get to do it at the same time as the up-down. In fact, I destroy my knowledge of the up-down. And I can't do it at the same time. I never get to learn both simultaneously. So there's a limitation in the direction I can measure an electron spin. I can only measure its uppiness or its downiness. And I never get to learn how much of uppiness or downiness. Just are you in the up bucket or are you in the down bucket? And that's it.
So that's what spin is. Electrons and all particles have this weird property that we call spin. Different particles have different allowed values of spin, but we are fundamentally limited in how well we can measure it. And this is why this experiment, this 1922 experiment by Stern and Gerlach is so striking because usually the effects of quantum mechanics are really subtle. Like you have to do these really detailed measurements and you tease out the quantum nature and it's all spooky and weird, but very deep down, this is like a tabletop experiment that you can do at home and blasting right in your face is the true nature of quantum mechanics. right there, and you can't get around it. How are we gonna make sense of this? Where does this property of spin come from? What does it mean? Well, like I said, in regular quantum mechanics, all this stuff, quote unquote, regular quantum mechanics, by the way. All this stuff is just tacked on with the justification, experiment said so. Like we have this grand, beautiful, theoretical infrastructure to explain quantum mechanics.
And then here's some rules of spin that we can't really predict. And by regular quantum mechanics, I mean the Schrodinger equation. The Schrodinger equation does not include spin in its mathematics. That equation is a whole other episode, but I need to bring it up because Schrodinger wasn't the only person to work on quantum mechanics. He wasn't alone. There was lots of people. And now it's time. There's someone else I need to introduce. One of my all-time favorite scientists. I mean, James Clerk Maxwell, don't worry, still king of the mountain. But putting up a good fight for that. Oh, my gosh. Paul Adrian Maurice Dirac. Paul Dirac, just a beast of a scientist. I am not joking around. By the way, he signed his papers P.A.M. Dirac. So people would wonder why I signed my own papers P.M. Sutter. There's the inspiration for that. Paul Dirac just made things happen. He wouldn't just solve problems. He would develop new mathematical techniques on the fly to solve those problems. And then decades later, actual mathematicians will go back and prove that what he did by pure intuition was actually legit.
This is the kind of guy that could and did go toe-to-toe with Einstein and win. He shared his Nobel Prize with Schrodinger in 1933 for developing quantum mechanics, but he doesn't get as much love today. You know, the Schrodinger equation is everywhere, if you pay attention to that kind of stuff. But outside of physics, he's not really in popular culture. But inside of physics, his name is on like half the stuff. Like the Dirac this, the Dirac that, the Dirac operator, Dirac function, the Dirac equation. He gets plain name recognition inside the world of physics. And here's why I'm bringing up Dirac. Here's the deal. Quantum mechanics was developed in roughly the 1920s. By the 1920s, special relativity was already old news. Einstein developed that in 1905. And everyone knew that special relativity was a thing. And if you're going to make a theory of nature, if you're going to describe some aspect of nature, it has to incorporate special relativity, the rules of special relativity. Schrodinger attempted to make an equation that described what the experiments of quantum mechanics were revealing, but also obeyed the rules of special relativity, what we knew to be true from a special relativity.
That equation didn't make any sense at all. So he abandoned it. He said, let's just let's just figure out all that special relativity stuff later. And instead, he went casting about found the existing language of wave equations, was able to apply that successfully to quantum mechanics. And that's our Schrodinger equation, using that to like interpret and understand our results from those experiments. So you can use the Schrodinger equation to make predictions and knowing that it's not going to be correct in pure special relativity. So it's an incomplete picture of nature. Then comes Dirac, who at about the same time is doing the same similar work. He wants to develop some equations to describe what the experiments in quantum mechanics are saying. But he really, really wants to bring in special relativity. He really wants to make this happen. He arrives at the same place Shrody did, and he figured it out. The trick, because initially these equations make no sense at all. The trick was to, you know, completely restructure the mathematical description.
So instead of casting about for some existing language, he invented a whole new language. He said, no, no, no, no. Here's how you interpret it. You're going to speak a new language. That equation, the Dirac equation, describes everything the Schrodinger equation does and more. It includes special relativity. So it's like having two languages to describe the same phenomena. The Schrodinger equation is based on one language, the language of waves, and we can use it to make progress and make understanding The Dirac equation includes the Schrodinger equation and so much more in a completely new language. That's another episode to really dig into that, what that language is and how we interpret quantum mechanics via the Dirac equation. It includes the Schrodinger equation, includes special relativity, and it includes spin. The concept of spin. naturally appeared in Dirac's solution for quantum mechanics. If spin wasn't already discovered, he would have been credited with predicting it. He ended up getting vindicated, though.
His equations not only included the Schrodinger equation and special relativity and spin, also naturally included something we had known before, something we now call antimatter. Antimatter was predicted by Paul Dirac in this exact same equation. So what is spin? Well, it's a horrible word for one. Spin, the concept of spin is based on our classical understanding of electrodynamics that simply do not apply to the quantum world. Better term might be, I don't know, magnetic response of a particle. I don't know. I guess there's no word. We should have just made up a word. We should have made up a word and we'd be so much better off. If you're lazy, you can think of it like an actual spinning metal ball. like pretend these little particles are charged metal balls. And, but let's not, let's not. And you know what? We're never going to speak like that again. Spin is built into the universe. Asking where it comes from is like asking where mass or charge comes from. It seems to be fundamentally connected to the relationship.
between quantum mechanics and special relativity. So at one level, you can think of it as just a set of rules. Like, hey, nature says there's this quantity called spin, and it's different kinds of particles that have different amounts of spin, just like different particles can have different amounts of charge or mass. But because of the rules of quantum mechanics, we're limited in how much of that spin, of that quantity, we can actually measure. But spin appears to come. instead from this unification between quantum mechanics and special relativity. It appears to be something much, much deeper than a set of rules. It's at this point, and it's so cool, it's so cool that you can do a tabletop experiment, See this quantum mechanical effect, which is usually super subtle. Quantum mechanics is not easy to tease out, but there it is right in your face, making itself manifest, making itself known. And not only is it this manifestation of quantum mechanics, it's at this intersection between quantum mechanics and special relativity.
Is that confusing? Too bad, Mother Nature doesn't care. I'd like to thank my top Patreon contributors this month, Justin G, Matthew K, Kevin O, Justin R, Chris C, and Helga B. Thanks so much to you and all my Patreon contributors, patreon.com slash pmsutter, to help make this show possible. Be this show. And thanks again. The other part of making this show, this show is the questions. I'd like to thank Dean B, Pete E, at Nurbans, Carrie Kale, and at Sojournal, who is going to send me 10 bucks. P.O. Box 3322, Columbus, Ohio, 4320-3322. Please. keep those questions coming. Go to ask a spaceman.com. You can follow me directly on Twitter at Paul, Matt Sutter, also on Facebook, also on youtube.com slash Paul M Sutter. Uh, go to iTunes, go, go forth and spread the word of spin. And I'll see you next time for more complete knowledge of time and space.