In the world of quantum mechanics, particles behave in discreet ways. One breakthrough experiment was the Stern-Gerlach Experiment, performed in 1922. They passed silver atoms through a magnetic field and watched how the spin of the atoms caused the particles to deflect in a very specific way.
Stern-Gerlach Experiment Simulation
Particle Spin and the Stern-Gerlach Experiment
Appendix 5: Right Experiment, Wrong Theory: The Stern-Gerlach Experiment
The Stern-Gerlach Experiment, Electron Spin, and Correlation Experiments
Philosophy of Quantum Physics Stern-Gerlach Experiment video
Transcription services provided by: GMR Transcription
Introduction: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest-running online astronomy degree program. Visit Astronomy.swin.edu.au for more information.
Fraser Cane: Astronomy Cast, Episode 374 of the Stern-Gerlach Experiment. Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos. We help you understand not only what we know but how we know what we know. My name is Fraser Cain. I’m the publisher of Universe Today, and with me is Dr. Pamela Gay, a professor at Southern Illinois University, Edwardsville, and that [inaudible] [00:00:39] quest.
Hey, Pamela, how are you doing?
Pamela Gay: I’m doing well. How are you doing Fraser?
Fraser Cane: Good, although saying professor of Southern Illinois University Edwardsville is actually tough. I struggle with it every single week. I have struggled with it for almost 400 times now, but we made it through.
Pamela Gay: It line wraps.
Fraser Cane: It’s very long; a very long title. Okay, so we can talk about the Hangoutathon, but I think by the time people listen to this it will have already happened.
Pamela Gay: It will, but it won’t be too late to donate. The weekend before this goes live on the internet; we are recording 36 straight hours of video on Google Hangouts, and trying to raise money to keep Cosmo Quest going. Without your help, we’re kinda done for. And I don’t mean to sound black, but that is the actual literal truth. I’m in the process of writing a giant NASA proposal, but if we get it, we won’t get it until October, and we need to keep things going until October, and we can only do that with your help.
So if you miss the Hangoutathone, and you want to see me keep doing awesome citizen science projects that allow you to contribute to publishable NASA research, go donate. CosmoQuest.org/hangoutathon, all one word. Every little bit helps. Ten dollars is more than an hour of a student’s time, and we need those students back.
Fraser Cane: That would be. Just watch Pamela go from a sane person to a crazy person over the course of 36 hours. Thirty-six hours.
Pamela Gay: You keep saying that, but it hasn’t happened yet.
Fraser Cane: Third time’s the charm.
Pamela Gay: I did confuse prosecco and prosciutto last year, but that was a tongue twister.
Fraser Cane: Okay. Not an actual descent into madness?
Pamela Gay: No.
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Fraser Cane: So in the world of quantum mechanics particles behave in discrete ways. One breakthrough experiment with the Stern-Gerlach Experiment performed in 1922, they passed silver atoms through a magnetic field and watched how the spin of the atoms caused the particles to deflect in a very specific way. So quantum mechanics – it’s been famously said if you think you understand quantum mechanics you don’t understand quantum mechanics.
Before this experiment can you again set the scene? I guess where were scientists at their understanding of quantum mechanics?
Pamela Gay: We’d gotten to the point of we understood that energy was quantized when it came to how electrons existed inside of atoms. So there was this notion that an electron had an allowed orbital energy that you could have up to two electrons per energy state. This is the poly exclusion principal. We’d started to get to the idea that there was an extraordinarily dense nucleus. Still didn’t know what was holding it together. We had gotten to the understanding of just how empty the rest of the atom was, but we were still confused with things like magnetism.
There was the understanding that a charged particle in motion interacts with magnetic fields, generates magnetic fields. And an electron in an atom is kind of a charged particle. And so there was the question of are these magnetic states just like the energy states also quantized? We didn’t know, and that was what led to this experiment.
Fraser Cane: So describe the setup then. How did they perform this experiment?
Pamela Gay: Well, it was 1922 and the place was Frankfurt, Germany. We had two scientists. There was Otto Stern and Walther Gerlach. And what I loved is where they were located at the University of Frankfurt you didn’t just have a physics department. No that was far too mundane. They had an institute for theoretical physics which is where Stern was located, and they also had an institute for experimental physics, which was where Gerlach was located. And I find deep pleasure in the fact that they sort of isolated these two communities from one another.
But Stern reached across the institutional divide and asked Gerlach can you devise an apparatus that we can subject charged particles to – in this case silver – and can you do this with a sufficient magnetic field that we will be able to tell are the magnetic states a continuum or discrete?
Fraser Cane: It’s sort of back to that same question that we talked about a few episodes ago: Is it digital or is it analogue?
Pamela Gay: Exactly.
Fraser Cane: So you’re saying can there be a discrete state? So what does that mean then? If there is a discrete state for the particle, what are the implications as opposed to it being just a continuum?
Pamela Gay: Well, in this case if there were discrete states, when they sent a stream of silver ions through the – in this case an inhomogeneous magnetic field – the silver atoms would split; some going one direction, some going to the other direction depending on their magnetic state. And so what you’d have is literally a splitting up based on magnetic field, one atom to the left, one atom to the right. But if instead you had a continuum of states, you’d have a smearing of the atoms instead where they went variable amounts to the left, variable amounts to the right, and some of them just didn’t really go anywhere. So these were the expected outcomes of the experiment.
Fraser Cane: So I can sort of imagine that it’s like if it’s some – either you take the charge on these electrons – if it’s some multiplication of the basic charge then they’re gonna lock in, and they’re gonna get that spin out. Otherwise, they’re gonna go the other way as you tune the magnetic field. But if it’s just a –
Pamela Gay: But [inaudible] [00:08:07] new case, the charge is the same. It’s the magnetic state that they were thinking might vary.
Fraser Cane: But then, as you said, if it’s continuum, you just get this spray depending on each individual electron. So they ran an experiment. They had the expected outcomes, and what did they find?
Pamela Gay: Actually confusion because as they were preparing to do this experiment, it was realized oh, – insert expletives in German – the angular momentum of electrons just might be zero. So if this was the case, instead of expecting a dichotomy of to the left to the right, what they actually expected was to the left, nothing to the right, so split of three different things. So there was this sudden we’ve been working on designing it, working on designing it, oh, let’s change what our expectations are now that we understand more about the angular momentum, the orbital angular momentum of the electron. But then the results they got was actually this splitting that didn’t match that expectation at all.
Fraser Cane: How did it split? What was the result? Tell me Pamela.
Pamela Gay: Well, the result was the original some to the left, some to the right.
Fraser Cane: None to the middle?
Pamela Gay: Yeah, which was kind of a head-scratcher.
Fraser Cane: So then once they had sort of seen that then they knew that it was magnetically quantized, but –
Pamela Gay: No, they initially knew it was confused. So what they had was this problem where they’d initially assumed that the magnetic moment they were dealing with would come from the orbiting electron in the silver atom. And the reason they were using the silver atom is because you have all of these stacked energy levels, and in the final energy level you’re left with one unmatched electron. And that one unmatched electron was going to be providing the magnetic moment, the orbital magnetic moment for the atom.
But then they realized you can actually do a lot of cancellation, and that orbital angular momentum goes to zero. But what they hadn’t thought about is well, what if the electron itself has something that we can’t really describe except to liken it to spin. So if you think about it, the earth has orbital angular momentum related to our passage around the sun each year. That’s one set of angular momentum, and it’s that kind of orbital angular momentum they were expecting to create the magnetic moment, the magnetic field that they were trying to find.
Fraser Cane: They were imagining the silver atom’s a little solar system?
Pamela Gay: Exactly. And that’s a bad way to look at it, but it’s still the best our human brain can really do. But the other place that we have angular momentum is our earth is kind of rotating about its pole. Our day-night cycle is another spin that creates angular momentum. And when they looked at the results, they realized wait, what if in a classical imagining of what’s happening, we consider this as rotation about a pole of the electron where you have north up and north down creating two different kinds of, in this case, spin magnetic moments that are creating this to-the-left-and-to-the-right splitting of the silver as it goes through the inhomogeneous magnetic field.
Fraser Cane: Whoa. So I guess the question then is did this give them a better understanding of what – to move away from that solar system idea of the atom into this more – because our modern idea of the electron – called the electron cloud that it’s not these electrons just spinning around like little planets going around the sun? That it is a region of probabilistic sense. So does this give them some of that understanding?
Pamela Gay: It didn’t quite get them there yet. But what it did start to get at was the notion that the electron was a lot more complex than originally assumed. We now have a particle that we know has charge that we know is a fundamental particle that you can’t really break apart any further, but it somehow has its charge if you look at it from a classical approximation distributed on the surface of this point, and that’s kind of confusing.
It also started to help add further understanding to another phenomena. It was realized that hydrogen has this weird line that appears at what we now look at as 20-centimeter radiation in the radio. This is the hydrogen fine structure forbidden line transition where there’s actually energy tied up in whether or not what we now know – or at least now refer to – as the spin of the electron and the spin of the proton. If they’re aligned that’s one energy state. And if they’re out of alignment that’s another energy state. And we can now see this weird line, and understand it using this magnetic spin.
Fraser Cane: You, as an astronomer, you are looking for places, regions of that kind of hydrogen right?
Pamela Gay: Exactly. And we find it’s a very infrequent – this hyper-fine structure transition – is a very infrequent transition. But when we look at massive clouds of hydrogen gas that don’t have that many collisions going on it’s possible for a hydrogen atom to just hang out long enough that it has a chance for this flip – sorry, it’s the 21-centimeter line – this flip at 21 centimeters, and we see it. And understanding this hyper-fine structure wouldn’t be possible without the Stern-Gerlach affect.
Fraser Cane: But when you see that – like in spectroscopy – when you see the presence of the hydrogen at that specific wavelength in some big vast cloud of hydrogen what does that tell you as an astronomer? What process is going on there?
Pamela Gay: What it tells us first of all it’s a really boring cloud of gas where very few collisions are taking place. If collisions were taking place other forms of energy transitions would take priority, and this very rare transition would never really statistically have a chance of happening. So first of all, it tells us the gas is boring and not colliding a lot and just hanging out. The other thing it tells us is that you actually can change energy states just by changing how the magnetic fields are aligned.
This kind of makes sense. If you’ve ever played with bar magnets if you try and push the north end of two magnetics together that takes energy. Whereas, if you try and have them anti-aligned with the north to the south and the south to the north of the two bar magnets that will readily snap into place. So it’s that difference in the required energy. The difference in the energy with the two particles, depending on how they’re aligned that causes a photon to be released with this very particular 21-centimeter radiation.
Fraser Cane: I mean it’s not star-forming regions?
Pamela Gay: No. Nothing that exciting?
Fraser Cane: It’s cold –
Pamela Gay: It’s cold.
Fraser Cane: But isn’t this like cold hydrogen gas left over from the Big Bang?
Pamela Gay: Right.
Fraser Cane: It hasn’t gone [inaudible] [00:16:50].
Pamela Gay: It can be reprocessed. It literally simply means this is cold gas that isn’t undergoing a lot of collisions.
Fraser Cane: Right and is not in the process of forming new stars or whatever, but could be clouds for future abuse?
Pamela Gay: Exactly.
Fraser Cane: So let’s go back to the experiment. So they performed their experiment. They got their results, and how was that accepted by the scientific community, and what were the implications?
Pamela Gay: Well, initially it led to a whole lot of head scratching because as I said there were these two theories on what should come out. One was initially it was split two ways and then it became split three ways, but then they actually saw it split two ways, and so the motivation for this theory was – well, it was a man named Summerfield, who came up with the initial theory that led to this experiment: the theory that it would get split the three different directions.
But like I said, this was one of those moments of experiments not do what it was supposed to do. And even with the original split: a lot to the left, split a lot to the right, and nothing in the center that splitting was based on the orbital angular momentum which was a very different value from the spin angular momentum. So what they were seeing was still less of an effect than what was expected.
Fraser Cane: It’s just a strange thing to think about when you think about actual atoms and each individual atoms having angular momentum. Right?
Pamela Gay: Yes.
Fraser Cane: And the electrons themselves as part of the atom, and that containing some of the angular momentum. It just seems really strange that you could break down the universe into these little, little pieces, and then you realize that the angular momentum of entire structures is made up. You would just add them all up, right?
Pamela Gay: What gets me about this experiment as well is they did this in 1922. And this was not an entirely safe experiment to be doing. Silver atoms aren’t something that are just regularly hanging around all by their lonesome. They had to superheat the silver to get it in a pretty much gaseous form going through their inhomogeneous magnetic field. And the reason they were using silver was, like I said, because it has this final electron by its lonesome and an outer most orbital. They also chose it because it was readily detectable on their photographic plate. Let’s face it, silver’s kind of easy to spot when you fling it onto a photographic film.
Fraser Cane: Should we be breathing superheated silver gas?
Pamela Gay: No, not really, no. It’s just not the healthiest thing for you. So here they were in 1922. We didn’t have amazing electromagnets like we have today. We were just starting to figure things out like that. We didn’t have the machine shops we have today. We didn’t have the vacuum hoods. All of these that would have made this a relatively straightforward, relatively safe experiment. Instead, we have a theoretician saying I need this level of magnetic field to detect this effect. We have an experimentalist saying okay, I’ve got it, and then working together with silver gas.
Fraser Cane: One of the things sort of talking quite a bit about with this experiment, it’s just this concept of spin. And I think this comes up quite a lot through quantum mechanics and through physics this idea that things on a particle like a proton, in an atom, are spinning. So when we talk about spin in terms of physics what are we talking about?
Pamela Gay: This is where we get back to your original statement of if you think you know quantum mechanics, you probably don’t. Spin is a word that we use because it allows us to think about what’s going on from a classic perspective. You can imagine the electron as this sphere with the charge on the outermost parts of this sphere. And as it rotates, just like the earth’s rotation generates a magnetic field, the electrons’ spin would generate a magnetic field. The thing is that’s not actually what’s going on, and we’re not really sure what’s going because it’s not like we can go in and observe the very essence of an electron.
There are people that argue that this is one aspect of string theory where when you see one spin it’s because you’re looking at one end of a string that is mostly rolled up into other dimensions, and when you see the opposite spin it’s because you’re seeing the other end of a string that’s rolled up into other dimensions. But this whole notion that it’s an electron with charge on its outside that’s just what we tell ourselves to make our brains not quite hurt as badly.
Fraser Cane: And when we say that something is spin up or spin down what are we talking about?
Pamela Gay: It’s literally does it go to the left as it’s going through a magnetic field, or does it go to the right as it’s going to a magnetic field? That’s our way of you might say one’s north, the other’s south, but that implies monopoles, so we can’t use those words. But it’s literally a way of expressing how it interacts with the magnetic field. You might think of it as North Pole is aligned upwards versus South Pole being aligned upwards.
Fraser Cane: It’s like a bar magnet, right? Like it’s a binary situation. You have a bar magnetic that’s got a north-south, you bring the north pole to it, it’s gonna flip it around and clamp onto the south end, but it’s not – I guess as it’s moving through that magnetic field, the magnetic field is then getting them to align into the right alignment to whether they’re gonna veer up, or they’re gonna veer down through that magnetic field.
Pamela Gay: And where it starts to get wrong as far as your stomach is concerned – because your stomach will try to do physics and fail mightily – is the spin is actually looked at in terms of different magnetic moments where you might have its spin is plus one-half or minus one-half. Or its angular momentum we’ll look at as being minus 1, 0 plus 1. And these are numbers that we use to represent what’s going on. But it’s important to understand that a lot of the rules of quantum mechanics are tools that we use to describe what we experimentally determined, but that doesn’t mean they’re actually describing the physical reality of what we’re seeing. It’s just a set of instruments, a set of math that allows us to get at predicting what will happen next. But that’s all it’s doing is very successfully predicting what has happened and explaining what we’ve seen.
Fraser Cane: And we did a great show – go back in the archive – we talked about entanglement, and spin is one of these characteristics that physicists use to demonstrate entanglement. And so you can sort of take this experiment to the next level. You can really contort it and start to get at these entangled properties of these atoms as these electrons are sort of passing through this apparatus.
Pamela Gay: And as you try and put this together – they got lucky with their particular atom of choice. It had an orbital angular momentum of 0, and so we were dealing with the electrons’ intrinsic angular momentum which is plus or minus one-half, but not all systems are equally elegant. Other systems you end up with additional magnetic moments that come from the orbital angular momentum being some different integer than 0, and so you have to add up all of these different bits to get at the total angular momentum, which reflects in the total magnetic moment of these particles and these atoms.
Fraser Cane: Had a lot of work been done – because it feels like this was sort of one of the parts of why it’s such a groundbreaking experiment was that from the moment they started to take atoms and run them through these magnetic fields, they really started to tease out a lot of the fundamental measurements, characteristics of the atoms. And that variations, flavors of this experiment are still being run today just in more complicated higher energies. But still, this is the way – apart from smashing them together – this is the way that physicists are getting at the fundamental way that the measurements, the masses, the spins, the charges, all of this stuff by running them through these kinds of – an entanglement, right?
Pamela Gay: That’s entirely right. When this started we were just starting to understand that the electric and magnetic forces were coupled. We were just starting to understand how charged generated magnetic fields, we were still only a generation into this. Where a lot of the discoverers in the late 1800s were still around as your senior emeritus faculty, and it was the new junior faculty who were playing with the new massive alternating currents that were being devised through new forms of generators.
It was new, more precise machining apparatus that were allowing us to do more and more detailed experiments. And then of course photography. That was still in its infancy back then, but at least at this point infancy meant 40 years in when we hit the 1920s. So everything was still new, and when you coat it with silver, shiny. And they were working hard to figure out all the new characteristics of the charge that Benjamin Franklin had started working with in the 1700s.
Fraser Cane: I mean, the calculations that Maxwell had done to really integrate magnetics and the electric field.
Pamela Gay: And we were starting to get to the day of Dirac Notation to try and understand how you add together the magnetic moments. We were starting to get the Schrodinger Equation to describe the wave nature. All this was coming out.
Fraser Cane: Dirac was the one who predicted antimatter right?
Pamela Gay: I don’t know. That’s a different [inaudible] [00:28:34].
Fraser Cane: It’s a show on its own. I forget the date, 1928? Cool. Well, that was awesome, Pamela. That was great, and we’ll see you next week.
Pamela Gay: Sounds good.
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Duration: 30 minutes