Have you ever gotten a math test back and found that you had gotten  a tricky question right, but for entirely the wrong reason?

Like, you made two mistakes that just happened to like perfectly cancel each other out? Well, that is basically happened to two German scientists just over a century ago, when they conducted one of the most important experiments in quantum physics history.

And they knew that the result they  got was important when they did it. But they were completely wrong about why. This is the story of the Stern-Gerlach Experiment.

It’s a story of thrifty science, cheap cigars, and a man who proved quantum physics was legit… despite believing the exact opposite. [♪ INTRO] Our story begins in the late 1910s, with a former postdoc researcher of Albert Einstein’s named Otto Stern. See, Stern had a problem with a new theory his old boss had helped to invent. You know it by the name of quantum theory, and it was created to explain a  number of weird experimental results.

But Stern was so skeptical that, in 1913, he threatened to quit physics if this  “nonsense” turned out to be true. And honestly, he was right to be concerned. Today we know quantum theory to be hugely successful at  describing how the world works.

It gave us technological marvels  like the microchip and the laser. But a hundred years ago, it was,  more or less, a loose collection of ad-hoc results, all of  which seemed to defy intuition. The most important idea, which is  baked into the theory’s very name, is that some physical things can only come in discrete “chunks” called  quanta, not in a continuous stream.

For example, according to  Einstein and physicist Max Planck, light is made of particles called photons. And these photons can only have  an energy value that’s a multiple of a certain number that pops up in  a lot of quantum physics equations. That number is called h-bar,  because it’s written like this.

But quanta aren’t just a feature that light has. And in the early days of the  theory, scientists had to work out exactly what other parts of  reality came in discrete chunks. One particular hot-topic debate was over something called angular momentum.

That’s a property that things  have when they are turning, in any sense of the word.  The more something turns, the more angular momentum it has. So the Earth, for instance, has angular momentum from two different sources: it  has some because it moves around the Sun as it orbits it in a curved path, and some from spinning on its own axis. And in 1913, the Danish physicist Niels Bohr worked on a model of the atom’s structure, where tiny electrons orbit a large  nucleus like a mini solar-system.

In this model, the electrons had  angular momentum from their orbit, like the Earth going around the Sun. But crucially, that momentum only  came in specific, discrete values. And while this revelation fit  well with the observations some experiments were churning out at the time, it also like, just bothered a lot of physicists.

See, describing the Bohr model of an atom like a solar system is oversimplified at best. They do not line up in a lot of ways, but there is one weird point of connection. Because due to some laws of physics that we don’t need to get into here, the planets in our solar system are all forced to orbit in a more-or-less flat plane.

But according to Bohr’s version of quantum theory, a similar thing happens with electrons. They don’t all orbit in one single plane, but they can only orbit in a subset  of all possible orientations. Stern thought this was a lot of hooey.

So he designed an experiment to test Bohr’s model against the older ‘classical’ theory. The idea was to shoot a beam  of silver atoms down some fancy vacuum tubes, exposing  them to a specially-crafted magnetic field that shot  them down a very narrow path. Their journey ended with the atoms smashing into a photographic plate which would  record exactly where they hit.

That “where” would reveal who was right. Bohr and his quantum collaborators, or Stern and the physics he had grown up learning. See, it was already well established  that a moving electric charge, like an electron orbiting a nucleus,  would produce its own magnetic field.

In a way, it would act like a teeny tiny bar magnet pointing in a certain direction. And if an electron were to  enter Stern’s magnetic field, it would get deflected. The less  aligned the two magnetic fields are, the more the electron gets deflected.

So if the classical theory were true, and electrons could orbit a  nucleus at any random orientation, the silver atoms fired down the  tube would each be deflected by random amounts, and form a  continuous stripe on the detector. But if Bohr’s quantum model was correct, and angular momentum could  only come in discrete chunks, you would see two blobs and a gap between them. Now, the reason Stern picked silver  atoms in particular was two-fold.

One, they would show up clearly  on the photographic plate. But two, he also knew that the electrons in a standard silver atom were arranged so that only one of them was in the  atom’s outermost electron shell. In other words, it was the only  one that would be at the mercy of the external magnetic field,  so these big honking silver atoms were basically acting like lone electrons.

So Stern had his plan. But  implementing it would be an entirely separate endeavor. For one thing,  he was more of a theory guy.

So he enlisted the help of  a talented experimentalist named Walther Gerlach, who more or less built and ran the experiment on his own in Frankfurt. And Gerlach had his work cut out for him, even ignoring the fact that  he did a lot of it solo. Like, first he and Stern had  to scrounge for money to pay for the thing, all while Germany was in the middle of its post-World-War-One hyperinflation period.

Einstein actually fronted  some of that cash himself, and it’s said that the two also  got funding from Henry Goldman, one of the original partners of Goldman-Sachs. But the challenges were not over yet. The whole apparatus was the size of a pen, and whether or not there would end up being a gap, the whole blob of silver would  only be a millimeter wide.

So any measurements had to be a thousand times more precise than that. It was a lot of hard work to get the equipment perfectly in place and operational. But late in the evening on February 7th, 1922, Gerlach finally struck gold. …Or, silver.

I guess he kinda struck silver. He detected the two separated blobs of deflected silver he was looking for, and even sent a postcard to Bohr  with an image of the result. Because Bohr wasn’t just  right about there being a gap, his model was also right in  predicting how wide the gap would be, which translates into how much orbital angular momentum an electron has: One h-bar.

Physicists were delighted, seeing the results as the ultimate triumph of  Bohr’s quantum model of the atom. And Stern was finally forced to accept that quantum theory was valid… but he did renege on his promise to quit physics. So, everyone lived happily ever after, right?

Next stop, lasers and microchips? Indeed not. You can see that there's  quite a lot of video left to watch.

Because only a couple of years  later, people started to realize that the story told by Stern  and Gerlach’s experiment was… kind of totally completely wrong. But it was also weirdly right. So let me explain.

As the 1920s crept onward, the physics community learned a lot more about the  intricacies of quantum theory and how it applied to different  elements on the periodic table. Silver, as you might remember,  is one of those elements. And the latest calculations were  telling physicists that silver’s outermost electron doesn’t have  any orbital angular momentum!

That meant the Stern-Gerlach  experiment should have produced one big undeflected blob in the  middle of the photographic plate, not two separated blobs with a gap in-between. Not even a slightly spread-out streak! So instead, Stern and Gerlach  had accidentally proved silver’s outermost electron had some hidden, extra source of angular momentum.

And it took a few years for anyone to actually recognize such a thing existed. In the late 1920s, physicists  like Wolfgang Pauli and Paul Dirac separately made predictions  that subatomic particles should have an intrinsic angular momentum. You’ll also hear this called spin.

And in our Earth-going-around-the-Sun  analogy from earlier, spin would be a bit like the momentum Earth gets from rotating around its axis. But spin isn't really like that, it's its own, bizarre, uniquely quantum thing. And to be clear, it is completely separate from Bohr’s orbital angular momentum.

And it was spin, not Bohr’s  orbital angular momentum, that Gerlach had seen when he  fired up his finicky machine. But just to add another wrinkle,  Pauli’s theory predicted that Gerlach should have seen a separation  amounting to only one half h-bar. Not the one h-bar he measured, and the one h-bar that Bohr predicted.

Luckily for everyone, Dirac  was here to save the day. He not only predicted that an electron  should have an intrinsic spin. He also said it should have an intrinsic propensity to being deflected by a magnetic field.

That propensity would cause it to be deflected by twice as much as it “should”. In quantum physics lingo, you’d say that its magnetic moment is equal to two. If Stern and Gerlach had tried  to look for electron angular momentum with different techniques,  they might have seen the difference between the spin and  the orbital angular momentum.

Like, they could have used the  well-known field of spectroscopy, where the difference is very important. But that’s easy for us to  say a hundred years later. Either way, inside their magnetic field, the electron’s intrinsic  half-h-bar spin wound up getting multiplied by its intrinsic magnetic  moment of two, to make one h-bar.

Two wrongs… predicting both  an incorrect angular momentum and magnetic moment …canceled each other out. And everyone spent a few years thinking the

wrong version of quantum theory was correct. But it did still prove that  some kind of quantum-ness was correct, whether Stern liked that or not.

And it wasn’t just Stern’s theoretical mistakes canceling out that made the experiment a success. Gerlach made an accidentally  helpful experimental blunder, too! See, Gerlach supposedly liked cheap cigars.

And back then, smoking in  the lab wasn’t considered to be an absolutely terrible idea. Which it is. So in one telling of the story,  Gerlach was only able to study the silver blobs on his photographic  plate once smoke from his cigar… which was laced with a bunch of sulfur… had reacted with the silver atoms  and turned the deposit black.

In fact, for the experiment’s  one hundredth anniversary, two scientists tested this  story by running the experiment while they puffed some cigar  smoke directly at the detector. For comparison, one of them also just smoked a cigar beforehand and then  breathed onto the detector. And of course there was the obligatory control.

They claimed that the silver  deposits were indeed only visible once they had reacted with the cigar smoke, forming the jet-black compound silver sulfide. The Stern-Gerlach experiment was quickly cemented as one of the most important  experiments in modern physics. But sadly, Stern and Gerlach themselves got swept up in the wider historical forces of the time.

Because of his Jewish background, Stern was forced to flee Germany with the rise of Nazism. He did eventually get a Nobel Prize in Physics, but mainly for other work he’d done. Meanwhile Gerlach… he wound up contributing to the Nazi’s failed equivalent  to the Manhattan Project.

And I don’t think that Christopher  Nolan's going to make that movie. But let’s not end on that  bummer. Let’s recap instead.

Because when it comes to quantum physics, it helps to come back around  to the important bits. Otto Stern thought that Bohr’s quantum model of the atom was totally wrong. Which is technically true, just not  in the way Stern originally meant.

Because with their experiment, Stern and Gerlach thought they had discovered the orbital angular momentum of an electron was equal to one h-bar, proving Bohr right. But actually, they discovered electrons have an intrinsic angular  momentum equal to one-half h-bar… thus confirming a more modern version of quantum physics to be correct. And not Bohr’s.

I mean, it’s an A-plus for effort, at least. And it’s why textbooks to  this day will tell you that the Stern-Gerlach experiment  discovered what we now call spin… even though the concept of  spin did not exist in 1922. And also Gerlach thought that  smoking in the lab was a good idea.

I suppose in exactly that one  situation, he may have been right. [♪ OUTRO]