Spin and the Stern-Gerlach Experiment

SternGerlach-plaque
Figure 1. A plaque at the University of Frankfurt commemorating the Stern-Gerlach Experiment. (Source)

The word “quantum” means a single share or portion. In quantum mechanics, this means that energy comes in discrete chunks, or quanta, rather than a continuous flow. But it also means that particles have other properties that are discrete in a way that’s deeply counterintuitive. Today I want to tell you about one such property, called spin, and the experiment that discovered it: the Stern-Gerlach experiment.

(The goal of the original experiment was actually to test something else. But it was revealed later, after the discovery of spin by Wolfgang Pauli, that this is in fact what Stern and Gerlach were measuring.)

Magnets

The Stern-Gerlach experiment involves magnetic fields. So before I tell you about the experiment itself, I need to quickly review some of the properties of magnets.

As you probably remember, the north pole of a magnet is attracted to the south pole of other magnets and repelled from their north pole, and vice versa—a south pole is attracted to north poles and repelled by other south poles. In other words, opposites attract.

Suppose we generate a very strong magnetic field (say, with a very big magnet or with a solenoid) and put a small magnet in the field, as shown in Figure 2. What happens to it? The north pole of the big magnet will attract the south pole of the small magnet, and the south pole of the big magnet will attract the north pole of the small magnet. Since the north and south pole of the big magnet are are equally strong, these attractions will be equal and opposite, and they’ll cancel each other out so that the little magnet feels no net force. As a result, it doesn’t move up or down—it just hovers in place.

little-magnet-in-big-magnet-schematic
Figure 2. We put a little magnet in a big magnetic field and see what happens.

Now suppose we create a big magnet whose north pole is more powerful than its south pole, as shown in Figure 3. (It’s not actually possible to make a magnet with a stronger north pole than south pole. However, we can create the same effect by using multiple smaller magnets.) What happens now?

little-magnet-in-big-magnet-schematic-inhomogeneous-field
Figure 3. If we create a magnetic field where the north pole is much stronger than the south pole, the behavior is different.

To answer this question, we must understand that the strength of a magnetic force depends on the distance between the interacting poles; the closer the poles, the stronger the force. This means that the net force the little magnet feels depends on its orientation, as shown in Figure 4. If the south pole of the little magnet is close to the north pole of the big magnet, the little magnet will be pulled upwards. If, on the other hand, the north pole of the little magnet is close to the north pole of the big magnet, the little magnet will be pushed downwards. If the poles of the little magnet are the same distance from the poles of the big magnet, the little magnet will feel no force. And of course, anything in between is possible. A little magnet whose south pole is just barely closer to the big north pole will feel a weaker pull than a little magnet whose south pole is very close to the big north pole.

inhomogeneous-field-forces
Figure 4. If we put a little magnet in a magnetic field that’s stronger near the north pole and weaker near the south pole, the force on the little magnet depends on its orientation.

The Stern-Gerlach Experiment

The Stern-Gerlach experiment, performed by Otto Stern and Walther Gerlach, tested whether subatomic particles behaved like little magnets. To do this, Stern and Gerlach created a magnet with a bigger north pole than south, just like the one described above, and shot a beam of electrons with random orientations through the resulting magnetic field. If electrons behaved like little magnets, then the beam would be spread out by the magnetic field, as shown in Figure 5. Some electrons would be pulled upwards, some would be pushed downwards, and some wouldn’t change direction, depending on the orientations of the individual electrons. But if electrons didn’t behave like magnets, then none of them would be affected by the magnetic field, so they would all just fly straight through.

single-stern-gerlach
Figure 5. What we expect to happen in the Stern-Gerlach experiment  if electrons behave like little magnets.

Surprisingly, although the electrons were affected by the magnet, they didn’t spread out as in Figure 5. Instead, the electrons split cleanly into two beams, as shown in Figure 6.

single-stern-gerlach-spin
Figure 6. What actually happens when the Stern-Gerlach experiment is performed on electrons. The electron beam doesn’t spread out like a fan, but splits neatly in two!

That’s very weird! It implies that electrons behave like little magnets, but only sort of. A magnet can be oriented any way it likes. But an electron can only have two orientations: either aligned with the big magnet or aligned against it. So the electron can travel up or down, but it can’t stay in between. This is a distinctly quantum phenomenon—the electrons behave like magnets fixed into a pair of discrete orientations, or states, as opposed to a continuum of possible orientations. An electron’s spin is what describes which of those two states it’s in.

 

A Cool Video

Here‘s a cool video I found on Wikipedia that shows what I just explained.

Where Does Spin Come From?

I won’t discuss it in detail here, but we can understand spin as emerging from the structure of the underlying quantum field theory that describes the behavior of a given particle. For those of you who know the lingo, it has to do with whether the underlying field is a vector or scalar field, and how large that vector is. (Among other sources, see Quantum Field Theory in a Nutshell by Anthony Zee.)

 Interpretation

The Stern-Gerlach experiment reveals a dramatic difference between the quantum world and the world we’re used to. It’s not possible for a particle to have any old orientation; it must be oriented either with the external magnetic field or against it.

But what if there is no external magnetic field? How is the particle oriented? Somehow the act of measuring the system changed how it behaves, or at least how we perceive it. These are questions that physicists struggled with in the early twentieth century as quantum mechanics was being discovered. Indeed, to some extent, physicists are still struggling with them.

In the next few weeks, I’ll address some of these issues. Next time, I will talk about an extension of the Stern-Gerlach experiment that helps us explore, if not answer, some of these questions.

Related Reading

This is only the latest in a number of articles that I’ve written about quantum mechanics. For example, I wrote a three-part introduction to the field:

  • In the first part, I describe some of the experiments that first revealed particle-wave duality.
  • In the second part, I use the Bohr Model of the atom to explain how packets of energy emerge from the wave nature of matter.
  • In the third part, I describe how we can interpret matter waves as probability waves.

More recently, I wrote a pair of posts exploring particle-wave duality.

I’ve also written a number of stand-alone articles on quantum mechanics:

  • Quantum mechanics uses complex numbers, so I wrote a short explanation of imaginary and complex numbers here.
  • I explain the Feynman path integral, which is a way of understanding quantum mechanics, here.
  • I use particle-wave duality and matter waves to explain quantum tunneling here.
  • I use quantum mechanics to describe how atoms form covalent bonds here.

Further Reading

Here are some additional resources on the Stern-Gerlach experment:

Acknowledgements

Thanks as always to Alexandra Fresch for her line-editing.

Recently I’ve had a lot of discussions on Google+  about the interpretation of quantum mechanics. (In particular, I’ve spent a lot of time talking to +Charles Filipponi and +David R.) This article was partly inspired by those conversations. Thanks, guys!

License

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