EDIT: With the help of @ducks the post now has illustrations to clear up the experimental set-up.

Introduction

I want to give an introduction on several physics topics at a level understandable to laypeople (high school level physics background). Making physics accessible to laypeople is a much discussed topic at universities. It can be very hard to translate the professional terms into a language understandable by people outside the field. So I will take this opportunity to challenge myself to (hopefully) create an understandable introduction to interesting topics in modern physics. To this end, I will take liberties in explaining things, and not always go for full scientific accuracy, while hopefully still getting the core concepts across. If a more in-depth explanation is wanted, please ask in the comments and I will do my best to answer.

Previous topics

Spintronics
Quantum Oscillations
Quantisation and spin, part 1

Today's topic

Today's topic will be a continuation of the topics discussed in my last post. So if you haven't, please read part 1 first (see link above). We will be sending particles through two Stern-Gerlach apparatuses and then we'll put the particles through three of them. We will discuss our observations and draw some very interesting conclusions from it on the quantum nature of our universe. Not bad for a single experiment that can be performed easily!

Rotating the Stern-Gerlach apparatus

We will start simple and rotate the set-up of the last post 90 degrees so that the magnets face left and right instead of up and down. Now let's think for a moment what we expect would happen if we sent silver atoms through this setup. Logically, there should not be in any difference in outcome if we rotate our experiment 90 degrees (neglecting gravity, whose strength is very low compared to the strength of the magnets). This is a core concept of physics, there are no "privileged" frames of reference in which the results would be more correct. So it is reasonable to assume that the atoms would split left and right in the same way they split up and down last time. This is indeed what happens when we perform the experiment. Great!

Two Stern-Gerlach apparatuses

Let's continue our discussion by chaining two Stern-Gerlach apparatuses together. The first apparatus will be oriented up-down, the second one left-right. We will be sending silver atoms with unknown spin through the first apparatus. As we learned in the previous post, this will cause them to separate into spin-up and spin-down states. Now we take only the spin-up silver atoms and send them into the second apparatus, which is rotated 90 degrees compared to the first one. Let's think for a moment what we expect would happen. It would be reasonable to assume that spin-left and spin-right would both appear 50% of the time, even if the silver atoms all have spin-up too. We don't really have a reason to assume a particle cannot both have spin up and spin right, or spin up and spin left. And indeed, once again we find a 50% split between spin-left and spin-right at the end of our second apparatus. Illustration here.

Three Stern-Gerlach apparatuses and a massive violation of common sense

So it would seem silver atoms have spin up or down as a property, and spin left or spin right as another property. Makes sense to me. To be sure, we take all the silver atoms that went up at the end of the first apparatus and right at the end of the second apparatus and send them through a third apparatus which is oriented up-down (so the same way as the first). Surely, all these atoms are spin-up so they will all come out up top again. We test this and find... a 50-50 split between up and down. Wait, what?

Remember that in the previous post I briefly mentioned that if you take two apparatuses who are both up-down oriented and send only the spin-up atoms through the second one they all come out up top again. So why now suddenly do they decide to split 50-50 again? We have to conclude that being forced to choose spin-left or spin-right causes the atoms to forget if they were spin-up or spin-down.

This result forces us to fundamentally reconsider how we describe the universe. We have to introduce the concepts of superposition and wave function collapse to be able to explain these results.

Superpositions, collapse and the meaning of observing in quantum physics

The way physicists make sense of the kind of behaviour described above is by saying the particles start out in a superposition; before the first experiment they are 50% in the up-state and 50% in the down-state at the same time. We can write this as 50%[spin up]+50%[spin down], and we call this a wave function. Once we send the particles through the first Stern-Gerlach apparatus each one will be forced to choose to exhibit spin-up or spin-down behaviour. At this point they are said to undergo (wave function) collapse; they are now in either the 100%[spin up] or 100%[spin down] state. This is the meaning of observing in quantum mechanics, once we interact with a property of an atom (or any particle, or even a cat) that is in a superposition this superposition is forced to collapse into a single definite state, in this case the property spin is in a superposition and upon observing is forced to collapse to spin up or spin down.

However, once we send our particles through the second apparatus, they are forced to collapse into 100%[spin left] or 100%[spin right]. As we saw above, this somehow also makes them go back into the 50%[spin up]+50%[spin down] state. The particles cannot collapse into both a definite [spin up] or [spin down] state and a definite [spin left] or [spin right] state. Knowing one precludes knowing the other. An illustration can be seen here.

This has far reaching consequences for how knowable our universe it. Even if we can perfectly describe the universe and everything in it, we still cannot know such simple things as whether a silver atom will go left or right in a magnetic field - if we know it would go up or down. It's not just that we aren't good enough at measuring, it's fundamentally unknowable. Our universe is inherently random.

Conclusion

In these two posts we have broken the laws of classical physics and were forced to create a whole new theory to describe how our universe works. We found out our universe is unknowable and inherently random. Even if we could know all the information of the state our universe is in right now, we still would not be able to track perfectly how our universe would evolve, due to the inherent chance that is baked into it.

Next time

Well that was quite mind-blowing. Next time I might discuss fermions vs bosons, two types of particles that classify all (normal) matter in the universe and that have wildly different properties. But first @ducks will take over this series for a few posts and talk about classical physics and engineering.

Feedback

As always, please feel free to ask for clarification and give me feedback on which parts of the post could me made clearer. Feel free to discuss the implications for humanity to exist in a universe that is inherently random and unknowable.

Addendum

Observant readers might argue that in this particular case we could just as well have described spin as a simple property that will align itself to the magnets. However, we find the same type of behaviour happens with angles other than 90 degrees. Say the second apparatus is at an angle phi to the first apparatus, then the chance of the particles deflecting one way is cos^2(phi/2)[up] and sin^2(phi/2)[down]. So even if there's only a 1 degree difference between the two apparatuses, there's still a chance that the spin will come out 89 degrees rotated rather than 1 degree rotated.

Introduction

I want to give an introduction on several physics topics at a level understandable to laypeople (high school level physics background). Making physics accessible to laypeople is a much discussed topic at universities. It can be very hard to translate the professional terms into a language understandable by people outside the field. So I will take this opportunity to challenge myself to (hopefully) create an understandable introduction to interesting topics in modern physics. To this end, I will take liberties in explaining things, and not always go for full scientific accuracy, while hopefully still getting the core concepts across. If a more in-depth explanation is wanted, please ask in the comments and I will do my best to answer.

Previous topics

Spintronics
Quantum Oscillations

Today's topic

Today's topic will be quantisation, explained through the results of the Stern-Gerlach experiment which was first performed in 1922. This topic treats a much more fundamental concept of quantum physics than my previous topics.

What is the Stern-Gerlach experiment?

In 1922 physicists Stern and Gerlach set up an experiment where they shot silver atoms through a magnetic field, the results of this experiment gave conclusive support for the concept of quantisation. I will now first explain the experiment and then, using the results, explain what quantisation is. If you would rather watch a video on the experiment, wikipedia provided one here, it can be watched without sound. Note that I will dive a bit deeper into the results than this video does.

The experiment consists of two magnets, put on top of each other with a gap in the middle. The top magnet has its north pole facing the gap, the bottom magnet has its south pole facing the gap. See this illustration. Now we can shoot things through the gap. What do we expect would happen? Let's first shoot through simple bar magnets. Depending on how its poles are oriented, it will either bend downwards, upwards or not at all. If the bar magnet's north pole is facing the top magnet, it will be pushed downwards (because then north is facing north). If the bar magnet's south pole is facing the top magnet, it will instead be pushed upwards. If the bar magnet's poles are at a 90 degree angle to the two magnets it will fly straight through, without bending. Lastly, if the bar magnet's poles are at any other angle, say 45 degrees, it will still bend but less so. If we send through a lot of magnets, all with a random orientation, and measure how much they got deflected at the other side of the set-up we expect to see a line, see 4 in the illustration.

Now we'll send through atoms, Stern and Gerlach chose silver atoms because they were easy to generate back in 1922 and because they have so-called spin, which we will get back to shortly. We send these silver atoms through in the same way we sent through the bar magnets; lots of them and all of them with a random orientation. Now what will happen? As it turns out all the atoms will either end up being deflected all the way up or all the way down, with nothing in between. 50% will be bent upwards, 50% downwards. So silver atoms seem to respond as if they were bar magnets that either bend maximally up or maximally down. In the illustration this is labeled 5.

If we were to take only the silver atoms that bent upwards and sent them through the experiment again, all of them would bend upwards again. They seem to remember if they previously went up or down rather than just deciding on the spot each time if they go up or down. What model can we think of that would explain this behaviour? The silver atoms must have some property that will make them decide to bend up or down. Let's call this property spin, and say that if the silver atoms chose to bend up they have spin up, if they chose to bend down they have spin down. It seems that these are the only two values spin can have, because we see them bend either maximally up or maximally down. So we can say the spin is quantised; it has two discrete values, up or down, and nothing in between.

Conclusion

We have found a property of atoms (and indeed other particles like electrons have spin too) that is quantised. This goes against classical physics where properties are continuous. This shows one of the ways in which physics at the smallest scales is fundamentally different from the physics of everyday life.

Next time

Next time we will investigate what happens when we rotate the angle of the magnets used in the experiment. This will lead us to discover other fundamental aspects of physics and nature, quantum superpositions and the inherent randomness of nature.

EDIT: part 2 is now up here.

Feedback

As discussed in the last post, I am trying something different for this post. Talking about more fundamental quantum physics that was discovered 100 years ago rather than modern physics. Did you like it? Let me know in the comments!