A layperson's introduction to quantisation and spin, part 1
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!
Thanks for posting. Adding a few pictures/videos really helps me visualize some of this stuff.
Is there any factor that decides what spin an atom will have? And is spin a constant property, or could we do something to the atom that would invert the spin?
The 50/50 chance is just that, a chance. There's no deeper reason that decides if it's up or down. It's a manifestation of the inherit randomness of the universe.
Spin is a constant property, but whether the spin is up or down can be changed. This we will see next post.
I think I may be misunderstanding something, because I read this as spin being constant and not. But if all of the previously emitted atoms go in the same direction the second time, is it random?
If that's covered next time, no rush with answering.
Whether they choose up or down is random, but once they made this choice they stick to it. There are ways to force them to choose again, which we shall see in the next post.
I enjoyed physics upto A-level and tried to understand quantum mechanics from textbooks but found the math too heavy back then. This was very interesting & accessible.
Also what the hell universe, you drunk?
If you think the universe is drunk now, just wait until the next post. The physics there is even weirder - a lot so!
Fantastic! I gathered from my reading the idea that spin wasn't like the rotational spin of the particle, but never ran across this experiment and its relating to quantum spin to the magnetic field. I've spent decades thinking that spin was just a mathematical term, after learning in high school about quantum numbers. Thank you! Now all I've been reading about your next topic is starting to make some sense. In particular the book Quantum Physics: the Theoretical Minimum gets rather obscure in terms of where this phenomena came from.
Thank you for the praise :).
The focus on mathematics in introductory physics courses is a mistake in my opinion. It would be much better to have students develop an intuition for how things like forces work and what energy is. Hiding the intuition behind maths isn't helping anyone.
EDIT: even physicists first understand nature through these experiments. Not through maths. The maths usually comes after they did an experiment like stern-gerlach's, from which they draw some conclusions that get turned into maths later.
In my next post (next week somewhere if I find the time) I will dive a bit deeper into what spin is and how it exhibits behaviour that can't be explained classically.
Are there any other properties that correlate with spin, physical, quantum, or otherwise? If I somehow separated a large group of atoms by spin, would I be able to do fun and/or scientifically interesting things with them?
Spin gives rise to two different classes of particles in the universe: fermions and bosons.
Some particles, like electrons and the particles that make up the atom's nucleus/core, all have half-integer spin (+-1/2, +-3/2, etc). So they are all fermions. We can add up all the spins in the atom and find the net spin of the atom. If it is half-integer it's a fermion, if it's integer it's a boson - per definition.
The cool thing is that they behave completely differently. At low temperatures a collection of bosons will all be in a zero energy state. However - fermions are not able to be in the same state and so a fermion gas at low temperature will still have a lot of energy.
As for cool applications of spin, MRI works by forcing the spins of the atoms inside a person's body to flip and measuring the energy difference that arises from this flipping.
I really enjoy your posts, and this one especially. They are very interesting to read, but I usually don't have anything to comment, so I only upvote. But just know that you have a loyal reader here.
Thank you for the kind comment.
To be honest, these bumping comments seem to help out my posts a lot. Because a lot of people only read and don't comment my topics tend to disappear quick with the default sorting. So I'd say just commenting that you found it interesting is worthwhile until the default sorting gets better, even if it is bad practice in general. Plus, they do encourage me to keep them coming :)
(If asking people to comment is controversial let me know and I'll delete this comment)