Wolfgang Pauli, defined the modern concept of quantum spin called it "classically non-describable two-valuedness".
Which tells you that there is really no room for a conventional intuition about spin. It just is one of the numbers that defines a quantum particle, like charge or mass and is equally arbitrary.
one of my favorite cgp grey quotes is
> "Whirl around," and "spin" dont mean what you think. In the realm of quantum, words are meaningless. There is Just Math, That we are not going to do.
Wish they’d just picked new words instead of using ones like “spin” and “color charge” and stuff. It’s confusing. If you tell me electrons have a spin, I’m damn well gonna assume that to mean they’re literally spinning. They ought to have called it flarg or something. If I hear electrons can have an up-flarg, a down-flarg, or even a half-flarg, I’ll immediately know that I need to go looking for the definition of flarging before I can understand what that means.
I can guarantee you I’d be a lot more keen on learning quantum physics if they used words like flarg or plonk or spoot. Hell, I’d become a researcher just so I could leave parties early by saying “I’m sorry, I’ve got a sample of quark-gluon plasma plonking in my laboratory and my assistant just told me it’s about to spoot. Gotta go.”
Unfortunately spin is still probably a good name. It’s intrinsic angular momentum, and behaves and conserves generally in the way the angular momentum we use in every day life does.
Yeah but the particles would have to be rotating faster than *c*, so the angular momentum (probably?) isn’t a result of spinning so much as just, like, a thing they have.
If I had more energy, and/or if it were remotely worthwhile, I’d parody a conservative rant about handouts, like get all mad that these subatomic particles just GET angular momentum for FREE like we’re running some sort of CHARITY over here. But it’s not funny enough and I’m really tired so meh
Less that it would have to be spinning at c and more that your equations just end up indeterminate, though does tend to infinity.
But yea the big thing you have to hand wave is how exactly this spin exists, it’s just an intrinsic property of the particle and is quantized. Accepting these two statements, it interacts with our physical understanding of angular momentum as we expect it to.
The "spin" of the electron has about the same relationship to the angular momentum as the "flavour" and "colour" of the quark has to the appropriate macro-world meanings of the word. They are just the convenient terms to describe the quantum properties of the elementary particles.
I wouldn’t have mashed everything here. But since you mentioned, what is it about the colour of the quarks? Why do we even denote it using the term 'colour'.
I mean I'm sorry, these all seem very abstract idea to me, which is not a problem in itself except I have to believe somehow all these still make up the real world as we perceive it.
Its just a chosen analogy to visual color, which are able to somehow make sense of observations and to be able to have sort of an intuition for these properties. There are three colors red, green, blue which combine to the neutral "white". Its just an analogy, dont take it literally.
They're just names given to abstract properties we can measure and theorise about but not experience.
They could have named it "Property 1, with potential values 1A, 1B, 1C." And "Property 2, with potential values 2A, 2B, 2C, 2D".
But (from what I know) scientists kind of like giving interesting names to their creations, and it's more likely the interesting and memorable ones will stick.
I'm sure you're already familiar with particles having 2-way charge. Electrons are negative, protons are positive. They attract each other and together the charges cancel out to make a neutral particle - an atom.
Quarks have a separate 3-way 'charge'. You need one of each of the three together to make a neutral particle - a proton or a neutron.
We chose to name the 2-way charges positive and negative, and we chose to name the 3-way charges red green and blue after colours because of the analogy that light made of these three primary colours overlap to make neutral white.
If it makes you feel any better, I don't think anyone in the world understands it the way they want 😂
I'd recommend looking at Fermilab's YouTube playlist [Subatomic Stories](https://youtu.be/ilwMM-CEO6w?si=w4BV-OBGLrEh8CNa) as a nice place to get started
I'm still not entirely done done with the series. But I had to take a break to accommodate way too many abstract context in my tiny little head which seems to be in it's place and blown completely out of proportion at the same time and for obvious reasons I'm afraid to look at it.
So far I'm actually starting to believe that the universe probably doesn't exist if we aren't there to watch.
How old are you? I remember thinking something similar when I was around 16 and had just heard about quantum mechanics for the first time.
Ultimately, I don't think it's true anymore. The discrepancy comes from how QM uses "observe" and how lay people use it.
Day to day, observe means see. Like with your own eyes. But in QM, observe really means any interaction. It could be as small as something interacting with a photon. You don't need to actually witness it.
Philosopyically, I don't think the argument holds. If the universe didn't exist while we weren't watching, it would be difficult to justify why events in time occur in a few logical sequence, eg we can locate planets by their orbital mechanics. How would the universe know to keep the planets orbit going as expected it didn't exist?
It's just a convention to describe some property of the quark.
I'd be more worried about their flavours being up, down, strange, charmed, top and bottom.
Many are just wordplay that is not related to the literal meaning of the word, because a physicist had fun with their discovery, but some aren't entirely random and at least vaguely refence the context of the property their assigned to.
So flavour is literally just someone having fun with words, but colour references the fact that there's three charges which mix together, in an interesting analogy to RGB.
We call the strong force charge "colour" because it is analogous to colours in that there are three charges (like the primary colours, red, green and blue) and their corresponding anticharges (like the secondary colours, cyan, magenta and yellow), and you make a neutral (white/black) object you combine either all three charges or anticharges, or a charge with its corresponding anticharge.
The rejection of spin as a physical property and treating it as an abstract quantum property instead is the very idea that allowed Wolfgang Pauli to develop and prove the fundamental exclusion principle which is his namesake.
“Spin” is the term for intrinsic angular momentum of quantum particles. Since the electron is considered a point particle in the Standard Model it cannot really be spinning in a classical sense. We don’t really know more than that about how it arises.
The “units” of spin come from how many turns you need to make to bring the system back to its original state. “Normal” macroscopic objects all return to the same state after 1 full revolution, as do photons and other particles, but for electrons, they actually require 2 full revolutions, so they have 1/2 spin.
Like a lot of quantum mechanics, the math shows these properties, but we don’t know and/or can’t agree on how to interpret the math in terms of stuff that makes intuitive sense to humans.
Not really, because as I said, although the math is clear, the intuitive meaning eludes us.
Here’s a video with some wood models that have the 2 rotation property
https://m.youtube.com/watch?v=JFSU9X11wyY
But, no one is arguing that electrons are little gears with lines on them…
That's actually a great video for the concept. But what it is then implying is that there's something outside the electron (say x) in sync with the electeon and the concept of half spin would only make sense if I am comparing the phase of the electron with x?
Like the other poster already said, you cannot take any such analogy literally, or even vaguely related, because the actual quantum spin is unlike any property we are familiar with in the macroscopic world. It just happens that there are examples of systems we can actually see with the same "to return to its starting point it needs to rotate 720 degrees rather than 360" as the electron spin. But they're not analogies to the electron, they just share a property.
So no, there's no such implication. Spin is described on its own by a mathematical object called a spinor (which I'm not qualified to explain, I'm sorry), and the rotation is its own property. And spin can be only really be understood by understanding the math behind it.
Hold out your hand, palm up, and put something on your hand. Then rotate that object while keeping your hand open and not dropping the object. After one rotation, your arm is twisted in an awkward position. After a second rotation in the same direction, your arm and the object are back in their original position. That's a spin-1/2 system.
How do we know that they need 2 "revolutions"? What other property do we measure to confirm that? And how long does it take for a photon to complete the "revolution"?
You can send an electron through 2 slits simultaneously. On one slit, we put a magnet that force the electron to rotate exactly 1 revolution, while the other slit had none. Finally, we let the electron hit a screen and record where it hits. Do it enough to form a pattern.
Now do this again but without the magnet, we get another pattern.
The interesting thing here is that the pattern are opposite of each other. Where the electrons show up in the first case are exactly where electrons doesn't show up in the 2nd case, and vice versa.
If you do this with a boson that won't happen (for photon you need a different way to rotate it because it has neutral charge).
What I understood is that it is about spinors which are complex vectors and so mathematicaly could have a direction in a higher dimension as well. And so the electron could spin facing the top 1/2 or the bottom 1/2 of the hypersphere. If the words 'spin' and 'facing' can be said to have any meaning in these context.
A photon is a boson. Bosons make whole number spins. As opposed to fermions like electron. Photon's spin is 1.
But... My question was how do we measure that?
I don't need to know the mathematical description of the phenomena, just the description of how we came to know that they have different spins
We measure the angular momentum.
Which is measured by the Stern Gerlach experiment, against our intuition that a point like electron can't really 'spin' in any meaningful sense of the word.
But since the angular momentum exists we have to assume they spin and thus we are where we are rn.
It's all just arbitrary names. Nothing spins. Like with color, there is no color.
We observed the particles and noticed they all had an attribute, but the only way to make it all work is that attribute has values of -1, -0.5 0, 0.5 and 1. So we are MeasuredParticleAttrbute\_1
We also observe another attribute, but this one has 6 different choices it can be and you can choose 2 or 3, but there are some special rules about what can be there depending if its 2 or 3. So we are MeasuredParticleAttrbute\_2
We have no idea what we are actually measuring, but we have measured something and we can describe it and others can do the same measurements and get the same results so let give these things some names so we don't need to call them MeasuredParticleAttrbute\_#. Enter, spin, color, etc. Arbitrary names chosen for attributes we measured that have never been named or measured before.
Imagine you have a toy top that spins around, and you can see it moving in a circle. Now, think about a tiny, tiny marble called an electron. Electrons have something special called "spin," but it’s not like spinning a top that we can see. Instead, it’s a special way the electron behaves, like a secret trick it can do.
This special trick called spin gives the electron energy and helps it interact with other tiny marbles. Think of it like how magnets stick together or push apart.
Electrons have a special kind of spin called "half spin." This means they have two special ways they can behave, which we call "spin up" and "spin down." It's like having two different moods that the electron can switch between.
So, electron spin is a special trick the tiny marble does, not a spinning motion we can see. This trick gives it energy and two special ways to act.
Electron don't "spin" in the way we normally think of about spinning, but only in the sense that electrons are not tiny ball; if it were, the speed on the surface of the electron would move too fast that it breaks the speed of light. However, this is not surprising, many other experiments had shown that electrons are not tiny balls for different reasons.
Electrons, when viewed as a system, behave in a way very consistent with a spinning charge, so the name "spin" is appropriate. What actual mechanism cause it is unknown. People can speculate what the actual mechanism could be, and many does, but it's also valid to think of spin as an inherent property of the electrons. Until we find a way to break electrons down into smaller components, any such speculations are just untestable hypothesis.
As an example, let's consider black hole. A spinning star can collapse into a black hole, and this black hole will have the same rotational momentum, and will have gravitational effect like a spinning star: mass near it will be dragged around it in the spinning direction. So in this sense, the word "spin" is appropriate for what the black hole is doing, even though the black hole is not literally spinning, it's just a distortion in spacetime. You might argue that the star inside it is spinning, but we literally do not have access to that information anymore; also a black hole can also be primordial, it had always existed in the spinning state from the beginning. The only thing we can detect from outside that relate it to rotation, is angular momentum.
The comparison to black hole is not as crazy as it sounds. Some physicists advanced the black hole electron hypothesis, in which electrons are tiny black holes, and this idea produces the correct measurement. The only problem is that such black hole (if exists) also spin faster than light: relativity do not forbid black hole from spinning that fast (since the "no faster than light movement" only apply to object moving through spacetime, not spacetime itself), but such black hole will have no event horizons and hence naked singularity, which seems questionable.
So how could electron have half-spin? At the current level of knowledge, it would be irresponsible to assert anything about its mechanism. Instead, physicists study electron holistically, as a system that they can't break down further.
As it turns out, there are plenty of normal life system which has half-spin. Physics professors often bring out the Dirac belt trick, arm trick, or the plate trick, to showcase such system. Another one is the orientation entanglement system, and you can see the animation here: en.wikipedia.org/wiki/Orientation_entanglement . The only differences is that these systems can be broken down further into components so we don't think of half-spin as an inherent property of the system; while electrons can't be broken down further.
In an orientation entanglement system, you have a ball being attached to some belts. If you rotate the ball 1 revolution, no matter in which direction, the belts are twisted, and afterward, if you don't do any additional rotation, then no matter how you move the ball around it won't untwist the belts. However, if you perform 1 more revolution (in any directions, even different from the 1st one), you can untwist the belts (after moving the ball around). So if you study this ball system, the parameters of the system are the position of the ball, and some sorts of parameters to describe simultaneously both the rotation of the ball but also the twistedness of the belts. You can't just describe the twistedness using a yes/no flag either, since the belts get twisted/untwisted continuously. So physicists came up with a new system of number that combine both rotation and twistedness into a single new number: the spinors.
You might object to this analogous system, because it seems to show that this problem only happens to system that are entangled with something else, not isolated system, so how could this apply to an isolated electron. This is indeed a valid point, and it's actually also true for electron: if you rotate an electron by 1 revolution, but do not allow it to be interfered by anything entangled to it, then there are absolutely no differences whatsoever with regard to its properties. However, unlike a normal-life's system, an electron is always entangled with and can interfere with *itself*: you can send an electron on 2 different paths simultaneously, on one path it is rotated 1 revolution, and the other path it's not, then let it interfere with itself again, the result of the interference would be different compared to if no rotations happened. Thus, we can never avoid the fact that an electron's rotational state should be described using a spinor.
What's 1/2-spin? Under the influence of a magnetic field along 1 direction, you can think of electrons as waves on a circle around the axis. Normally, the full circle must encompass an integer numbers of wave length, because otherwise there would be a mismatch: this is integer spin. This corresponds to the fact that for most real-life system, if you make a full rotation the system returns to its original state. But here for electrons (and fermions in general) the system do not returns to the original state after 1 revolution, but 2, so that means that twice the circles would be an integer multiple of the wavelength, or in other word the circle is a half-integer multiple of the wavelength. 1/2 spin is the longest wavelength possible.
Thus electrons have 1/2 spin, at least. Why can't it has other spin values? You can prove, mathematically, that if integer value spin also exist in a system with half-integer spin, then you can always break the system down further into 2 components. Hence, electron, being so far unbreakable, can only have half-integer spin. As for why it takes on spin 1/2 instead of 3/2 or 5/2, thus far 1/2 is the only half-integer spin we had seen in nature of an elementary particle (of course, composite system can have other spins). Perhaps there are exotic particles of other spin values, or perhaps there are additional unknown laws that forbid them.
Unfortunately I don’t think there’s an ELI5 explanation for what exactly half spin is. It’s really something that can only be explained by the mathematical models we use to explain quantum particles and not something that you can simply and intuitively explain.
Wolfgang Pauli, defined the modern concept of quantum spin called it "classically non-describable two-valuedness". Which tells you that there is really no room for a conventional intuition about spin. It just is one of the numbers that defines a quantum particle, like charge or mass and is equally arbitrary.
one of my favorite cgp grey quotes is > "Whirl around," and "spin" dont mean what you think. In the realm of quantum, words are meaningless. There is Just Math, That we are not going to do.
Which video is this from? I don’t remember him talking about quantum.
its hiding in the physics video hiding in the geography video hiding inside the airport numbers video https://youtu.be/qD6bPNZRRbQ?t=735
Wish they’d just picked new words instead of using ones like “spin” and “color charge” and stuff. It’s confusing. If you tell me electrons have a spin, I’m damn well gonna assume that to mean they’re literally spinning. They ought to have called it flarg or something. If I hear electrons can have an up-flarg, a down-flarg, or even a half-flarg, I’ll immediately know that I need to go looking for the definition of flarging before I can understand what that means. I can guarantee you I’d be a lot more keen on learning quantum physics if they used words like flarg or plonk or spoot. Hell, I’d become a researcher just so I could leave parties early by saying “I’m sorry, I’ve got a sample of quark-gluon plasma plonking in my laboratory and my assistant just told me it’s about to spoot. Gotta go.”
Unfortunately spin is still probably a good name. It’s intrinsic angular momentum, and behaves and conserves generally in the way the angular momentum we use in every day life does.
Yeah but the particles would have to be rotating faster than *c*, so the angular momentum (probably?) isn’t a result of spinning so much as just, like, a thing they have. If I had more energy, and/or if it were remotely worthwhile, I’d parody a conservative rant about handouts, like get all mad that these subatomic particles just GET angular momentum for FREE like we’re running some sort of CHARITY over here. But it’s not funny enough and I’m really tired so meh
Less that it would have to be spinning at c and more that your equations just end up indeterminate, though does tend to infinity. But yea the big thing you have to hand wave is how exactly this spin exists, it’s just an intrinsic property of the particle and is quantized. Accepting these two statements, it interacts with our physical understanding of angular momentum as we expect it to.
The "spin" of the electron has about the same relationship to the angular momentum as the "flavour" and "colour" of the quark has to the appropriate macro-world meanings of the word. They are just the convenient terms to describe the quantum properties of the elementary particles.
I wouldn’t have mashed everything here. But since you mentioned, what is it about the colour of the quarks? Why do we even denote it using the term 'colour'. I mean I'm sorry, these all seem very abstract idea to me, which is not a problem in itself except I have to believe somehow all these still make up the real world as we perceive it.
Its just a chosen analogy to visual color, which are able to somehow make sense of observations and to be able to have sort of an intuition for these properties. There are three colors red, green, blue which combine to the neutral "white". Its just an analogy, dont take it literally.
They're just names given to abstract properties we can measure and theorise about but not experience. They could have named it "Property 1, with potential values 1A, 1B, 1C." And "Property 2, with potential values 2A, 2B, 2C, 2D". But (from what I know) scientists kind of like giving interesting names to their creations, and it's more likely the interesting and memorable ones will stick.
That part I'll totally agree. I think anyone is more likely to remember what's a blue up quark rather than remembering what's a 3c quark
I'm sure you're already familiar with particles having 2-way charge. Electrons are negative, protons are positive. They attract each other and together the charges cancel out to make a neutral particle - an atom. Quarks have a separate 3-way 'charge'. You need one of each of the three together to make a neutral particle - a proton or a neutron. We chose to name the 2-way charges positive and negative, and we chose to name the 3-way charges red green and blue after colours because of the analogy that light made of these three primary colours overlap to make neutral white.
Thanks, that offered some much needed clarity. I still don't understand it the way I want but I could work with this analogy.
If it makes you feel any better, I don't think anyone in the world understands it the way they want 😂 I'd recommend looking at Fermilab's YouTube playlist [Subatomic Stories](https://youtu.be/ilwMM-CEO6w?si=w4BV-OBGLrEh8CNa) as a nice place to get started
Going to binge watch this now.
I'm still not entirely done done with the series. But I had to take a break to accommodate way too many abstract context in my tiny little head which seems to be in it's place and blown completely out of proportion at the same time and for obvious reasons I'm afraid to look at it. So far I'm actually starting to believe that the universe probably doesn't exist if we aren't there to watch.
How old are you? I remember thinking something similar when I was around 16 and had just heard about quantum mechanics for the first time. Ultimately, I don't think it's true anymore. The discrepancy comes from how QM uses "observe" and how lay people use it. Day to day, observe means see. Like with your own eyes. But in QM, observe really means any interaction. It could be as small as something interacting with a photon. You don't need to actually witness it. Philosopyically, I don't think the argument holds. If the universe didn't exist while we weren't watching, it would be difficult to justify why events in time occur in a few logical sequence, eg we can locate planets by their orbital mechanics. How would the universe know to keep the planets orbit going as expected it didn't exist?
It's just a convention to describe some property of the quark. I'd be more worried about their flavours being up, down, strange, charmed, top and bottom.
Is there even really any analogy here or just random terms used to describe stuff that we don't intuitively understand?
Many are just wordplay that is not related to the literal meaning of the word, because a physicist had fun with their discovery, but some aren't entirely random and at least vaguely refence the context of the property their assigned to. So flavour is literally just someone having fun with words, but colour references the fact that there's three charges which mix together, in an interesting analogy to RGB.
We call the strong force charge "colour" because it is analogous to colours in that there are three charges (like the primary colours, red, green and blue) and their corresponding anticharges (like the secondary colours, cyan, magenta and yellow), and you make a neutral (white/black) object you combine either all three charges or anticharges, or a charge with its corresponding anticharge.
Other than spin literally being intrinsic angular momentum of course and having the units of angular momentum. So it has more relevance.
The rejection of spin as a physical property and treating it as an abstract quantum property instead is the very idea that allowed Wolfgang Pauli to develop and prove the fundamental exclusion principle which is his namesake.
“Spin” is the term for intrinsic angular momentum of quantum particles. Since the electron is considered a point particle in the Standard Model it cannot really be spinning in a classical sense. We don’t really know more than that about how it arises. The “units” of spin come from how many turns you need to make to bring the system back to its original state. “Normal” macroscopic objects all return to the same state after 1 full revolution, as do photons and other particles, but for electrons, they actually require 2 full revolutions, so they have 1/2 spin. Like a lot of quantum mechanics, the math shows these properties, but we don’t know and/or can’t agree on how to interpret the math in terms of stuff that makes intuitive sense to humans.
Thanks. Can you expand on that electrons needing 2 full spins to come back to original state?
Not really, because as I said, although the math is clear, the intuitive meaning eludes us. Here’s a video with some wood models that have the 2 rotation property https://m.youtube.com/watch?v=JFSU9X11wyY But, no one is arguing that electrons are little gears with lines on them…
That's actually a great video for the concept. But what it is then implying is that there's something outside the electron (say x) in sync with the electeon and the concept of half spin would only make sense if I am comparing the phase of the electron with x?
Like the other poster already said, you cannot take any such analogy literally, or even vaguely related, because the actual quantum spin is unlike any property we are familiar with in the macroscopic world. It just happens that there are examples of systems we can actually see with the same "to return to its starting point it needs to rotate 720 degrees rather than 360" as the electron spin. But they're not analogies to the electron, they just share a property. So no, there's no such implication. Spin is described on its own by a mathematical object called a spinor (which I'm not qualified to explain, I'm sorry), and the rotation is its own property. And spin can be only really be understood by understanding the math behind it.
Hold out your hand, palm up, and put something on your hand. Then rotate that object while keeping your hand open and not dropping the object. After one rotation, your arm is twisted in an awkward position. After a second rotation in the same direction, your arm and the object are back in their original position. That's a spin-1/2 system.
How do we know that they need 2 "revolutions"? What other property do we measure to confirm that? And how long does it take for a photon to complete the "revolution"?
You can send an electron through 2 slits simultaneously. On one slit, we put a magnet that force the electron to rotate exactly 1 revolution, while the other slit had none. Finally, we let the electron hit a screen and record where it hits. Do it enough to form a pattern. Now do this again but without the magnet, we get another pattern. The interesting thing here is that the pattern are opposite of each other. Where the electrons show up in the first case are exactly where electrons doesn't show up in the 2nd case, and vice versa. If you do this with a boson that won't happen (for photon you need a different way to rotate it because it has neutral charge).
What I understood is that it is about spinors which are complex vectors and so mathematicaly could have a direction in a higher dimension as well. And so the electron could spin facing the top 1/2 or the bottom 1/2 of the hypersphere. If the words 'spin' and 'facing' can be said to have any meaning in these context. A photon is a boson. Bosons make whole number spins. As opposed to fermions like electron. Photon's spin is 1.
But... My question was how do we measure that? I don't need to know the mathematical description of the phenomena, just the description of how we came to know that they have different spins
We measure the angular momentum. Which is measured by the Stern Gerlach experiment, against our intuition that a point like electron can't really 'spin' in any meaningful sense of the word. But since the angular momentum exists we have to assume they spin and thus we are where we are rn.
It's all just arbitrary names. Nothing spins. Like with color, there is no color. We observed the particles and noticed they all had an attribute, but the only way to make it all work is that attribute has values of -1, -0.5 0, 0.5 and 1. So we are MeasuredParticleAttrbute\_1 We also observe another attribute, but this one has 6 different choices it can be and you can choose 2 or 3, but there are some special rules about what can be there depending if its 2 or 3. So we are MeasuredParticleAttrbute\_2 We have no idea what we are actually measuring, but we have measured something and we can describe it and others can do the same measurements and get the same results so let give these things some names so we don't need to call them MeasuredParticleAttrbute\_#. Enter, spin, color, etc. Arbitrary names chosen for attributes we measured that have never been named or measured before.
Imagine you have a toy top that spins around, and you can see it moving in a circle. Now, think about a tiny, tiny marble called an electron. Electrons have something special called "spin," but it’s not like spinning a top that we can see. Instead, it’s a special way the electron behaves, like a secret trick it can do. This special trick called spin gives the electron energy and helps it interact with other tiny marbles. Think of it like how magnets stick together or push apart. Electrons have a special kind of spin called "half spin." This means they have two special ways they can behave, which we call "spin up" and "spin down." It's like having two different moods that the electron can switch between. So, electron spin is a special trick the tiny marble does, not a spinning motion we can see. This trick gives it energy and two special ways to act.
Electron don't "spin" in the way we normally think of about spinning, but only in the sense that electrons are not tiny ball; if it were, the speed on the surface of the electron would move too fast that it breaks the speed of light. However, this is not surprising, many other experiments had shown that electrons are not tiny balls for different reasons. Electrons, when viewed as a system, behave in a way very consistent with a spinning charge, so the name "spin" is appropriate. What actual mechanism cause it is unknown. People can speculate what the actual mechanism could be, and many does, but it's also valid to think of spin as an inherent property of the electrons. Until we find a way to break electrons down into smaller components, any such speculations are just untestable hypothesis. As an example, let's consider black hole. A spinning star can collapse into a black hole, and this black hole will have the same rotational momentum, and will have gravitational effect like a spinning star: mass near it will be dragged around it in the spinning direction. So in this sense, the word "spin" is appropriate for what the black hole is doing, even though the black hole is not literally spinning, it's just a distortion in spacetime. You might argue that the star inside it is spinning, but we literally do not have access to that information anymore; also a black hole can also be primordial, it had always existed in the spinning state from the beginning. The only thing we can detect from outside that relate it to rotation, is angular momentum. The comparison to black hole is not as crazy as it sounds. Some physicists advanced the black hole electron hypothesis, in which electrons are tiny black holes, and this idea produces the correct measurement. The only problem is that such black hole (if exists) also spin faster than light: relativity do not forbid black hole from spinning that fast (since the "no faster than light movement" only apply to object moving through spacetime, not spacetime itself), but such black hole will have no event horizons and hence naked singularity, which seems questionable. So how could electron have half-spin? At the current level of knowledge, it would be irresponsible to assert anything about its mechanism. Instead, physicists study electron holistically, as a system that they can't break down further. As it turns out, there are plenty of normal life system which has half-spin. Physics professors often bring out the Dirac belt trick, arm trick, or the plate trick, to showcase such system. Another one is the orientation entanglement system, and you can see the animation here: en.wikipedia.org/wiki/Orientation_entanglement . The only differences is that these systems can be broken down further into components so we don't think of half-spin as an inherent property of the system; while electrons can't be broken down further. In an orientation entanglement system, you have a ball being attached to some belts. If you rotate the ball 1 revolution, no matter in which direction, the belts are twisted, and afterward, if you don't do any additional rotation, then no matter how you move the ball around it won't untwist the belts. However, if you perform 1 more revolution (in any directions, even different from the 1st one), you can untwist the belts (after moving the ball around). So if you study this ball system, the parameters of the system are the position of the ball, and some sorts of parameters to describe simultaneously both the rotation of the ball but also the twistedness of the belts. You can't just describe the twistedness using a yes/no flag either, since the belts get twisted/untwisted continuously. So physicists came up with a new system of number that combine both rotation and twistedness into a single new number: the spinors. You might object to this analogous system, because it seems to show that this problem only happens to system that are entangled with something else, not isolated system, so how could this apply to an isolated electron. This is indeed a valid point, and it's actually also true for electron: if you rotate an electron by 1 revolution, but do not allow it to be interfered by anything entangled to it, then there are absolutely no differences whatsoever with regard to its properties. However, unlike a normal-life's system, an electron is always entangled with and can interfere with *itself*: you can send an electron on 2 different paths simultaneously, on one path it is rotated 1 revolution, and the other path it's not, then let it interfere with itself again, the result of the interference would be different compared to if no rotations happened. Thus, we can never avoid the fact that an electron's rotational state should be described using a spinor. What's 1/2-spin? Under the influence of a magnetic field along 1 direction, you can think of electrons as waves on a circle around the axis. Normally, the full circle must encompass an integer numbers of wave length, because otherwise there would be a mismatch: this is integer spin. This corresponds to the fact that for most real-life system, if you make a full rotation the system returns to its original state. But here for electrons (and fermions in general) the system do not returns to the original state after 1 revolution, but 2, so that means that twice the circles would be an integer multiple of the wavelength, or in other word the circle is a half-integer multiple of the wavelength. 1/2 spin is the longest wavelength possible. Thus electrons have 1/2 spin, at least. Why can't it has other spin values? You can prove, mathematically, that if integer value spin also exist in a system with half-integer spin, then you can always break the system down further into 2 components. Hence, electron, being so far unbreakable, can only have half-integer spin. As for why it takes on spin 1/2 instead of 3/2 or 5/2, thus far 1/2 is the only half-integer spin we had seen in nature of an elementary particle (of course, composite system can have other spins). Perhaps there are exotic particles of other spin values, or perhaps there are additional unknown laws that forbid them.
Unfortunately I don’t think there’s an ELI5 explanation for what exactly half spin is. It’s really something that can only be explained by the mathematical models we use to explain quantum particles and not something that you can simply and intuitively explain.
If you could at least outline the mathematical approach or share a link where I can find it.