Is Spin Angular Momentum afterall? ('What is Spin?' follow up) 

This is so profound! I never thought of it this way. Best video yet.

When you speak it always seems like you are just about to break out into laughter......it is actually a lovely quality of your voice.

"Realising you’re completely wrong is actually really exciting" I wish more people could have this view, especially in science.

It is not that the particles in bar magnet don't have angular momentum. It is just that there are lots of particles with angular momentum inside the bar magnet, and all these angular momentums are in different directions and hence tend to cancel each other out.

I cant believe these explanations have been here for over 7 years. Thanks. And you explain better than most creators 7 years later

This was amazing. I had never heard anyone explain why people talk about spin and angular momentum in the same breath, but then turn around and say they aren't the same thing.

These video's are just the best.

First of all, awesome to see another video, and really cool of you to own up to being wrong. It's a natural part of life, especially when you're dealing with such a complex topic, and using it as an opportunity to educate others is awesome. Now onto the homework... 1) So my general view on quantum phenomena is that they should be viewed by their own properties rather than projecting more familiar, semi-analagous behaviors onto them. I think that's a lot of what makes quantum mechanics confusing to a lot of people: You set up expectations by analogy, but those expectations aren't met because the two things aren't actually the same. It's like the argument recently put forth by Ed Frenkel on Numberphile that, while we say that an electron is both a wave and a particle, it's really neither. It's an entirely different object that shares some properties with both those things. More generally, things at the quantum level just don't behave classically, and while it's obviously not a good idea to just throw out everything and start over, holding onto too much classical baggage when we look at quantum systems seems to me to cause more confusion than it alleviates. So on this specifically, I don't think you can call spin angular momentum, but it seems like you can call spin and angular momentum versions of the same underlying phenomenon. Which I suppose we could then decide to just call angular momentum, but then that's confusing. Either the overarching concept or the classical expression of it probably needs a new name, although I'll leave it to people who understand it better than I to decide what. Perhaps let the underlying concept be Angular Momentum and call the classical-only version where an object is actually spinning "Rotational Momentum"? A little research shows that that's already an occasional name for it. 2) My immediate reaction is möbius strips. That would imply, if we follow the analogy (Which can be dangerous...) that as the spin processes, it's also slowly rotating on some axis. I have no idea what axis that would be, though. 3) Well, I'm pretty sure I don't fully understand the procession process, but it appears that the torque would always be parallel to the machine, so that the procession wouldn't impact the angle of the magnetic field relative to the field of the device. As for why that would give you a proportional response, I would assume it has something to do with being non-quantized. if the magnetic field of the passing object is fully horizontal, then the forces it experiences from both sides would be balanced, with equal repulsion and attraction. If it's fully vertical, it'll be either completely attracted or repelled by both sides, so its movement will be dominated by the stronger South magnet, moving whichever way that one wants. Because in classical mechanics we don't usually see these binary on/off switches, there has to be a gradient in between while the magnetic field rotates from one point to the other. If the question, though, is WHY we don't see those binary switches... I'm afraid that's not something I understand nearly well enough to answer. That does bring up an interesting question for me, though: If the South magnet is dominant no matter what, either attracting or repelling, what purpose does the North magnet serve? Couldn't you get the same result by just throwing things past the South face of a normal magnet? Acknowledging, of course, that you could easily have flipped the two and made the North magnet stronger. My point is, why do you need it to go between both poles?

I just discovered your channel today and HOLY MOLY WHERE HAVE YOU BEEN ALL MY LIFE. I love how you interact with your viewers, all your explanations, and am currently binge watching all your videos ! Can't wait to see more of your amazing work !

Thanks for clarifying a concept that baffles me for years. You did such a AWESOME job in explaining difficult things in simple words and relate-able examples. This is now officially my favourite channel for physics. =)

On why this kind of intellectual honesty is the bedrock of good science. You may have been wrong, but , m'lady, thou art a true scientist indeed.

@ 5:28 Are you using 'left hand rule' to get the sign of the torque? :O Conceptually it doesn't matter, but would you mind clarifying?

This is probably the clearest explanation of angular momentum I've seen. Your videos are awesome.

A positron asks an electron: "give me a 360º just so I can check if you look fine in that spin?" the electron complies and the positron replies "who are you?". The electron gives another spin and the positron relived: "There are you, there was a strange guy moments ago right where you are!" lol! QED pikaboo.

I'm convinced! I think whether or not classical analogies are silly depends heavily on the listener. An analogy only works if the listener already has an 'intuitive feel' for the analogue. I myself didn't really understand RCL circuits, until I was shown how they are similar to mass-spring-damper systems. (Inductor ~ Mass, Capacitor ~ Spring, Resistor ~ Damper) But the important part is that I already had a feel for masses, dampers, and springs, and that analogy wouldn't have worked otherwise. So saying "Intrinsic Angular Momentum" would really only be useful if the listener already has a feel for classical angular momentum. So if you wanted to explain spin to a physics student, this analogy might work. Explaining it this way to a lay-person probably wouldn't. It's all about the audience, and if the audience already has the intuition, saying "Intrinsic Angular Momentum" shouldn't hurt. After all, if the math is similar anyway, why not?

I just stumbled upon your channel and I love it!! I'm solving sakurai cover to cover and after watching a few videos you made me think of little details I didn't really think about before. Thank you so much for that!! PS. Your drawings are adorable.

I just would like to thank you sooooo much for these videos. You're helping me a lot with the classes. And honestly, your videos are for sure one of the best teaching materials I've ever seen on RU-vid.

Amazing video, I don't know why they didn't explain stuff like this in my QM courses, especially since we spent so much time on the Stern-Gerlach experiment. These are some pretty solid arguments. Another good argument which you skipped, is that spin is measured in the same units as angular momentum, which of course implies that they are similar.

2:03 "Realising you're completely wrong is actually really exciting" Few things makes me genuinely happy as seeing other people realise and/or admitting this. In a world where a majority hold on to a certain view in absurdum, the ability to change position and seeing that as a something good, is the very engine of our collective understanding of nature. Plus I usually go very well together with people having this ability.

I finally understand why the spin of electron is said to be 1/2.

If we accept the definition of angular momentum as the generator of rotation, then spin is definitely an angular momentum due to the commutation relation implies that spin's unitary operator is the unitary operator for rotation. Thus, spin shares the same mathematical structure as angular momentum. Furthermore, the angular momentum that is conserved is the total angular momentum J and NOT the orbital angular momentum L. Meaning, that spin is also angular momentum.

In general, the information obtainable from the videos on this channel is priceless and the humor in the videos is great. Neither of the two should be taken lightly. With that said, if there exists anyone on youtube with a more pleasant voice, may the noble viewers bless me with a link (seriously). Oh and umm... 1) Yes, I find everything you say convincing. Not to mention, I've always had the radical belief all particles are composed of light trapped tightly in a rotating pattern. I've been able to use it to understand General Relativity in the past. I've now found yet another thing (namely spin) that works naturally with this view. A friend informed me that this view is used in some well-known theory. Too bad I'm a mathematician and not a physicist and thus I don't know the theory. 2) Whaaat?! That's weird. I can't explain it but it does beg the question: Does this occur regardless of which direction you rotate the electron? (What I mean here is, if you could grab an electron, you could twist leftward and watch it rotate or you could twist downward or a combination of left & down etc.) 3) I got a C in Classical Mechanics. General Relativity and QM (and higher math) the fun stuff. 4) You sure you're not just milking youtubers to do your homework for you :) ? (No one would mind anyways)

The argument was very good, and it definitely convinced me, but I think you should explain more about how angular momentum and torque work. And I'm really excited to learn about that commutation relationship...

This was fabulous to watch and realise. When you talked about angular momentum my brain started to roll on itself thinking: "Torque...and the spinning wheel effect!" Haha. This crazy aspect of CM has been covered well by other Day-to-day Physics channel (Ve and SE in particular) but I still suck at remembering the technical terms. Once again, I like it how you bring all these different aspects of Physics under a single video! You really surpass yourself and impress all of us with your dedication to the subject at hand. This is ultimate professionalism in motion.

Excellent. I was missing this part. I've read many times that spin is angular momentum but I never knew why.

The surface of a cylinder is a 2 dimensional sheet wrapped around a non-observable external axis. The surface of a toroid is a cylinder wrapped around a non-observable external axis. So, a toroid is a 2 dimensional sheet wrapped around two other axes that happen to be orthogonal. So to me, spin simply tells us the orientation of those two axes. The reason that electrons then cause a charge when they move is due to the gradient of their spin caused motion (one axis). The reason magnets have charge is due to the gradient of their spin caused by alignment (the other axis). Electricity and magnetism are the two axes around which space-time are wrapped to form the toroid.

I'm new to the channel and I just started college so I'm not as informed as you guys, nevertheless I love the video and the comment section, like writting before talking or simply saying I think. Hopefully I'll ve able to join you guys after a few semesters but until then I'll keep watching!!! thanks guys all of you

very nice videos, very good explanations, you explain the complicated terms by very simple words. I enjoy your explanations, I have sett all and I will see them again. I will recommend my students to see them also.

Thanks so much for the videos! The resulting force vector in a spinning object is not so counter intuitive if we think in a spinning top. The reason it wont fall when spinning is precisely the direction and magnitude of that vector which pushes it upwards, when the spinning top loses energy it starts the precession around the center of gravity, which is analogous to the larmor precession in magnetic objects

Ooh...I really wish I had time to write more, but for now I'll just address the 2nd question. The 720 degree rotation requirement comes from recognizing the object's connection to its environment. For example, grab a coffee mug and pour some water in it to incentivize not tipping it over. Hold your hand out, palm up, with the coffee mug resting on your hand. Now rotate the mug 360 degrees. The mug by itself looks like it's back to the original position, but your arm is now awkwardly bent with your elbow pointed toward the ceiling. Keep rotating another 360 degrees (in the same direction) and you'll find the true original state returned. Try it!

I found this video's argument quite convincing, and I'm amazed by the "rotating 2X to get back to original" part! I wish to see more proofs or examples of this if it's possible! Thank you! (I'm thinking if this is really what I think it is, spin might introduce us to the additional "hidden dimension(s)" in our universe!

This girl is ground-breaking in her approach to physics education (especially her homeworks!)

I appreciate the questions with the info? Thanks for including us in the dialogue?

I really loved this video. Thank you very much. But as Eugene pointed out, a bar magnet also has a component spinning around it.

I really love your videos and this one is no exception! (even though I didn't do any of the homework from the last one...) You want more inclusive homework? Tell people to watch more of your videos. :P Seriously, watching your videos is already an incredible way for non-specialists to get acquainted with all the details you're talking about. I'm not sure you can make everything into a "try and use some counter-intuitive common sense here" like you did for the entangled spies and their messages, sometimes the topic is indeed a bit more abstract. That being said, I found today's video pretty accessible, the classical analogies work really well (at least for what you touched upon here). I'm thoroughly convinced with the Stern-Gerlach experiment that spin is a kind of angular momentum. Definitely a weird kind, since you need two complete precessions to return to an original state, but still. :) (and btw, I can't easily think of a classical example for that double-spinning property)

360º rotation not being a symmetry seems super weird to me. A circle ○ has infinite rotational symmetries A square □ has 4 rotational symmetries A triangle △ has 3 A line | has 2 An arrow ↑ has 1 Idk how to get 0.5 symmetries (720º rotational symmetry)

HUGE thumbs up for this...I wish more youtube videos about the Stern Gerlach experiment made that distinction about bar magnets. A few of the videos ive seen on here dont do that and it can be kind of misleading. Good job on this one tho.

Do you know about Einstein de Haas effect. Its basically shows experimentally that if you change the magnetic moment of an object it starts rotating and vice versa.

Thanks so much for making this video! I don't fully understand the maths behind the the equation you mentioned:(S,S)=i*h bar* S. If you ever have the chance I would love to learn a little more about the maths behind spin! Thanks again, this video was super helpful!

So I was curious and searched it online, I found this: "In quantum mechanics, we describe the states of objects as elements of a Hilbert space HH. The crucial thing is that not all elements of this space represent physically different states - if we have two elements ϕϕ and ψψ and they are related in such a way that one can be obtained from the other by multiplying it with any complex number cc, i.e. ϕ=cψϕ=cψ, then they are the same state. This is analogous to two arrows with different length pointing in the same direction describing the same direction. Only the direction of the Hilbert space element has immediate physical meaning, not the length (though it is not completely irrelevant, "phases" play a role, but this is not relevant here). Now, it turns out that there are two different ways how such elements of a Hilbert space can behave under a full rotation by 2π2π - they either stay the same, ψ↦2πψψ↦2πψ, or they change their sign, ψ↦2π−ψψ↦2π−ψ. But −1−1 is just a complex number, so ψψ and −ψ−ψ are the same state, and a rotation by 2π2π does not change any state at all. Objects whose states stay the same are called bosons and have "integer spin", objects whose states change sign are called fermions and have "half-integer spin". The Bloch sphere you refer to is not the Hilbert space of a system, but the projective Hilbert space. The projective Hilbert space is obtained by just identifying all vectors in the Hilbert space that lie on the same ray ( = have the same direction = are complex multiples of each other). Thus, ψψ and −ψ−ψ are the same point in a projective space, hence in particular on the Bloch sphere, and a 2π2π rotation does nothing on a projective space either way - as it should, since each point of the projective space is a physically distinct state." Credit link: physics.stackexchange.com/questions/167469/how-do-you-rotate-spin-of-an-electron

amazing, i recommand leonard susskind and his brilliant explanation of spin, thanks a lot

Great video! But why is the electron drawn as having planetary rotation and not intrinsic rotation? Is this the orbit around the nucleus of the silver atoms in the Stern Gerlach experiment?

As a layperson to quantum mechanics who does not follow the math, spin is one of the crazier concept. Thanks for the video. I have read many opinions on spin and I greatly appreciate your intellectual honesty by putting big questions on what it really is. I'm curious though from a practical sense. Is the spin or "intrinsic angular momentum" the main attribute that allows MRI? When ever I read about how an MRI works they are speaking of the spin of a hydrogen atom or proton like it is in the classical sense. Does the magnet of an MRI try to realign the hydrogen in this Lamar frequency you spoke of? I don't understand then how hitting the hydrogen with RF puts energy into the hydrogen causing change in spin which it spits right back as a radio frequency the scanner picks up. If MRI works on the same principles you state, it would be interesting to tie it together. Not to mention is the hydrogen in a super position state in any part of that MRI process? If so when? I'm a huge fan of the video's. Please help make some sense with how reality works!!!! PS. Us old codgers remember holding a bicycle wheel at its axle while spinning and trying to move one hand up and one down to feel the force of angular momentum. That experience helped me with your segment explaining the classical vectors.

I'm not sure if it is measurable, or if some quantum weirdness will get in the way, but as far as I can tell, the most important thing about angular momentum is that it is conserved. It doesn't like to move. If you could create a spinning particle and see the angular momentum of the rest of the system decrease, it would mean that spin IS angular momentum. But is this possible?

How Precise does the tip have to be to work? is there a particular angle only that will make the machine work?

Thank you! But what is the great reason to define angular momentum you mentioned at 1:42 please?

I wonder, how spin detection experiment will go if we will start to shrink the linear size of the apparatus? What if we will reduce its length all the way to the size of a single atom (shielding magnetic fields before and after)? Will the result be exactly the same?

So. why does it suppose to turn around twice, and what are the classical things behave like this?

I have 2 problems, but before that I would like to appreciate the videos. These are awesome. I like specially (like in this one) when you admit to a mistake, this not only teaches that it is wrong, but why and how. 1. You said it takes 2 rotation to get back to its original state? Why? 2. I have always heard that classic mechanics and quantum physics cannot stick together, so why is it that we use something like precision (that seems like gyroscopic precision) to define the movement of electrons?

As I said in the other of yours videos on Spin - I like your way of thinking. I personally am trying to build an understanding of quantum ... stuff, and most publicized information is focused on naming things rather than explaining them. So if you follow them you end up with lots of information to memorize and still about 0% understanding ... and I hate having no understanding even more than memorizing useless stuff :) (it's useless for me if I don't understand it). I might have overused the word 'understand' already, but just wanted to say that analysis of experiments and observations, and the repeated process of making conclusions, testing them, correcting them (as they're usually wrong) etc... eventually getting closer to the truth is what gives me some bits of understanding (some might even go as far as to call it science ;) ) if not of the actual subject matter at least at the current stage of science. I just recently discovered your channel, but I feel I'll be spending quite some time around here :)

Dear Ms Through the looking glass, please read Finnegans Wake by James Joyce - I'm convinced he's one of the few people who understood superposition. Your views on it would be hugely appreciated. At the moment , I am trying to decide if reading the wake is the 'collapse of the wave function' or if assimilation of meaning nanoseconds after reading it is the 'collapse of the wave function'.

It's like my brain can finally understand it somewhat. These videos thank you.

A little late to the party. But I had a question. I'm not a student of Quantum Mechanics (just interested) so this might be a totally insane question: If we use a Stern Gerlach apparatus and pass a Boson with zero spin (g/Y/Z or H) we know for sure that it will go straight so can we say its wave-function for position base will be an eigenstate of position, say, |ψ> = |a> (where position "a" is in the middle of top and bottom) so, we don't need to define it as a superposition of top and bottom. But we know this before we even measured it. Does it mean we will never be able to determine the momentum of such Boson since we have sort of determined its position? I don't know if it makes sense and I'm pretty sure I don't understand the first thing about it that's why this question came to my mind out of ignorance.

so I kind of get the torque argument, but wouldn't the angle get effected over time anyway? the magnet is much larger than the electron, I'm assuming, so if the magnetic force is acting on a "spinning" particle for a relatively long time, isn't it? sooner or letter it should have an alignment effect on the spin axis? yes, the angular momentum will resist change and will wobble around like crazy, as explained in the video, but it should stabilize over time in a way a gyroscope would? which is why the particle actually ends up flying out of the apparatus unlike a regular magnet that would just stick to its top (or bottom) midway.

So if you threw a small bar magnet into a the Stern-Gerlach experiment while giving it mad angular momentum, would it work?

Hi Looking Glass. I'm not sure if you still read the comments of these old videos, but I'm confused how Larmor precession has anything to do with spin. You said in the original spin video, that spin is an observable with only two states, up or down. If the electron is already spinning either up or down, then it wouldn't experience any precession, right? So how can Larmor precession prove that electrons have intrinsic angular momentum? In fact, electrons behave more like bar magnets that go either to the top or the bottom rather than spinning charges that might have a smoother distribution.

I'm very far from being a math or physics expert but your second question on rotating the electron twice to get it back to original state. It reminds of the time when we were taught what pi(3.14) was. pi=180 degrees 2pi=360=0 degrees AKA the starting point

Will you start making videos on classical mechanics? Please, if possible then make it. Thanking you.

I am currently working on my own independent model of particle spin which has concluded that an asymmetry in the Big Bang sent all condensing fundamental particles (which I call monopoles) into a 3 dimensional spin (or spin on all 3 axis). The geometry proves that this 3D spin would experience a phenomenon called "gimbolock" which would have had the effect of cancelling out 1/2 of 1 of the axis of spin creating the situation where upon each 360 degree rotation the particle would be upside down, therefore taking 2 complete cycles to return back to its original inertial reference frame.

I wonder what the effect is on neutrinos. They have no charge, and thus no magnetic field generated by moving charges, so spin has to be more than just magnetism. (Apparently neutrinos do have a magnetic moment, created by splitting into a W boson and an electron, but that is a property of the electron and W boson, not the neutrino. Right???)

Please don't feel bad about not producing videos fast enough by your standards. We love you anyway :)

Sounds like you are talking about giro's to me. Isn't the 2 x cycle before returning the wobble effect? Hey, could this be the cause of the wave effect particles have? Or maybe its charge, as in 1st time it is in "up" and second it is in "down" position.? Huh! Just my crazy thinking.. I just cannot help it...

At somewhere around 7:33 you stat talking about. You would think it going around once would be in the position it was in but you said it would have to go around twice to be in the original position it was in. Can you help me understand

This video really helped with the concept of intrinsic angular momentum. Is there a next video that follows up on this?

If the spin has a non-vertical direction, then why don't we observe electrons only going halfway up or down? Why do they all go all the way?

Question: The way that a particle being affected by the EM force to cause it to not only maintain a position, but an orientation; this sounds remarkably akin to the effects of superconductors (I think that's the one) will do the same thing, maintaining an affected object's position AND orientation?

What happens when the Stern Gerlach experiment includes multiple magnets, like an octagon arrangement/configuration of N/S poles?

Doesn't spin be a caracteristic related to the topology of our space (space-time ?) which informs about the "relation" between the particle and the observer, rather than a caracteristic of the proper particle itself?

I have a request, although it might be a bit out of line for me to a make this request. If that is the case, please ignore the request. Could you please make a video on the various reasons why Spin cannot be like a particle actually spinning along an axis? Is it just that it takes 2 rotations instead of one to get to it's original position? Or are there other reasons why the analogy doesn't work? I'd really like to know.

so to answer your question 2, in case there is a feature that does a counter spin, then its understandable that it would take two rotations to get back to initial state.

I don't understand. Why does it take rotating twice to return the particle to its original state? And if the state oscillates like that, then how come it either goes up OR down in the magnetic tunnel thingie? Shouldn't it just hover in the middle?

For the two rotations thing, try the following thing: Hold a belt by its ends. Make sure it's untwisted. Now, without changing the orientation of your hands, try to get the belt twisted (you will have to pass the belt through your arm). The twists go in two full rotations per maneuver.

Mithuna, please look into this once again, I have a hunch this is wrong. The gyroscopic precession is true only when the angular momentum of the spinning object and torque experienced are comparable, which is not true in SG experiment as the torque is super high when compared to the electron's spin. Just imagine a thing orbiting @0.0001deg/s. Can this not be flipped even at high torque's?? Something else is happening. Some kind of oscillation. I don't know, this is guess work.

Your description of 2x rotation applies to particles with spin 1/2. A particle with spin 1 only needs to rotate once. I'm not doing the math for the rest of the possible spins...

at 5:30 shouldn't your torque point into the page from the right hand rule? I think your L vector should have been precessing the opposite direction this whole video.

I think particles like photons are in orbit likely with dark matter particles giving them an apparent axial wave or circular helical wave as they travel, depending on the orientation of the orbit. I think light travels thru the 2 polarized filters when a 3rd is introduced at 45 degrees because some particle orbits are deflected into that orientation or circular and pass thru. Perhaps the angular momentum despite a particle not spinning on its own axis due to the spin outside of the center of mass, perhaps due to either a dark matter particle, or a particle's own induced force.

Bohr, Pauli, Hisenberg, Born, Dirac and Jordan used classical mechanics to "kick-start" quantum mechanics in about 1922. Spin was not considered in the early development of QM as I understand it. I've left Einstein, Planck, de Broglie and Schrodinger out. Schrodinger came up with wave mechanics in 1926 but did not include any "spin". To infer that the electron has angular momentum is to say that the electron is a particle rather than a wave surrounding the nucleus. But also my understanding is that electron also has intrinsic "spin" that is the electron itself exhibits "spin" characteristics. The problem that the physicists had was how did a ball of charge hold together while spinning at a relativistic rotational speed? Also how could it be a point particle, because if it were then it would have an infinite energy? de Broglie thought that the electron was a wave and a particle at the same time, and the electron "surfed" more or less on the wave. This gave rise to the "pilot" wave theory, which I think has been proved wrong. No wonder some of the brightest minds in the world had trouble getting their heads around QM.

I'm trying to understand the difference between bosons and fermions, and basically what I'm getting is that bosons have integer spin and fermions have fractional spin. But I don't see why that makes a difference: if spin is kinda angular momentum ish, then isn't a different magnitude just stronger or weaker? Why does a particle with spin -1 behave so differently from a particle with spin -3/2 that we put them in different categories and apply different maths to them? I don't know if that made sense, but any help would be appreciated

I don't know about #1 or #3, but #2 reminds me of what happens when you follow the face of a mobius band. You have to go around the center of the band twice before you reach your starting point. I really don't know if this has anything to do with precessing particles though. Hm.

So, with regard to spin in QM, we are really just redefining angular momentum in a broader more abstract sense?

why is the south pull stronger? I thought that it would be the other way. Because there is more material in the north pole at the same distance.

Hi. I don't know most things about physics but I'm eager to learn. About angular momentum, if a particle was spinning, its outside, really all the points inside apart from the centre would be revolving around the centre point inside the particle. I'm not sure if this is correct, but wouldn't this mean all the points of the particle, I guess apart from the centre point, have angular momentum? Thus would the particle have angular momentum? Again, I'm really not sure - I'm quite a dunce when it comes to physics, but if someone could tell me, I'd me much obliged. Thanks!

Spin angular momentum is important because total angular momentum is conserved. If you flip the spin of an electron, you have to transfer that angular momentum somehow (such as via a spin 1 photon).

I know this is an old video, but I looked at question 2 and immediately thought "Möbius loop". Hopefully self-explanatory?

how about the argument that spin and angular momentum are interconvertible? if a spinning electron hits in atom, the electron may reverse its spin, and the atom picks up a unit of angular momentum.

Hmm, isn't our hand everybody's favourite example of an object that you have to rotate twice before it resumes its original configuration? I think there is a video on youtube of a coke can tied to two posts by elastic bands which also has that property. As for angular momentum - if it obeys the mathematical relations of angular momentum are we not to call it such by virtue of the correspondence principle? Also is it not possible to separate the total angular momentum to spin (intrinsic) and orbital (tangential) angular momentum, even for classical systems? But then, the obvious retort would be, if any set of operators has the structure of SU(2) is it fair to call it angular momentum? I'm not sure if that is a sensible objection though, I feel that it must have been answered.

is the lamour precession kind of a gyroscopic effect ??

Mind blowing... Does the electron have to complete 2 full processions have to do with the spins being spin 1/2? What's a half spin anyways? :-/

angular momentum may be a good way to explain to people who have studied classical physics, because it behaves similarly. But i think it conflates classical and quantum ideas. The difference in the results between wire loops and quantum particles are just too different to assume the mechanism is the same. What evidence do we have one way or another? How can a quantum object have a moment of inertia? and if it can, wouldnt it be probabalistic in nature due to uncertainty in the distribution of 'mass'?

hi, i would love if you can enlight me. Here is my question: currents in wire generate a magnetic field. This magnetic field is known to be there because of its effect on a moving charge. However it is possible to explain 100% exactly the effect on a moving charge just by electrostatic charges moving + relativistic effects (dimension contraction). Do you know that? If yes we can go on. I then thought that this means the ‘magnetic force’ is a pure fictionnal force resulting from electrostatic + relativity, as ‘coriolis force’ or ‘centrifugal force’ are fictionnal forces resulting from gravity + movement. However, how does that fit with the quantum mechanics spin? Is magnetism also a pure fictionnal force at quantum level, or does it have a more sssential existence? Well, that was my question, thank in advance for any insight.

Spin has the same units as angular momentum. Photons have linear momentum, despite zero mass, since they move at the maximum speed allowed by the system. Something with zero moment of inertia (like a point particle) can have non-zero angular momentum if it rotates at the maximum angular velocity allowed by the system.

do you ever plan to do a followup video on this??

Is the half spin due to quantization or "intrinsic angular momentum"?

I find your videos so incredibly helpful, however, at the level I'm currently studying I admittedly find some of these concepts hard to understand from only basic knowledge, but if exams go to plan then I should be set to study physics for the rest of my life. In the meantime are there any books I can easily get my hands on that may help with my predicament?

So, is the angular momentum in normal particles like a gyroscope?

Spin is not intrinsic angular momentum, it's a feature of the geometry of physical space. From Noether's Theorem, we know that rotational symmetry (of matter) corresponds to conservation of angular momentum. The symmetry corresponding to spin appears to be conformal -- e.g. rotational with dilational invariance. Consider when matter collapses into a black hole. We know spin is conserved, but where is it? Mathematically, spin is represented by a 2-dimensional complex surface embedded in some Hilbert space. This is where conformal symmetry meets holography. Holography is one resolution to the Black Hole Information Paradox, which states that the entropy of a black hole is proportional to its surface area and not its volume. One can construct a flavor of AdS/CFT correspondence without string theory via the ansatz that spin is the orientation of observables in a non-commutative geometry. That is to say, there exists a representation of every linear hermitian operator that carries intrinsic spin.

4:56 That's like a tiny gyroscope, right? Or am I missing something? Edit: Wikipedia says it is similar to a gyroscope. So there's an analogy here with stationary top-heavy objects and gyroscopes.

Spin is the result of an SO(3,1) symmetry of spatial rotations and rotations of the worldline in the Minkowski space of special relativity (i.e. Lorentz invariance). The group SU(2) is a double cover of SO(3,1), and so the algebra of angular momentum and spin is the (Lie) algebra of SU(2), and there are two intrinsic quantities (up and down) that spin can take on... at least for fermions which are a certain representation of the group. Sometimes you just need relativity in your quantum physics.

So would this mean that electrons DO have spin?

angular momentum=spin + orbital angular momentum (tau=S+L)....whats with the spin without the spin?