Is Spin Angular Momentum afterall? ('What is Spin?' follow up)
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- Опубликовано: 6 сен 2015
- On why I was very wrong. In my previous video, I said that spin isn't very linked to angular momentum at all- but in fact, there's a key property of angular momentum that spin has, suggesting they are linked after all.
Previous video (What is Spin?): • What is Spin? | Quantu...
Book recommendation: Modern Quantum Mechanics by Sakurai. This is a classic textbook that I hadn’t read until recently, but I’m now such a fan. However, I think that you will benefit most from this book if you already know the basics of QM and what a deeper look. That said, the only prerequisite is linear algebra.
Homework:
I’m interested, did you guys find this video’s argument convincing? Should we call spin intrinsic angular momentum? Is it weird to even try and explain spin with classical ideas and using classical analogies? Is intrinsic angular momentum inherently meaningless phrase anyway? Every time I ask these sorts of questions I get a really diverse set of opinions all well argued so this should be fun.
Second, I mentioned that you can only get an electron back to its original state by rotating it twice. Last time, some people commented that this isn’t so weird- some classical things do this. What do you think of this? Do you know an example?
Finally for the classical mechanics fans, I explained why a rotating thing in a stern-gerlach machine doesn’t just flip and point up. But now explain why the force that it experiences is proportional to how much it was pointing up to start.
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"Realising you’re completely wrong is actually really exciting" I wish more people could have this view, especially in science.
+1 and in other fields too...
It's an attitude I want to have more often, because it lets you learn a lot more. But of course it's always a blow to the ego (probably not a bad thing either!)
I could be an optimist, but...I'm pretty sure most all scientists DO think that. Even when our hypothesis turned out false,we still have learned a good deal.
This is so profound! I never thought of it this way. Best video yet.
+The Science Asylum Wow, thank you so much, that's really lovely!
@@LookingGlassUniverse wow! U r so humble.
owao
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.
Ah, this is what it is. I was trying to put my finger on it and it's a trait I have heard in another RUclipsr whose name currently escapes my memory.
Clickspring?
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.
Thank you for bringing this up! The bar magnet is magnet because of spin. And actually, their spins are mostly aligned. So I don't understand why the magnet doesn't have an overall angular momentum... Do you know what's going on there?
+Looking Glass Universe In my uneducated opinion (which might be wrong), it's due to the fact that the orientations are sufficiently opposite as to cancel. If you did all the vector additions, you'd come up with a number sufficiently close to zero as to be discarded.
+ordieth117 Would this explain why individual particles can be monopoles? i.e. an electron is negative, while a proton is positive
+Looking Glass Universe Most of the electrons of an object are in pairs of opposite spin, even ferromagnets. Only a few electrons per atom are unpaired and aligned. One possibility is that other paired electrons may have enough total orbital angular momentum to compensate without significantly affecting the net magnetic field.
But even if that isn't the case, electrons carry almost none of the mass - and therefore momentum of any kind - of an atom. So to answer your question: you may be right. A magnet might have some angular momentum because of e- spin.
But if it did it would be analogous to the angular momentum an airplane has because of its engines.
Bar magnet has some finite magnetic field so all the spins don't cancel each other and so the angular momentum should also be finite. Although it is strange for me that a bar magnet having a finite magnetic field will have finite angular momentum, But I don't know whether I am right or wrong. Please explain this, sir.
These video's are just the best.
That means a lot coming from a RUclipsr who is themselves very good at their craft. Thank you :)
aww you don't mean that *blushes* :P But seriously your videos go hand in hand with my Physics education at uni :)
That's so nice to know that they helped you :)!
+Looking Glass Universe torque was the exact thing my physics teacher talked about a week ago.so yeah it is pretty much hand in hand
+Looking Glass Universe Cute voice, and helpful explanation !
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.
I cant believe these explanations have been here for over 7 years. Thanks. And you explain better than most creators 7 years later
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.
+Incongruent I id be embarrassed if i got things wrong and id want to delete that first video if i were her. that's just me!
@@ptyamin6976 but I think her previous video was very important to help us understand this video.
Through your honesty and self-deprecation, you are helping me be able to imagine myself as a scientist more easily. I have this mental image of a scientist as a person who is smarter than me and who makes fewer mistakes than I do. You are helping me understand that just because you don't get it right away, that doesn't mean you're not good enough. It just means you have to keep trying and asking questions (of your fellow scientists and of the universe). These realizations are all things that I knew on an intellectual level, but you are helping me feel them on an emotional level as well.
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 think that in order for a south pole to exist, a north pole must too, to counter it.
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. =)
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 RUclips.
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.
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.
A joke for 2 people.
@@siddharthakumarsingh Sad and true. Now three.
@@Fish-ub3wn
Now still three. Just so you know :) . But I guess that the spin somehow don't show the same face twice.
@@En_theo Policeman stops a car.
"Tell me your name, your passenger's name and show me your loicense."
"My name's Heisenberg and that guy is Schroedinger"
"Do you know at what speed exactly were you driving past the sign with the 60 mark?"
"It is impossible to determine the exact speed at the exact location, sir"
"Place your hands on the wheel and tell me what is in your trunk?"
"His cat, sir, but it may be dead..."
@@Fish-ub3wn
What do we want ?
Physics to explain the world !
When do we want it ?
We cannot tell !
This is probably the clearest explanation of angular momentum I've seen. Your videos are awesome.
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 !
Wow! Thank you so much! I'm glad you like the interactions with viewers because that's certainly my favourite part too. I'll release a new one soonish- you should do the homework for it :)
could we have a hint of what the theme might be? :3
I finally understand why the spin of electron is said to be 1/2.
@ 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?
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)
Excellent. I was missing this part. I've read many times that spin is angular momentum but I never knew why.
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.
amazing, i recommand leonard susskind and his brilliant explanation of spin, thanks a lot
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.
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
I appreciate the questions with the info? Thanks for including us in the dialogue?
This video really helped with the concept of intrinsic angular momentum. Is there a next video that follows up on this?
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.
Isn't the conserved angular momentum in hydrogen L? Which is why l is a good quantum number. I remember distinctly that the L^2 operator separates out when we solve the Schrödinger wave equation for the hydrogen atom, as it should since the potential is spherically symmetric.
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.
Oh my, this is really high praise. Thank you so much :D!! I really appreciate it!
WHoaaa you explain this so well! I can really understand the concepts :)
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
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!
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 just learned something, this channel is awesome
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.
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 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
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?
+Frame of Essence I think this is one of the best comments on here! For one reason or another, I've spent a lot of time in science classes talking about the debate between 20th century physicists about whether physics was just a set of equations to explain the universe, or if it has to be "visualizeable". This debate was at that time centered around an electron's wave function, and the quantum leaps of electrons. I was always slightly confused about this, because I have an "intuitive feel" for the electron cloud. Don't get me wrong, there are plenty of things in quantum that I don't get, but one thing I like about these videos is that they help me get the ideas behind the equations.
+Leslie Colton One of the best comments on here? Thank you! Developing an intuition for complex mathematical systems is a hobby of mine. Whenever I find something interesting, I make it into a youtube video. Quantum still barely makes any sense though. :P
Just checked out your channel! Very impressive, I'm surprised you don't have more subscribers. At least you have one more now!
+Leslie Colton Thanks!
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...
Thanks a lot for letting me know- I didn't spend anywhere near enough time on the classical mech. Like I said, that stuff is hard so I felt like it deserved it's own video if I wanted to explain it fully. So instead I glossed over it :/
I'll do my best with the commutation relation bit!
Great wonderful analysis.
What happens when the Stern Gerlach experiment includes multiple magnets, like an octagon arrangement/configuration of N/S poles?
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 love this example!! Besides the suggestion to use a cup with water in it. I did it with my phone and realised I would have certainly split the water :P
Exactly as you said, it's about the object's relationship to the environment. The environment, in this case you, doesn't also rotate, causing the problem.
Looking Glass Universe Thank you for the awesome video, but could you please explain how the electron would be "connected" to the surroundings as the cup is with the arm?
the water in the cup, (I recomend using something with foam on it like beer in a glass so you can see the rotation of the water) will not have followed your rotation. But is set into motion, rotating slower than the cup, but continous spinning once the cup is stoped.
I imagine it should be possible to construct a mechanical tool, which inner parts will rotate exactly half the speed the outer ones do.
WOW! Thanks a lot Nick Okamoto for suggesting this example! You can simplify this: (1) Attach a charging cable to your phone. (2) With left hand: Hold the cable tightly from 10-20 cm away from phone. (3) With right hand: lower phone UNDER the level of the left hand AND rotate phone 360 deg. Cable should be now curled. (4) With right hand: raise phone OVER the level of the left hand AND rotate SAME direction by 360 deg. Cable is no more curled and you are back to the original state AFTER 720 deg.
Thank you! you are a fckin geniuos. The answer is in the higher dimensions, the true environment of spin, electromagnetism and gravity (and other fields). It became clear now! Thank you again!
Thank you! But what is the great reason to define angular momentum you mentioned at 1:42 please?
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 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.
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)
+srpilha What is your example? I can't picture anything.
+Liam Axon that's what I'm saying, I can't think of a classical example, but she mentioned people have said there are some.
+srpilha yeah i would like to know too! hmm...
+srpilha I can only think in abstract terms like a "semi-spiral". In my mind, I start to draw a circle but at the same time this line is raising in height (z direction?). By the time I complete 2PI I'm at the same XY coordinates as the starting point but at a different height. From there, I keep drawing the circle but now lowering the height (z). This way, when I complete 4PI I'll be exactly at the same place that I was at the beginning. Problem is, I don't know if this count as a classical example since I just made this up xD
Thanks a lot for your extremely kind words! I'm really glad these videos work for you. Yes, it isn't possible to relay some of the more abstract ideas using 'common sense'.
Yeah, the rotating 2x thing is very strange to me! I will talk about some so-called classical examples of this in the video about it :)
superb you have given me a eureka experience
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?
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?
You are brilliant.
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?
Thank you ,you bought me a lot of time
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...
So why do moons/stars spin backwards creating an angular problem?
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.
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 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???)
new video hype
Great video! Also, motivation for finally cracking open the Sakurai book :)
Though this is also hard for me I'm always fascinated by how hard it is to get my head around. Sometimes classical arguments help and sometimes they don't.
One thing I find confusing in the SG device is whether the angular momentum that is needed for it to work comes from the spin (ang. mom.) of electron or from its orbit around the nucleus?
I had Sakurai on my desk for a year... Then the person I borrowed it from asked for it back so I had to read it asap. Otherwise I would have probably never got round to it. I can't recommend it enough though! When you read it, let me know what you think!
Ah, so they seperate out the angular momentum from the orbits and from the spin by using atoms such as silver. The total orbital angular momentum for it is 0, so any other 'angular momentum' is from spin.
Looking Glass Universe Ah thanks so much that's the bit I was missing, and I'll definitely let you know.
Btw, you are a great explainer and I apreciate most of all the enthusiasm you show for these topics :)
Thanks a lot, that's really nice :)
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.
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)
That's a great way to put it to highlight the weirdness! But I guess the particle still does actually have 1 rotational symmetry, (rotate it twice), it's just that if it followed the rules we expect it would have 0.5
+Looking Glass Universe The best visualization I could find of what it means for an object to have 720º rotational symmetry is this upload.wikimedia.org/wikipedia/commons/6/6e/Spin_One-Half_%28Slow%29.gif
(It's a .gif, give it a few seconds to animate)
It's pretty interesting. The square object thing is the same when rotated 360º. But the spaghetti field stuff it's attached to alternates each rotation (requiring 2 rotations 720º to make the system the same again)
Nice one!! That's a good example.
This comment is a bit late, but it comes from the SU(2) group.
Put a twist in it.
It's like my brain can finally understand it somewhat. These videos thank you.
How Precise does the tip have to be to work? is there a particular angle only that will make the machine work?
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
+RuneR96 twice means 720 degrees, tats the reason she called it weird
:D
Oh, ok, I didn't understand it that way. thanks for elaborating :)
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...
Will you start making videos on classical mechanics? Please, if possible then make it. Thanking you.
I wonder if the magnetic moment of the electron could be due to interacting magnetic components of the cloud of virtual photons surrounding the electron (carriers of the electric force) reinforcing and adding up to something measurable. Analogous to how magnetic moments of atoms spontaneously align and reinforce themselves when a magnetic material cools down from the Curie temperature. It's probably more likely that Quantum Electrodynamics already has a way to explain this, I just don't understand it.
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'.
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?
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.
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 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?
+Mayank Sharma 1. probably because of imaginary numbers
2. i think its more like angular momentum is so fundamental of a property that it works in QM. normal probability, however doesnt. you have to use QM waves that describe probability
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 if you threw a small bar magnet into a the Stern-Gerlach experiment while giving it mad angular momentum, would it work?
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.
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.
Technically, you could also pass your arm through your arm to do this, but I think that's harder to do.
Notice: "Something on a Möbius strip by Alex Tritt"?
Alex Tritt6 months ago2. Something on a Möbius strip?
It's in the direction of John Williamson work on the electron, spin, charge, et. al.
The angular could be the momentum of the photon (perhaps in momentum space).
The 720 degree rotation is consistent with Professor Williamson's work,
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.
What if an electron is just vibrating in space in either vertical alignment or in horizontal... May be at some angle too... That'll explain the idea of spin and also how an electron possess energy that it can transfer to other particles by changing its vibration frequency.
spin orbit coupling maybe? the energy levels you find for light atoms actually can be rather very well predicted by the vector model of the atom, so if the orbital angular momentum can add vectorially to spin ...and produce a new value of angular momentum denoted by J .....this must mean that spin IS angular momentum...i mean you can't add apples and oranges and get MORE apples ....
is the lamour precession kind of a gyroscopic effect ??
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
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.
+Erik this may be possible with additional dimenssions like in the Kaluza klein theories ??
Teedjay Gendron That's kind of where I was going with this but I lack the knowledge necessary to follow up on that. =|
Yes, me too! and we're at the edge at where even the scientist are not sure a that point, That's why there is multiple theories.
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).
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.
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.
The difficulty arises from thinking of the electron as a charged point-like "object" moving "in space." There is a better way to intuitively understand what a spin-1/2 particle represents.
Imagine you were hasty in getting dressed one day, and you accidentally twisted your belt one half turn without noticing, like a Mobius band. Now, without releasing the clasp there is no way to remove the twist in the belt - it's now an inherent topological property of the belt. You also know there has to be at least one point along the belt where it has a half-twist of 90°. If you try to flatten out the belt all the way around your waist, there's always a nonzero area it has to perform the twist even if it is "localized" to a small area. Whether it is localized or spread over the whole belt, there's still exactly one point in the middle of the twist perpendicular to the flattened part of the belt.
Now if you try to add another 180° half-twist somewhere else along the belt - still keep it clasped - you will find that doing so actually creates _two_ individual half-twists next to each other with opposing orientation to each other. This "twist/anti-twist" pair doesn't change the overall topology of the belt, which is still overall that of just one half-twist, and they can always be brought back together to "annihilate."
This doesn't help with spin because it's only 1 dimensional, and so of course there is no concept of angular momentum in the belt example. But if you can wrap your head around this simple example, try to think what other combination of twists and topologies are possible in 1D, then challenge yourself to visualize how this would work on a 2D or higher dimensional surface. Once you have the general idea "under your belt" (*womp woomp wooomp*) then move onto to thinking about how the various symmetries of local topological properties would govern the dynamics of wave propagation.
This girl is ground-breaking in her approach to physics education (especially her homeworks!)
Model - Smallest
ruclips.net/video/nnkvoIHztPw/видео.html
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!
Just found you channel and you’d be such a fun classmate to have
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.
oh and if you do happen to read this...do you have any idea what kind of math governs the exchange between the magnetic fields? Differential Calculus?
Im barely getting started with derivatives so its still going to be a while for me but I like to know where Im heading. lol. Thanks and keep up the good work.
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.
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?
The word I missed in the video was: Gyroscope. There is an analogy. And rises more questions about fundamental "truths" (?) about particles. OK, I draw again weird conclusions in my head now. :-) Nice video, let us keep the discussion the same and not writing here nonsense. Besides, I have no time for QM now and I am just a non educated person who happens to think about weird stuff sometimes. Lucky for me I am busy right now with other things. Or was until today, when I sent in my second "paper" to officials. The first one was two weeks ago and had 12 pages and was reasonably received, at least from certain people whose view I consider important.
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.
the revolving charge theory and other confusion prevailed uptill the emergence of the dirac equation for quantum mechanics in 1928. It is a relativistically consistent formulation of quantum mechanics in the sense that time and space enter into the dirac equation symmetrically. The pauli spin matrices which uptill then were just taken as "it works so just use the damn thing" then emerged as subsets of the dirac matrices.
2. Something on a Möbius strip?
Something, something, dark side
Spin of Indivisible Particle : Watch...
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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.
I always thought a particle as present in our space like a node with a wave in other space now when you rotate such a particle for 360 degree the wave in other space gets twisted halfway because it is attached to our space where the particle is materialized it takes two rotations of the particle in our space to rotate the wave in another space by 360 degree. Look at the watch it takes minute hand to move 360 degree 12 times to move hour hand 12 hours (thats 360 degree). If someone who is able to watch only minute had (ie particle ) and not whole clock (wave function) will say that spin of the minute hand is 1/12 . Presence of electron in two different dimensions causes this phenomenon some also call it superposition.
I know the videos old, but I did have a few thoughts I thought I could add. I feel as if a few terms will need to be defined.
Momentum is defined as an object with a certain mass, moving with a certain velocity. Now this object can be moving in a linear direction (so say forward), or it can be moving in a circle (like a dog chasing it's tail, or if a figure skater spinning). Angular momentum is an object moving with a certain mass and velocity, in a circular motion. Particles have this intrinsic property and it's called "spin". They also have a magnetic moment, that is, a magnetic field that is surrounds them, and the direction of this magnetic field is dependent on the direction of the spin. By direction, think of how in diagrams of the earths magnetic field you have arrows that show current going from the south pole to the north pole, same thing here. The direction of the spin (so on a 2d plane, left to right, or right to left) determines the direction of the field (which direction north and south are pointing, up or down).
That is a 2d plane however, in reality in a 3d plane, these electrons have these 2 states (up and down or rather +1/2 or -1/2) in an any direction. When you apply a magnet above and below these electrons, you are now restricting their orientation. They will come out random, but align to either the top magnet, or the bottom, and thus when they move through they will create 2 distinct dots.
Take the analogy of the figure skater above spinning. While in the xy plane their body is rotating, in the z axis they are not moving. I.E. If you looked at them from a birds eye view, their position would not be changing. Now imagine while the figure skater was spinning, they were able to do Michael Jacksons smooth criminal tilt. This is precession. When a magnetic field is applied, the particle will precess around the axis of the direction of the magnetic field (i.e. if the magnet field that is applied is pointing north, the particle will precess north). This precession is in the form of a full circle. This precession is termed larmour precession.
This precession is going to have a particular frequency (e.g. the time it takes to complete a full circle). It's rate will be dependent on the type of particle it is and the strength of the magnetic field applied (stronger force applied, complete the circle faster). This is the larmour frequency. In terms of applications and larger picture, it's important to note electrons, protons, and neutrons all have this property, but not all of them have magnetic properties. This is because this up and down magnetic field can cancel each other out, say for example when you have an even amount of particles. Atoms with odd numbers of particles have particles with magnetic fields that are not cancelled out (think unpaired electrons in orbitals), and that allows them to have magnetic moments that can be manipulated using an external magnetic field (such as Iron in the experiment).
I'd summerize by saying "spin", magnetic moments, and other factors defined by quantum numbers, all describe properties of a particle. I look at it as how we define what it means to be a plant, cell wall, photosynthesis or a mammal, laying eggs, breathing oxygen, etc. Particles have innate properties as well that defines how they function, and thus, they are described by these functions. We can say an electron, just as we say a human, but just as being human is defined by particular properties, being an electron is defined by particular properties.
A mobius strip requires you go around it twice in order to get to the same place/state (place + orientation).
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?