Was watching a video about physics last night and at a certain point they explained the Stern-Gerlach experiment and I got so angry I had to turn it off for the night
ME: Quantum physics isn't "weird", or mystical, or unknowable in some way that means we have to abandon the scientific ideal of understanding the universe. Quantum physics follows specific mathematical rules, and it follows them rigidly; it's just the math happens to not follow our intuition of everyday objects.
PHYSICISTS: *Explain literally anything about quantum spin*
ME: This is BULLSHIT and you are MAKING IT ALL UP
Will make another go at the video today. I'm hopeful/unhopeful because when I found the videos I was like "oh thank goodness, finally someone is going to explain to me how quantum spin works" and so far their explanation for how quantum spin works is "somehow"*
* They have repeated that one word in almost every critical sentence of the video
Okay so the video was pretty good https://www.youtube.com/watch?v=pWlk1gLkF2Y and did a better job of explaining spin than anything else I've ever seen (it's sort of in a series of 3, in the next one they're gonna take a go at the spin statistics theorem… looking forward to that, that's another thing I've tried and failed to comprehend before) but I'm still lost and I'm not sure if I'm lost the expected amount or more lost than normal
Here is what I am trying to figure out:
* PBS SpaceTime Guy suggests the spinor nature of fermions is best understood as the behavior of lines of connection between particles, rather than behavior of particles themselves. He notes "twisting" the lines of connection produces spinor behavior (2 rotations to return to original state) whereas a regular rotation doesn't. Fine. Here is my question:
Does this "lines of connection, not an object" kind of rotation *also* explain non-orientation?
(1/3)
He gives this useful visualization where he shows that the cube-with-attached-streamers example (which I've seen before) can be expanded to like, a high-N N-gon with a streamer on each face. So I imagine a 3D grid of 26-gons, each streamered to its adjacent/adjacent-diagonal neighbors. Then I imagine every n-gon simultaneously spinning with *random* orientations and speeds. Do they avoid tangling?
PBS-ST-G suggests thinking about phase, not rotation. But does my 26-gon idea *work*? (2/3)
I ask because that way non-orientedness stops being "shocking" because orientation is an irrelevant local symmetry anyway, and I could think about the unoriented spin value as like "rotation energy".
---
I also was gonna ask questions about how spin fits into LQG braid matter and "holographic" universe hypotheses but such such questions are absurd and "cranky" I think I should not try to ask them until I understand the normal one. Maybe I'll see if my PhysicsForums login still works (3/3)
And yeah, yeah, I get it, it's okay for quantum numbers to just be arbitrary "things" that have no classical analogues, the video mentions even Pauli wants me to think of spin as "classically non-describable two-valuedness", I'm usually okay with thinking this way. But if that's what spin is then *why does it impart mechanical angular momentum, literal macroscopic classical angular momentum, when you apply it correctly*?? I have always struggled to let this go and I kind of feel like I shouldn't
@mcc I remember being in a Facebook group of Physics student memes during my Physics Bachelor's and at some point someone innocently asked "What is spin?" wanting a genuine answer but the entire group got dumbfounded when they realised that there's no coherent explanation for it and it became an inside joke/meme in the group for months.
"What is spin? Oh, it's the angular momentum of a particle but not really."
@mcc@mastodon.social it's all just names for properties that are based on classical analogies and visualizations. like you said, people cling to that classical viewpoint but we have known for 100 years now it's simply wrong. we should probably reformulate our quantum vocabulary (not that i have any idea what that would look like lol)
@mcc@mastodon.social reminds me of how electric current and magnetic fIeld lines are perpendicular - dimensionally linked but not the same thing!
@mcc dunno if you have seen before but Supriyo Datta has a wonderful lecture series about nanoelectronics where spin transport is covered.
@dunderhead I will look for that, thank you. I am always curious for more youtube/nebula documentary content.
@mcc Could you provide the link of the video so I can be mad too?
@triple I am watching this series:
https://www.youtube.com/watch?v=pWlk1gLkF2Y (spin)
https://www.youtube.com/watch?v=EK_6OzZAh5k (spin statistics and the pauli exclusion principle)
https://www.youtube.com/watch?v=26ZmKqLNSZ8 ("anyons", I think this might be speculative nonsense but I don't think I'm going to understand it until I've watched the first two)
"PBS SpaceTime" has sensationalist video titles but IME they are quite good on scientific rigor
@mcc i’d have to watch the video again…i’m thinking maybe it’s like magnetism in that sense? essentially it’s got two value options, positive or negative, & the interplay of these creates these connection lines which are seemingly more complex than more standard macro-level magnetic lines (tho obv those can be complex…) due to the quantum nature of the forces at play…
*note i am just thinking out loud here, am an amateur physics-enjoyer at best, nearly failed it in college. i am a commoner!
@mcc Where can I learn more about imparting classical angular momentum?
@jamiemccarthy An example would be 0:48 in the "electrons do NOT spin" video above, where he describes, but does not fully explain, an experiment involving the basic "an EM field can make a metal thing rotate" behavior.
I have also seen an experiment described where you fire a beam of particles with a specific quantum spin at a macroscopic object and eventually it starts rotating. Because I don't have a cite on this experiment, it is possible that I have misunderstood it.
@mcc @jamiemccarthy It's important to remember that when the person on the rotating stool flips their bike wheel around, the angular momentum of the combined person-wheel object does _not_ change.
In this analogy, what the EM field does it tell all the little people in the atoms to reorient their wheels.
So I wouldn't call it “imparting” momentum because no momentum is transferred or incurred. The EM field is uniform; it doesn't push the object.
@nex @jamiemccarthy "what the EM field does it tell all the little people in the atoms to reorient their wheels"
How does it do this?
@mcc @jamiemccarthy Good question! Beyond my understanding, unfortunately.
I suspect it could be similar to the meme from @engravecavedave's post: “Imagine a compass needle reorienting when the field turns on, except there's no compass needle” ;)
https://chaos.social/@engravecavedave@mastodon.social/with_replies
@mcc @jamiemccarthy P.S.: Currently trying to get into work mode and tidying up browser tabs; thought I'd share these links:
This paper looks interesting but waaaaay over my head: https://arxiv.org/pdf/1908.08682
This article explains how electron spin might be helping you hoard more data right now on the desk right in front of you https://annas-archive.org/scidb/10.1038/35010132
@mcc @nex @jamiemccarthy given an external magnetic field, magnets will reorient themselves to align their poles along magnetic field lines to the extent they are able, e.g. dipoles want to be antiparallel.
@mcc fwiw i found this answer helpful https://physics.stackexchange.com/a/555357
why does it impart mechanical angular momentum, literal macroscopic classical angular momentum
@mcc This thread is the first time I heard this and I thank you for it. It sounds absolutely bonkers and I will watch that video this weekend.
@clacke Note I am not sure I am completely right in my description. But the videos are interesting.
There are another two plus one just on spinors.
@mcc probably way out of my depth here but this makes me think about how observing quantum phenomena seems to stick them into a certain state… Maybe they just appear to be stuck because we don’t actually know how to see them differently? i.e. we are the ones who are stuck in a local frame of reference
@macbraughton The Stern-Gerlach example seems to suggest this is at least part of it
@mcc I can only smile and nod here as my grasp of calculus is just barely getting to the point where I can actually start to follow the math involved in making sense of this
@mcc Can't answer that at the moment, but I'd say for the purpose of understanding quantum spin, this is unnecessarily and massively overcomplicating things. The shape of the object and the number of attached Dirac-belts doesn't matter here. Those are just a visual aid to distinguish two states in which the rotating object would otherwise look identical.
@mcc Demonstrating that there are macroscopic physical examples of spinors is probably meant to make it seem more intuitive than changing, say, the colour of the face of a cube as it rotates and showing you have to rotate it twice to get the colour back (i.e. essentially the approach in the video I mentioned), but in relation to quantum spin it's still an abstract analogy.
@mcc I don't see how this analogy could be helpful here; I also didn't get the impression that O'Dowd was trying to imply anything like that.
To me this is a completely ordinary rotation, it's just that some objects (spin n + .5 where n is integer) behave like that under rotation — this seems familiar when you've used quaternions for 3D graphics or similar.
Watching this could help: https://www.youtube.com/watch?v=pKKy2mmsziI
@mcc Btw., I just rewatched the SpaceTime video (first saw it years ago) and found it quite well made — which was definitely in part due to having seen it and similar lectures about the topic before. So I've already developed a certain tolerance to this weirdness, but still I still had to occasionally pause the video at a few points to mentally catch up. That's how I discovered that other video: YT suggested it as related and I watched it in those breaks.
@mcc Suppose you're helping someone learn square roots and they're currently learning for their first test for which they need them.
If you told them to take the square root of -1 as a practice example, you'd *want* them to say “this is BULLSHIT!”, right? I think this is a normal an necessary step towards understanding
@nex Imaginary numbers are easier for me to understand because numbers are not real. Imaginary numbers are fake but natural numbers are also fake. It doesn't really matter if they behave one way or another. They behave how we decide to define them.
But magnets are real. They interact with things I can see and touch. So it is harder for me to just go "I guess it's just an arbitrary mathematical object with arbitrary mathematical properties"
@mcc Ah, yeah, my comparison doesn't quite compile there because the types of the two different bullshits turn out to incompatible :)
My thinking was more like: Some electronics stuff gets easier and more understandable when you have complex numbers, and it's similar with quaternions, spinors, tensors …
@nex @mcc While it might seem minor, I've found utility in thinking of imaginary numbers as values that square to -1 rather than being the solution to sqrt(-1). We already know that sqrt doesn't provide all solutions (e.g. -7^2 is also 49), so adding more objects that sqrt doesn't understand seems reasonable. If you've played with quaternions, you have 3 orthogonal basis vectors, i, j, and k, which all square to -1.
@nex @mcc And if you've encountered any of the Geometric Algebras (cf https://bivector.net/) or Clifford Algebras, you'll encounter arbitrary numbers of orthogonal basis vectors that might square to -1, 0, or 1.
@gomijacogeo That site is great! I came across it when I watched the first ~10 lectures of https://www.youtube.com/watch?v=mas-PUA3OvA&list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS a couple years ago. I'd like to continue with that (or just plain PGA) some time, but I need to find a practical application (in the sense of a project I'm working on) first, because otherwise I find it too hard to learn/retain it properly.
@gomijacogeo @mcc Hmm … intuitively, this kinda makes sense because in practice, I need to know that i⋅j = k, j⋅i = −k, etc., so I'm very focused on multiplication.
But pedantically, “what squares to −1?” and “what x = √(−1)?” are equivalent, right? Interpreting the latter to ask only for positive x seems more like a notational convention. Kinda like the division symbols ÷ and / can have different meanings in some texts (e.g. same operation, but different precedence).
@nex @mcc Like I said, it might be a minor nit soothing a pedantic mind, but again, if I lead with i=sqrt(-1) and j=sqrt(-1) and k=sqrt(-1), then I would expect a student to think I just said i=j=k and now I have to unwind that. But if I say that i != j != k, but i^2 = j^2 = k^2 = ijk = -1, we can start working through the implications of how the algebra works.
@gomijacogeo Ah, gotcha. So in my hypothetical example of teaching middle-schoolers, I'd have to find a way of introducing imaginary (and complex, probably) numbers before talking about i² = −1. Hmmm …
@mcc@mastodon.social came here to recommend this one. it got me closest to understanding but I still don't understand
@mcc Sorry, don't have anything better than grinding through the MIT 8.04 and 8.05 classes on YouTube. Allan Adams (8.04) is an amazing lecturer though. Spin doesn't really appear until lecture 23, and you do need most of the rest of the course to handle the eigenvectors, eigenstates, operators, etc that form the vocabulary of the lecture. https://www.youtube.com/playlist?list=PLyQSN7X0ro21XsVfRHhiWGEEJigdjpF3s
@mcc In handwavy terms, we don't interact with 'spin', we interact with magnetic moments, but to have a magnetic moment, you need units of charge and angular momentum, but the angular momentum is a hidden/quantum variable. For *handwave* other quantum reasons, the values of angular momentum must be integral units apart. Angular momenta on the whole integers (... -2 -1 0 1 2 ...) live in a space that corresponds to the unit sphere and momenta that land on the halves live in SO(3) because math.
@mcc Similarly, because math, integer spins commute (i.e. xy = yx) whereas half-spins anticommute (xy = -yx), which has implications for how their wave equations behave, which gives you the behavioral differences between the bosons (integer spin) and fermions (half spin).
@mcc Another really good video series is Sean Carroll's "Biggest Ideas" series - https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX
@gomijacogeo Oh I used to read his blog, it was decent!
@gomijacogeo oh, that's interesting