What can be gleaned from this model is that there's some sort of double rotation involved when viewed in 3 spacial dimensions. I am not fully certain but as I recall, when described using quaternions/octonions this double rotation seems to disappear or at least becomes much more natural - it might just be an artifact of the default mathematical model we use in dealing with quantum physics.
@@infinummjb there is, in fact, a sort of double-rotation in the case of a true spin-1/2 object embedded in a field. The Dirac belt trick displays this well; instead of the double-rotating element being a gear, it is the ribbon/belt. The Dirac belt trick is a closer analogy to the "real" process--in the belt trick, the distortion/displacement is a close analog to the distortion/displacement of the field under rotation. In effect, what the belt trick shows is that the *space itself* (well, the field, technically--basically a set of vectors paired to a coordinate space) can twist about through one rotation (coming to a state that is not the original state) and then all the way through a second, coming to the original state. Still, though, there is indeed a double-rotation :) it's really neat.
The reason it is an unintuitive physical property, is because it is not a physical property. There are no electrons to be spinning up out down. This is a physical representation of something that is abstractly mathematical.
@@luciazazel2683 It seems to me like spin 1/2 is very similar on a conceptual level to how imaginary numbers represent rotation. Is it almost like “rotating” through an imaginary spatial dimension? I’ve always understood spin as the quantization of angular momentum is that still a good way of describing spin when you are working with non integer spin?
@@Stalutes64 Indeed so! There is, in fact, a component there that involves the complex plane. If you look up "what causes the Pauli exclusion principle", you can find an excellent explanatory video that touches on this in a more rigorous way. Yes, spin is a type of quantized, abstract angular momentum--it's not just a heuristic, it is actually a type of angular momentum, and its effects are only tangible in non-integer-spin particles/systems (the latter referring to, principally, quasiparticles). Good observations!
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@@wizard7314 A demonstration isn't an explanation. It looks like the intention was to just share a visualization. After all, the video's title *is not* "Explanation of Spin 1/2."
This one is more useful and more realistic. It’s based on Dirac’s belt trick but I think it’s clearer. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Nat-EsReXtQ.html
@@ralphclark is that the PBS one? I like their model with the tangled ribbons only getting untangled after a second spin. Speaking of not explaining anything- is it even possible to explain spin or charge at all?
There is no physical representation of spin, it's a purely mathematical "concept" that describes behavior. Nice work here, and I hope it helps folks gave a bit of intuition regarding spin.
In nature, form and function are usually intertwinned. I don't see why something that arises from mathematics must necesarily be an abstract "concept" that we use by convention and not a consequence of physical reality.
Another way to think about it is to hold a cup in your hand, with its bottom in the palm, and try to rotate it without the coffee spilling out (so your cup has to stay upright during rotation). If you try to do that, you will have to turn the cup under your armpit, stretch the arm out, do a weird turning motion with your hand, and then retrieve the arm. It's a fun thing to try. If you pay attention, you'll notice that the cup will have turned 720° while performing this action.
Bonus points for making the positron spin clip the electron spin clip played backwards instead of just spinning the model in the other direction. They need to have these in classrooms!
Very cool. I've always use the idea of a waiter holding a tray. You can rotate the palm of your hand 360 degrees without dropping the tray, but your elbow will end up pointing up. Do it again, and you're back to where you started.
An elegant, graphical representation of an extremely complex physical phenomenon. I wish there had been lecturers like you when I was at university. Your efforts are greatly appreciated.
Astounding! A beautiful model. Even the perpendicularity of the up and down states is shown! We know that neither electrons nor their enantichronal counterparts, positrons, rotate --which is represented by the base and its basal cog, remaining static. And yet their spin state is so clearly modeled by the remainder of the model! Many thanks. First video of yours that I've watched. Yet I subscribed immediately.
It’s infuriating that we have such deep understanding of the mathematics of quantum objects, yet are so completely and utterly unable to have an intuition of what it really looks like (probably nothing, actually). Our brain is just ill equiped to truly understand quantum mechanics, because it doesn’t relate to much of our experience of the world.
@@hundredfireify But we cannot also deny that there is a possibility that the human brain will evolve a new way of looking at things. We often take it for granted that we look at a 3d representation of the world on a 2d surface of our computers and phones. The first time people saw moving pictures on a screen was probably quite shocking. Now, we expect moving pictures on glass screens. Granted, it may not be as close to the quantum world, our intuition will improve even more. I'd like to think Einstein's general relativity has improve our intuition on spac as more than a "gap in something" but as the actual something where things "actually happen". Whether there is a biological marker for remains to be seen. Probably future generations. Our eyes will of course always fail us because we will never be able to see the quantum world firsthand but how our brain processes information about that world can be approximated. My guess is that the main driver will be the change in how our brain handles expectation about the world around us. People who will be born with the height of virtual reality technology will probably become more susceptible to concepts not grounded on purely tactile experience. Just like we don't question the fact that when you are talking to someone on the phone, you don't mistake them being inside the device or in your ears, they'll be able to process the concept of quantum mechanics without much resistance from expecting things needing to be "actually touching".
The electron is a sphere of light and the muon is a sphere of darkness that acts as gravity. It is this pair from which all elements are made. This is rather controversial, as it proves God, "In the beginning, God created light & he divided it from darkness" The fact we broke down the atom into quanta and all we're left with is a {sphere of light} attached to a {sphere of darkness} is quite concerning for particle physicist. So instead of acknowledging God and his creation they would rather confuse themselves in lost equations that lead to nowhere.
@@IZn0g0uDatAll We have not quantized the electron any further and all evidence suggest its energy or spin is infinite. We are in agreement the electron is a building block of life & I'm explaining to you this {electron} is quite literally a {sphere of light} that proves the existence of God when it was said "In the Beginning, God created light" as we now understand light to be the building block of all matter, or in this case, the electron, a literal {sphere of light} that has {infinite energy} [never stops spinning] You don't seem genuinely interested so I'd rather not waste my time explaining why the 'muon' is actually just gravity/dark matter/energy.
@@grandunifier3169 i think if you believe in god, you shoukd just keep it at that instead of trying to justify your belief with some very badly digested pseudo scientific mumbo jumbo. None of what you writes makes any sense.
maybe it's time we start recognizing that most 'teachers' are incompetent. they also teach us nonsense like: 'English uses an alphabet' - despite the fact that every literate English speaker knows full well that English writing is not remotely alphabetic. 'English has plurals' - despite the fact that 'plural' means more than one, but you can have 'no dogs', 'one dog', 'two dogs' and 'some dogs', which makes suffix-s look more like a non-singular marker... until we consider 'every dog'. 'English has verb tenses' - despite the fact that all of the alleged tense markers also appear on nouns and adjectives, like '-ed' being an alleged past tense marker appearing on adjectives: 'a walked dog is a happy dog', '-ing' appearing anywhere: 'the shouting man is disturbing my sleeping', and '-s' being the same one that allegedly marks plural nouns: 'the dogs run fast' vs 'the dog runs fast'. and this last one, which is called 'simple present tense' when it appears on a verb indicates something that's timelessly true, like 'seven plus three is 10', with that 'is' being the standalone form of suffix-s. '1+1=2' - despite the fact that most of mathematics exists specifically because this is virtually never true. for instance concepts like, fraction addition, unit conversion, and like terms, all exist to handle cases when 1+1 is most decidedly not 2, as in the following list of examples: 1 dog +1 dog = 2 dogs; this is the only kind of example that Whitehead and Russell considered in their so-called proof which appeared in the 1910 publication Principia Mathematica 1 dog +1 quail = 2 wings; expected values, but for the wrong reason... oops 1 dog +1 quail = 6 legs 1 half +1 third = 5 sixths 1 foot +1 yard = 48 inches 1 frog +1 pond = 1 pond 1 C water +1 C dirt = some mud '2^3 is 2 multiplied by itself 3 times' - despite the fact that this describes 2^4, since 2 multiplied by itself once would be 2*2, which isn't 2^1, but 2^2, so 2*2*2 isn't 2^2, but 2^3, and 2*2*2*2, or 2 multiplied by itself 3 times, is most decidedly 2^4, and not 2^3. and even if we say this slightly more correctly as: '2^3 is 3 copies of 2 multiplied together' this doesn't remotely explain zero exponents or negative exponents, which also can't be explained by what Euler said in Introductio inAnalysin Infinitorum Vol. 1 Ch. 6 #97-99, where he simply asserted that zero exponents yield 1, negative exponents yield unit fractions, and this can be shown by way of taking a random positive exponent and decrementing it. this is nonsense because even Euler partially realizes his mistake in #99 when he notes that a base of 0 doesn't behave as he's claimed, but he still doesn't really fix his mistake, he just treats this as a special case, which ends up giving us some of the indeterminate forms. but, if you pay attention just a tiny little bit you'll notice that the 1 which appears when the exponent is non-positive is always there as the initial condition to exponentiation, and that this should be extremely obvious. since exponentiation is iterated multiplication by definition its initial condition must be the multiplicative identity, which is 1. so 2^3 isn't really 2*2*2 as everyone conventionally claims. instead 2^3 = 1 *2 *2 *2, which now yields 3 multiplications by 2. and this now explains why 2^0 = 1, since this has zero multiplications by 2. and why 2^-3 = (((1 /2) /2) /2), since this has -3 multiplications, or 3 divisions, by 2. and now there's also no mystery as to why 0^0 = 1, since the value of the base is completely irrelevant when the exponent is 0, by definition.
@@beeble2003 In chemistry, you usually learn how orbitals are filled with electrons, using the Pauli exclusion principle and knowing that electrons prefer to fill orbitals with lowest energies. This has a very intimate relationship with quantum numbers. Specifically, principal, azimuthal, magnetic, and, most importantly, spin projection. If you remember about two arrows in a box, that corresponds to two different spin projections
This was not ever a thing I thought I'd have a mental model for. I recognize that the reality is more complex, but holy hell is this a helpful way for a layperson to feel a little closer to the subject matter. Very, very well done.
I love how the example at the end loops like four times. Demonstrations like this really should always include a long looping sequence at the end of the video
Given we're often told that "spin" is something of a misnomer for what's going on way, way, WAY down there at the subatomic level. Still, your geared wooden discs demonstration is a BRILLIANT way to visualize what is probably an impossible-to-see phenomena. And as your quote at the end suggests, even Feynman didn't come up with this. So THANK YOU, Sir Watts, for helping me better grasp what I've always found elusive!
Excellent!!! My professor told be don't try to visualise it. Just think like it's there. Now my head feels more relax than before for such visualisation. Thanks a lot.
that description of the positron as an "electron going backwards in time" was striking. i've wondered if all the "missing" anti-matter of the big bang didn't head off with an opposite arrow of time to ours into an anti-universe
@@TheZenytram thanks i do get that but that question of mine remains. i've seen it pop up elsewhere. i've also wondered on a related note if certain particle/anti-particle asymmetries would disappear if they could (somehow) be observed in opposing arrows of time
Beautiful woodcraft! A little critique: It certainly looks like an elegant implementation of the most simple double cover possible (a circle double covering a circle). However, the double cover seems only superficially related to the sphere double covering SO(3), which I think is the origin of sphin and which I believe is the effect you tried to emulate in lower dimensions. To go further, I am not quite sure how your representations of up and down actually relate to spin up and spin down. However, I am just a lowly geometer whose attempts to pierce the deep mysteries of quantum mechanical geometry have yet to succeed, so maybe by doubt is wrongly placed...
Interesting statement from Feynman from 1965. I have seen other representations using differing models (PBS Space Time's version) which I personally think shows the physical properties a bit better but this simple one does do an excellent representation of how these properties align to the mathematical matrices so thanks!
Sweet two-dimensional model in the 3 spatial dimensions of real life representing a 2D representation of a 3D, and sometimes 4D... Reality... Great work.
the problem with this demonstration is that you can make any gear ratio you want - it could also be "spin 1/3". But there is fundamentally no spin 1/3 in reality.
Feynman … still even more correct after all these years…. The fact that nothing is actually spinning probably escapes most that now think they understood something.
@@robertw1871 I was just kidding, we know it's more complex than that. Actually, except for the entanglement experiments, the analogy shown in the video works pretty well.
@@En_theo It really doesn’t, as what is called spin is a quantum of magnetic moment and nothing is actually spinning, it’s just telling you what state the magnetic feild is in. It’s a good analog of the mathematics, but not an actual electron. It’s a case of exactly how Richard explained it, if you think you understand it then you don’t, man was a genius. You’re trying to imagine an object doing something, it’s not an object, it has no dimensions or form so that’s the difficulty. It’s just a set of properties at a point in a feild.
@@robertw1871 It's ironical that you talk about not understanding QM, because the theory does not actually know what's happening in there. It's not that "it does not spin", it's more like "we don't know what's going on". So yes, the analogy works very well except for entanglement. How could you tell the difference if particles had a specific internal structure (or something like chords) and that inside it, spinning is possible because FTL movement would be possible on small scales (that's just an example). You cannot say "it does not spin", you can just say that the idea of spinning can't be explained with the rules we established so far for large scales objects. What happens inside a particle is a mystery so far.
The duration is 3:14 🥺😭 my heart melted their. So much thankful for the video, it helped a lot❤❤❤ when he says he says a positron is an electron moving back in time, chef's kiss🤌🤌🤌
I just love how people persist in not coping with the knowledge about the wave/field aspect of sub-atomic things. to understand that, review the clip in another channel about turning a sphere inside out. From there you will start to see the energy state , only 8 or less in the outer shell make more sense. the shell is the field and the electron doesn't actually exist in the atom, just the field. Oh, and the 1/2 comes from how many times it has to turn inside out to get back to origin state. and that will help you understand the other spins like 1/3 & -2/3.
So 1/3 means that it has to turn 3 times? It's unintuitive because in my mind 1/2 get translated into "half" and 1/3 into "a third" of something, not 3 times. 2/3 is even more confusing, I guess it means it reverses every two third of a rotation. Though it doesn't tell me how many rotations it needs to return to the original state, 6 maybe?
@@souljastation5463 - that is what the planar illustration has a limited use. 1/2 would be turn inside out twice to be a full oscillation. For negative, more like turn outside in. For 2/3 or 1/3 you are dealing with 2-d objects in 3-d space, so 1/3rd = invert 3 dimensions to get a full oscillation; or 2/3 means invert 3 dimensions to get 2 oscillations. The trick is not assuming those dimensions are automatically x,y,z Better to think of it like changing color which means changing wavelength or harmonic.
Spin is an integral characteristic of a substance, like its mass, density, etc. American science again confuses people this time not with Schrödinger's cats, but replacing the terms rotational mechanical moment and quantum number.
Naaaaah we call it spin bc in the equation, in which it was first derived, it looks like angular momentum. I mean it's no more confusing than talking about color charges or positive and negative charges, they're merely ways of expressing a new concept that words did not exist for.
@@Anankin12thank you for the info! It left me with more questions! The SG experiment explanations online seem to cover two flavors, electrons and magnets which deflect in "patterns"... the former being discreet and the latter continuous. Consider that the magnets only appear continuous because some parts have spin up and some spin down. Each individual particle always deflects by a specific force/direction. If you get three up and two down the forces would sum somewhere in between but closer to up. So, I was wondering if you knew if we could build matter where all of the particles (that have 1/2 spins) have the same spin orientation? How would that stuff deflect in the SG experiment? Would this stuff act like a monopole magnet? How fucked would chemistry be? I could be in left field as well! If you have time/are willing to answer of course. :)
Nothing about an electron actually spins, it’s a statistical method of defining a property. What an electron actually is can’t be visualized, but it’s more charge moving in a feilds, or a disturbance in the feild itself that couples to other feilds….
Query: With the notations given, could there be a theoretical particle that has two electrons and two positrons orbiting the nucleus? Is that how those matrices are to be read? With the models in mind, I know that it would be impossible, and I know about matter-antimatter annihilation, but then why are there two separate vectors for going around the other direction?
But the cog angles are arbitrary, they could be any 360 degrees so you don't have two spin states, but infinitely many. Also the cog ratios are arbitrary so you have an arbitrary number of rotations required for return to previous state. You might say that these up/down 1/2 spins represent two classes of behaviour of this model, but many more classes of behaviour might be imagined. So the model although interesting does not throw any light on the spin phenomenon.
This is what I was thinking, the idea that you have to spin a spin 1/2 system by 720° to get it to return some state has some links but I don’t think anything else in the video is relevant to an actual quantum mechanical spin 1/2 system
I'd wager that the most common mass produced spin 1/2 object that people work with regularly is a 4 stroke engine. the valve timing is exactly like this, since each cylinder goes through a full crank rotation with its valves closed for compression and combustion, and then with the valves moving during the crank rotation associated with intake and exhaust.
Despite really nice models: how real is this for wave equations? Some say the electron spin is lile such a rotation, others say it is not, so that there isnt anything rotating classically. Still electrons create a magnetic momentum
I am pretty sure electrons don’t actually spin. It is true that they have a magnet momentum, but if you measure its magnetism and use the upper limit of size of an electron then calculate the speed which they rotate you get a result faster than light, so we can conclude that its magnetism doesn’t come from a classical rotation.
@@brunojambeiro6776 hmmmm but magnetic moment is believed to be a direct result from the spin of the electron and its angular momentum, and so are you taking the the magnetic moment that results from angular momentum into your calculations as well?
@@dylanmiley5642 Not exactly sure what you mean by that. The magnetic moment the electron have is a result of its angular momentum, which is connected to it’s spin, but despite it being called spin, electrons don’t rotate around its own axis. It’s angular momentum is intrinsic to the particle. What i had showed is that such angular momentum could not be a result a classical rotation of the electron. Btw I an no expert, try searching science asylum spin, I belive he gives a better explanation in the video.
@@brunojambeiro6776 im not an expert either, im simply a masters student in electrical engineering with an interest in this realm. From my understanding (and with reference to the textbook "Magnetism and Magnetic Materials" ) within a magnetic material, electrons both have an orbital angular momentum as well as spin, and as magnetism is a relativistic correction to the coulomb force, both of these components lead to magnetic moment.
Yes. However, spin is a measurement of energy (angular momentum). In the g-2 muon experiment, the spin was determined from the amount of energy in the electrons which decayed from the muons. It has been proposed that electrons are made of two massless particles with opposite “chirality “(yet another insufficient analogy) , which is like “right-handed” “ left-handed “ rotation. The flipping back and forth of chirality is said to be the cause of mass. We don’t know what an electron is it’s just the math that makes us come up with more ideas.
"quire knowledge about the internal parts of the electrons, " There is no present evidence for an electron having internal parts. Characteristics yes, parts no. Which is the problem for physical representations of spin. I really like this demo BUT its an analogy and not related to how electrons really do anything. The are the best tested fit to the idea of a fundamental particle.
This spin 1/2 representation is equivalent to Möbius torus knot, in which case the aether has to flow twice around the electron to get to the same spot in the original orientation.
I think the whole “traveling back in time” metaphor does a disservice to science communication. It confuses more than it helps. Nothing is actually going back in time.
That would be a particle that returns to its original state after only half of a rotation. Two choices for definition here: either the spin number is how many rotations to return to the starting point, or how many times you return to the starting point per rotation. Physicists chose the latter, although as you say, the former is more intuitive. I don't know why, probably convenience in writing out the equations.
iv been doing a spin 1/2 with my lighter when i get bored as i twirl it around my finger. One twirl gets to gas release facing away from my thumb and then with two i get the gas back at my thumb. I learned somthing new! =D
The spin 1/2 demonstration is awesome, thank you. However, I must admit if one turns over the table, the clockwise direction and counterclockwise will turn one into the other. This doesn't happen with a positron, one cannot change its charge by simply choosing a different coordinate system (or rather an inertial system).
This might be a dumb question, but how do you measure the spin of an electron? What sort of instruments could you use to measure something so small? Also, how exactly does a particle travel backwards in time?
1st electrons are one of the easiest particles to detect their spin, just detect their magnetic field (I guess that's how it's done, but it's more complicated than that). And positrons don't move backwards in time, only their electric charge (and magnetic field) *behave* like if they were moving in reverse. All antiparticles have this pseudo-reversed-time (except self-antis, like Photons). The only particles that REALLY move back in time are nega-particles (particles with negative energy). This is why I think "antiparticle" is a misnomer, because an opposite electric charge is just that. A *REAL* and valid antiparticle should be opposite in *every* property (negative mass and energy achieves exactly that)
