I know that a particle can have an orbital momentum and a spin which is intrinsic to the particle and doesn’t really have to do with the particle spinning. But can particles have an additional momentum due to its “actual” spin? Can a particle spin in the first place? And if so, what are the consequences of this motion?
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To me, when you ask Can a particle spin in the first place?, this contradicts what you (correctly) said at the start of your post. I think you might need to expand on that, (but the answer, if you mean something similar to spin in the classical world, will still be "no" :) , unless you clarify what you are asking. – Dec 13 '18 at 21:43
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Quantum mechanical spin has nothing to do with actual spinning, at first scientist thought it might but then realised that if the particle were spinning then it’d have to spin faster than light. My question is: can a particle actually spin? Like, classical spinning. If not then why? – Kirtpole Dec 13 '18 at 21:51
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What are you including in the term "particle" here? Is that restricted to fundamental particles like electrons and protons? Or are you allowing e.g. molecules and larger aggregates? – Emilio Pisanty Dec 14 '18 at 08:59
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1You all miss his question: if an electron has size then it can have an orbital momentum by its own. Correct? And he is asking about this. In other words: can the absence of orbital momentum be seen as proof of electron to be point-like? – F. Jatpil Dec 14 '18 at 09:40
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I think it is an interesting question. Answer is no, but I do not know why. Actually composite particles like proton still only have "spin". Well, they tell it is a composition of quarks spin and orbital momenta... But I do not get it. If proton has spatial structure than it can rotate at arbitrary rate... or cannot? See here: https://physics.stackexchange.com/questions/268089/ – F. Jatpil Dec 14 '18 at 09:45
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If a proton or electron were to be spinning there would be an amount of charge being accelerated. Wouldn’t it have to emmit radiation? Maybe that’s a reason why particles dont spin. Unless one postulates that particles (assuming they have dimension) have their charge accumulated in the center. I really dont know – Kirtpole Dec 14 '18 at 16:53
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But rotations are tricky. Even if it were perfectly symmetrical if it rotates and charge is accelerating and so it must radiate energy. It's just like Mach's Principle, the universe knows whether something rotates or not. – Kirtpole Dec 15 '18 at 04:14
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Here is some perspective which may help.
We know that if a macroscopically-sized and charged object is physically spinning, it will exhibit a magnetic moment. Experiments demonstrate that the electron actually possesses a magnetic moment, but other experiments demonstrate that as near as can be determined, the electron is a point that has no diameter. So, if it has a magnetic moment but has no diameter, then what exactly is doing the "spinning" in the case of an electron?
Years ago, the physicists studying this did a calculation in which they plugged into the equation for the magnetic moment the known value for that of an electron, its charge, and a reasonable guess for its diameter (based on an experimental upper bound) and discovered that to produce the measured value for its magnetic moment, the electron would have to be spinning so fast that at its "equator", it would be moving much faster than the speed of light.
This meant that the classical concept of "spin" for big objects fundamentally did not hold for something like an electron, and that it was not useful to imagine that a point particle was physically "spinning" around its central axis.
So there you are: the electron presents us with a magnetic moment, suggesting it is revolving- while at the same time it has no diameter, and even if it did, there's no way for it to generate that moment without violating special relativity.
Welcome to the world of quantum mechanics!
niels nielsen
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"as near as can be determined, the electron is a point that has no diameter" and "based on an experimental upper bound" suggest to me that the electron could have a diameter largely inferior to the quoted "upperbound", thus making it's linear speed at "equator" NOT exceeding speed of light, what am I missing here ? – Guiroux Dec 14 '18 at 08:30
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1I think you missed the question. He is asking: can electron, in addition to its intrinsic spin, still have an "orbital" momentum? Can it have two "rotations": the intrinsic one and a true, spatial one? He has no problem of "spin being no -explainable", but he asks: can there be something in addition to this (no-explainable) spin? – F. Jatpil Dec 14 '18 at 09:31
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@niels nielsen " to produce the measured value for its magnetic moment, the electron would have to be spinning so fast that at its "equator", it would be moving much faster than the speed of light." Is there a mathematical formulation for that that you could point me to? I read that in multiple places but haven't been able to find the calculation you were talking about. I'd appreciate if you could refer me to it. – EM_1 Apr 08 '21 at 13:35
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@user626542, I will look and edit my answer if I find a good reference. -NN – niels nielsen Apr 08 '21 at 16:56
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@niels nielsen I found it in griffith's quantum mechanics. It's a calculation where the electron is taken to have some radius r called the classical electron radius. $r=\frac {e^2}{4\pi\varepsilon_0c^2}$. If fthe angular momentum of the electron is taken to be $\frac{1}{2}\frac{h}{2\pi}$, the velocity of a point on the equator indeed comes out to be greater than c. – EM_1 Apr 09 '21 at 12:16
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My question is: can a particle actually spin? Like, classical spinning.
Two answers: no and nooooooooo :).
First off, we don't have accurate measurements of the size, if it actually has any, of an electron, for example.
All of the properties we give elementary particles are chosen to make sense when scaled up to the classical world, but they are analogies, we really don't know what exists, if anything, at the tiniest scales.
What you are asking is really a philosophical question, in my opinion, because physically/experimentally we can't measure below a certain scale.
So I can't say for sure that there isn't a minute "thing" spinning, despite my silly comment at the top, but what an electron "is" and how it behaves. seems much more likely to have a more subtle answer than anything remotely classical.
Virtual and Real Particles is a good read for how a particle is described in quantum field theory.
If we aren’t sure that particles are of finite size, then how could scientist show that the particle wasn’t actually spinning? Even at really high rotations (but still slower than the speed of the light) wouldn’t the magnetic moment be measurably high?
We can't be absolutely sure that it isn't spinning, but classical spinning wouldn't explain the behaviour of an electron, in any event.
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1If we aren’t sure that particles are of finite size, then how could scientist show that the particle wasn’t actually spinning? Even at really high rotations (but still slower than the speed of the light) wouldn’t the magnetic moment be measurably high? – Kirtpole Dec 13 '18 at 22:14
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We can't be absolutely sure that it isn't spinning, but classical spinning wouldn't explain the behaviour of an electron, in any event. – Dec 13 '18 at 22:16
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All we can say with certainty is that we do not have a mechanical model of the electron. Its size appears smaller than can be detected and then there is the half integer value. This makes it hard to represent it by a small spinning object. If we do, we need it to spin so fast that its outer parts move at near light speed, with a large gamma value. The point is that relativity is not the issue. Dynamically electron spin is like any, quantized, angular momentum.
my2cts
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