Classically or Quantum Mechanically. Spin of earth or macroscopic object appears well understood classically. But what about spin of fundamental particles. Like that of electrons, protons, neutrons and quarks? How do these particles attain spin? Is the spin of all electrons (any particle) same in unforced condition? Why only 2 states of spin (Pauli), ideally there could be infinite spinning orientations.

Your question is a little misleading; spin or isospin is an intrinsic property of quantum particles, not something they "attain". As far as I can say anything about it, spin is required, without isospin lots of observables would have no explanation (i.e. underlying theory). It explains the different ways electrons propagate in different kinds of materials, for instance, and it explains Fermi-Dirac statistics ("energy levels"). Take a good look at some of the lectures online that cover the Stern-Gerlach experiment(s), and a gander at the Einstein-deHaas experiment where its authors thought the electrons had gyroscopic motion, and why they were almost right, but why they were out by a factor of 2.

Spin is required and it is there... So how does a fundamental particle acquire it? My focus is more towards mechanics behind. And also how do we conclude that all same type fundamental particles have same magnitude of spin (in a given ref) and why it be same?

It's a good question and my answer may strike you as unsatisfactory, but it is what I have understood from my study of QM. The QM concept of "spin" of fundamental particles is not really the same thing as spin in classical mechanics. What we observe is that many particles have an intrinsic angular momentum. This shows up for example in the observed intrinsic magnetic moment of particles such as protons or electrons. It seemed natural, early in the c20th, to assume that these little balls, as they were pictured, were spinning like tops. But famously, in QM, it turns out first that these "particles" are not pure particles but also waves. And it turns out that this intrinsic "spin" angular momentum does not in all respects behave like a classical spinning top. According to the QM model, intrinsic spin is as fundamental a property of a particle as mass or charge. You can't "stop" the spin unless you destroy the particle and you can't increase it either: it is fixed. The orientation of the spin in space, and hence the direction of the magnetic moment (if the particle is charged) can be altered and this is observed. When you mention 2 states of spin, I think this is what you are referring to, in that you can have two electrons (for example) occupying what is otherwise the same state, provided their spin orientation relative to one another is opposed: what we often show as "up" and "down". But in fact the intrinsic spin of an electron has only one value (1/2) and it is the orientation that has 2 values. You also ask about the number of spin orientations. This can indeed be infinite for a free particle in the absence of a magnetic field (whether external or due to the presence of another nearby particle). However, if a charged particle is subject to a magnetic field, the orientation of its own magnetic moment to that field will result in different energy states. Under these conditions only a set number of energy states, corresponding to different orientations with respect to the field, are allowed. This is an example of the quantisation that occurs whenever QM objects are subject to any form of constraint. In this case it called "space quantisation", as it is depends on orientation in space with respect to the field acting on the particle. There is a well known effect in spectroscopy called the Zeeman effect which illustrates this: https://en.wikipedia.org/wiki/Zeeman_effect In summary, it results in splitting of spectral lines, as a result of energy levels in the atom which were the same in the absence of a field becoming different when a field is applied, due to spin orientations of the electrons, and the orientation of any orbital angular momentum they may have (some electron orbitals require the electron to have orbital angular momentum and some do not).

I enjoyed your post very much. When you say particles can be seen as waves I thought waves to be way of mathmatically describing a particle at some level would it not remain a particle or a group of particke moving say like the ocean. Thanks if you can indulge my question even if maybe off topic but I can follow the way you explain things. Alex

Good comprehensive response. Does not matter if I am satisfied or not, because I am looking beyond standard text. Bohr model....splitting of spectra lines... New energy levels...Zeeman effect.....spin...chemistry. This associates spin with energy level, now why only two spin states...since the orientation decides further energy level, ideally we should have multiple sub energy levels as spatial orientation at least for free particle can be random. Do two electrons in the context get aligned after capture or they are captured with specific orientation only? Later is a difficult selection. Secondly angular momentum is a mechanistic property, to me it appears unlike charge or mass...so how a particle acquires this and that too precisely?

The number of allowed spin states is a function of the amount of angular momentum. A single electron has a spin 1/2 and this can only be orientated so that it has a projection along the external field axis (normally called the z axis by convention) of +1/2 . h/2π or -1/2 . h/2π. (These are the numbers that come out of the QM maths). If you have an entity with a spin of 1, you have more possible z axis projections, viz. +1 , 0, or -1 all multiplied by h/2π. In all cases you have the most +ve projection and then a series differing each time by one, through to the most -ve projection. These are the only orientations possible, i.e. corresponding to stationary states, in QM. The same is true for the orientation of orbital angular momentum. Regarding the question about other orientations, they do not correspond to stationary states, as they are not solutions of the time-independent Schroedinger equation. That means they have no existence, other than transitionally en route to a stable state. This can be thought of, qualitatively, as a consequence of the wave nature of matter. Only standing wave, resonant states have stable existence. (rpenner will tell me this is a toy model and I don't disagree, but I find it helps me to have a picture in my mind of roughly what is going, on even if it is a bit naive.) As for what determines the orientation of an electron that is a matter of statistics (lower energy states tend to be populated more than higher energy ones, and, in atoms, of the Pauli Exclusion Principle, according to which no two fermions (=entities with half integer spin) can occupy the same quantum state. That is why you can get 2 electrons into each atomic orbital, one spin up and one spin down. If they have different spin projections relative to one another they are in different states, even though everything else, apart from spin, is the same. We use this in chemistry to explain the Periodic Table, via something called the "Aufbau Principle" which you may have come across, putting 2 electrons into each allowed stationary state (or "orbital"), starting with the lowest energy and moving up through the various allowed stationary states until the electrons balance the +ve charge on the nucleus for that element. But this is getting onto another topic. One final observation. One really has to let go of the idea of spin as something "given" to a QM entity. As I said in my first response, in QM, intrinsic angular momentum (called "spin" for convenience, but not really spin as in classical mechanics) is just as fundamental as charge or mass. It is intrinsic in the same way. If a proton does not have a charge of +1, it is not a proton. If it does not have a spin of 1/2, it is not a proton either. A photon by the way has spin of 1, making it a boson rather than a fermion.

Haha, who knows? Some people like to think of the wavefunction as a piece of maths that describes the behaviour of what are in truth particles. It's a point of view. As a chemist I don't share it. I've spent too much of my education preoccupied, directly or indirectly, with the energy of electrons in atoms and molecules and in chemical bonding, which results from the wavelike superposition of atomic orbitals to form molecular orbitals. These entities are wavelike, with +ve and -ve phase, like a wave. It has become natural for me to think of the wave as at least as fundamental as the particle. I often think the reality is a wave but with the proviso that it can only interact in whole "units", which we call quanta. Certainly that is what the double slit experiment seems to suggest to me. But I do not pretend I have thought about it very deeply. When you think about it, though, the idea that nature consists of "particles" - more or less pointlike mathematical entities - is fairly unnatural too. I might even suggest, a bit tongue-in-cheek, that it is just that ever since the time of Newton it has been a useful device to get rid of complicating factors such as shape, to keep the maths simple.Please Register or Log in to view the hidden image!

1) Spin is an empirically observed property of the way phenomena (specific particles) are observed to behave. So what it is is a question about fundamental reality which I classify as metaphysics — being trained in physics, I will restrict myself to how it behaves. One way it behaves is Thomas precession which in 1925 explained why hydrogen atoms with electron and proton with aligned spins had precisely the energy separation they do from the case with anti-aligned spins. https://en.wikipedia.org/wiki/Spin–orbit_interaction 2) Newton didn't describe angular momentum or energy, those conserved quantities were discovered by others, but the conservation laws appear to be fundamental and can be proved as theorems of classical or relativistic physics. According to Noether, that goes hand-in-hand with the physics of the universe having rotational symmetry and time-translation symmetry, respectively. 3) Quantum mechanics gives a view on the behavior of things where complex numbers finally become not just clever mathematical tricks but pretty vital to physical models. Probability requires the sum of probabilities of all possible outcomes to be 1. Since quantum mechanics describes probability as the square of the modulus of a complex number, quantum mechanics requires a property called unitarity to ensure the sum of probabilities of all possible outcomes does not change from 1. 4) When you combine the ways of describing inertial frames in special relativity, the freedom to choose the origin of the coordinate system (4 time and space translations), the freedom to choose the orientation of a right-handed spatial Cartesian coordinate system (3 spatial rotations), and the freedom to choose a standard of rest or equivalently to pick out a time-like direction of the time axis (3 Lorentz boosts) and relate all 10 degrees of freedom together you get the full inhomogeneous Lorentz group, which is commonly called the Poincaré group. This is the symmetry group of flat space-time according to special relativity. Weird things happen when you combine boosts and rotations in 3 spatial dimensions and that's a Thomas-Wigner rotation. 5) In 1939, Wigner combined special relativity and quantum mechanics and wrote out all the unitarity representations of the Poincaré group. That is he established what things could exist in a physics which respected both unitarity and the Poincaré group. So for particles with m > 0 we have those with integral and half-integral intrinsic angular momentum. In other words, spin is as fundamental as special relativity or quantum mechanics. It is incorrect to assign spin to any internal motion because we have neither the empirical evidence of such motion or the physics to relate such internal motion to observable behavior. Spin is intrinsic angular momentum of quantum particles. 6) Finally, the spin-statistics theorem says particles (in 3-dimensional space) says particles with half-integral spin act like fermions, while particle with integral spin act like bosons which relates to the stability of matter and thermodynamics, tying fundamental particle physics to the lives and deaths of stars. Since we can't take spin apart and examine it in any physics we have, we use it (along with mass and couplings to other particles, like electric charge) to classify particles. Because of Wigner's classification, unlike mass in the Standard model, intrinsic angular momentum is likely to remain as fundamental in our descriptions of the behavior of things unless some new theory completely overturns our understanding encapsulated in special relativity and/or quantum mechanics. In fact, spin-networks and spin foams have been raised as candidates to try and explain space-time itself, which would make spin more fundamental than the idea of distance. Heh heh.

.....what spin is is a question about fundamental reality which I classify as metaphysics..... That should curb the further discussion on this.

[QUOTE="exchemist, post: 3442680, member: 268413]The only Svetlana I can think of is Stalin's daughter.....[/QUOTE] Svetlana : The gymnast. Her spinning was so beautiful, so metaphysical!

Svetlana : The gymnast. Her spinning was so beautiful, so metaphysical![/QUOTE] Well there you go! I told you how much I learned from membership of this forum.

Spin is something you can think of as a quantum-observable, in the context a beam of particles can be separated into two spin-polarized beams. You get a classical observable when you count particles in one or the other spin state, you use some kind of incidence counter. Spin doesn't commute with measurement in more than one dimension. When you split a beam of electrons into two spin-polarized beams with a classical magnetic field (as in a Stern-Gerlach apparatus), this is where the quantum spin measurement or preparation is. It's why you can't prepare the spin to be up along say, the z axis, then prepare it again but in another direction, say down along the y axis, and expect the two 'operations' to commute.

Yes, this is another manifestation of the Uncertainty Principle. To put it another way, if you know the angular momentum projection along the z axis, you cannot know anything about the corresponding projection component in the x-y plane - it is indeterminate.

Svetlana Khorkina, last I checked, had more moves named after her than any other gymnast, possibly because her extension on the z axis forced innovation. A sequence of spins start after 1:20, and another - including an iconic move - after 2:50.