B Understanding Spin: A Basic Explanation for Beginners in Physics

[saboo_tage]

I know that I'm kinda asking for a lot here, but can any of you give me, a person with lesser experience in physics, a basic explanation of spin? I've found out that a particle's spin can be compared to a transistor, but that didn't really tell me what it actually is. What does it define? For instance, meters define length, square meters define area, etc. Can anyone put what spin defines into those terms?
Also, as a bonus question, what does relativistic mean in layman's terms?

 

[haael]

There are at least 3 different notions of spin.

1. Spinning, aka going around in circle. Composite particle's spin is a sum of spins of its constitutients plus orbital angular momentum. Some people say that spin has absolutely no in common with circular movement. This is not true. Orbital angular momentum can be only an integer.

2. Magnitude of spin. It comes in discrete quantities. The standard convention is assigning numbers differing by 0.5. So we have spin 0, spin
0.5, 1, 1.5, 2 and so on.
Important facts:
- There is a theorem that particles of integer spin are bosons and of fractional are fermions.
- There is a suspicion (but no proof) that no elementary particle can have spin greater than 2, only composites can have more.
- All known elementary particles have spin 0, 0.5 and 1. The only known particle with spin 0 is the Higgs boson.

3. Geometrical object representing spin. For magnitude 0 it's a scalar, for 0.5 it's a spinor, for 1 it's a vector, for 1.5 it's a kind of cartesian product of a vector and a spinor, for 2 it's a symmetrical rank-2 tensor (matrix).
There is also an important notion of spin projection onto the particle's direction of movement. Sometimes it's called the z-component. This is the basis of particle classification. When you hear about spin-up and spin-down, it's the z-component.
In numerical terms, z-component's possible values always differ by 1 and span from -magnitude to +magnitude.

It's important to know the relations between all those concepts.

 

[drvrm]

I know that I'm kinda asking for a lot here, but can any of you give me, a person with lesser experience in physics, a basic explanation of spin? I've found out that a particle's spin can be compared to a transistor, but that didn't really tell me what it actually is. What does it define? For instance, meters define length, square meters define area, etc. Can anyone put what spin defines into those terms?
Also, as a bonus question, what does relativistic mean in layman's terms?

The concept of spin of bodies in day to day world (classical) is related to rotation about a fixed axis ...say a top rotates ...spin will be measured by its rotational velocity/angular velocity and the mass distribution about the axis ...
a term spin angular momentum or spin energy can also denote its state of motion...our Earth spins about its axis and has rotational angular momentum . spin angular momentum can be measured in unit of (N.m.s) or (kg ·m^2·s^-1)
In classical physics spin is a rotation of a body.

<I've found out that a particle's spin can be compared to a transistor, > your above statement touches an area of particle(micro world) where classical physics is replaced by quantum descriptions and again 'spin' in quantum physics comes out to be a non mechanical model - in particle physics where one describes the particles as constituent of an atom ...spin is defined as 'state' of a particle say electron , proton and neutrons... the group of fermions which has two states of spin.
pl.elaborate your question further.

 

[Khashishi]

Consider an object made up of smaller parts. We can hierarchically calculate the total angular momentum in the object. The total angular momentum is the sum of the angular momentum of each part. The angular momentum of each part can be divided into two parts: the orbital angular momentum (which is due to motion of the center of mass of the part around the center of mass of the greater object) and the intrinsic angular momentum (which is the angular momentum "inside" the part). For example, the angular momentum of the solar system would be the sum of angular momentum of motion of all the planets (and other objects) around the center of mass (in the Sun) as well as the angular momentum due to the rotation of the planets (and other objects). We can go down the hierarchy and eventually we have a part made up of particles. We still have orbital angular momentum of the particles, and intrinsic angular momentum of the particle. By analogy to a classical spinning object, we call the intrinsic angular momentum of the particle "spin", even though we are way past the regime where classical mechanics operates. The fundamental particles have no substructure that can explain the intrinsic angular momentum. It's just an intrinsic part of the nature of the particle.

Also, when you get into the quantum regime, you notice that angular momentum is quantized. This is a fundamental fact of nature, that all angular momenta (both spin and orbital), projected on to some axis, is in integer multiples of $\hbar/2$. Furthermore, all fundamental matter particles have odd integer multiples (and are called fermions), and force carrying particles have even integer multiples (and are called bosons).

 

[saboo_tage]

I think I need to clarify, when talking about spin, I'm not referring to angular momentum, I'm referring to the property of particles. Something like the spin of an electron, for instance. Also, is there a difference between regular spin and quantum spin?

 

[Khashishi]

Spin of particles is still angular momentum. Electrons have angular momentum. The main difference between classical spin and quantum spin is that angular momentum is quantized to multiples of $\hbar$ (when measured on an axis). $\hbar = 1.0545718 \times 10^{-34} \mathrm{m}^2 \mathrm{kg} / \mathrm{s}$ is too small to notice on macroscopic scales, but changes everything on quantum scales.

 

[saboo_tage]

Spin of particles is still angular momentum. Electrons have angular momentum.

Really? I watched some youtube videos on the topic, they claimed that electrons having angular momentum was ruled out because of that it had to be rotating at the speed of light or something. There was another point against it that had something to do with that if electrons had it, then neutrons have to have had it too, which isn't possible or something. (not quite sure on the last one, it wasn't really explained clearly)

 

[Khashishi]

Neutrons also have spin.

The argument that the youtube videos were trying to make is this: an electron can't be thought of as a 3D geometric object with finite volume which is rotating about an axis. If we used the classical electron radius (which is not the electron radius), we calculate some motion greater than the speed of light. But all this says is that the electron isn't some 3D spinning object. It still does have intrinsic angular momentum.

 

[saboo_tage]

I see, so does this mean that the refusals over that the electrons have angular momentum were because of that they used the classical electron model which yielded results over lightspeed, while with the new model, they ruled it in again because they didn't know the size of the electron?
Because if so, how is angular momentum related to spin up/down, fraction spins, etc.?

 

[drvrm]

I think I need to clarify, when talking about spin, I'm not referring to angular momentum, I'm referring to the property of particles. Something like the spin of an electron, for instance. Also, is there a difference between regular spin and quantum spin?

I think one can view 'spin' as an intrinsic property of elementary particles ; similarily as the quarks have colors say Blue Green and Red but its state of the quarks and not usual colors.
Two groups of particles have been found ...Fermions having half integral spin quantum numbers and Bosons having integral spin quantum numbers.their properties are different when they are forming groups in a particular state.
The vector model of these particles treat spins as ankin to classical angular momentum,

 

[Khashishi]

Spin up is just shorthand for saying that the z-component of the angular momentum equals $\hbar/2$. For spin down, it equals $-\hbar/2$. Due to quantization of angular momentum, there are no values in-between. And because the electron has no size, it isn't possible to geometrically torque one up to a higher angular momentum than $\hbar/2$. If we tried, it would become something that wasn't an electron.

 

[saboo_tage]

Spin up is just shorthand for saying that the z-component of the angular momentum equals $\hbar/2$. For spin down, it equals $-\hbar/2$. Due to quantization of angular momentum, there are no values in-between. And because the electron has no size, it isn't possible to geometrically torque one up to a higher angular momentum than $\hbar/2$. If we tried, it would become something that wasn't an electron.

my head is about to explode hahaha
first off, what is the z-component and why does it equal ℏ/2? How is the Planck constant related?
Also, upon reading a bit about quarks and other subatomic particles, I've discovered that the quarks and leptons have 1/2 spin. What does this mean? And what does it mean that the gauge bosons have 0 spin and the Higgs boson has 1 spin?

 

[Khashishi]

You got it mixed up. Gauge bosons have 1 spin. Higgs has 0.

When we say a particle has spin s, what we really mean is that if we measure the angular momentum of the particle along some axis, we will get a result between $-s \hbar$ and $s\hbar$ (inclusive). So, for an electron, it's between $-\hbar/2$ and $\hbar/2$. But the possible values take steps of $\hbar$ so the only possible results are $-\hbar/2$ and $\hbar/2$.

The only gauge boson I'm qualified to say anything about is the photon. What it means is that light carries angular momentum. If an atom absorbs a photon, it also absorbs one $\hbar$ of angular momentum. Generally, this goes into changing the orbital angular momentum of the electron around the nucleus (putting the atom in an excited state).

 

[Khashishi]

By the way, when we have freedom to choose our coordinate system, we typically point the z axis up, which is why we call it spin up/down. It's just a convention, and you can use whatever axes work best for the problem.

 

[saboo_tage]

Oooooh that clarifies a lot
So basically, ℏ/2=1/2 spin?
But the main question I had is still something I can't wrap my head around. What does spin measure? To say that it measures angular momentum makes no sense to me, I associate that with rotation; the rate at which something rotates.
I think that generally what I suffer with is understanding the notation for spin (I can't connect spin up/down with spin 0, 1/2, 1, 1 1/2, 2, etc.) and what the effect of spin is in the real world.

 

[saboo_tage]

Wait never mind, ℏ/2 can't equal spin 1/2 because that would suggest that a particles spin is determined by what particle it is

 

[saboo_tage]

So far I've gotten this: spin up= ℏ/2, spin down=-ℏ/2
I still don't understand spin 0, spin 0.5, spin 1, spin 1.5, etc

 

[saboo_tage]

But let me see if I've got this right: does spin up or ℏ/2 mean that the "north pole" of the atom is pointing upwards on the z axis?

 

[Khashishi]

Spin up means that if we make a measurement of the angular momentum on a vertical axis, we get $+\hbar/2$. You need to just abandon trying to visualize the internal structure.

 

[saboo_tage]

Or wait, I think I understand a bit more now, the spin of a

Spin up means that if we make a measurement of the angular momentum on a vertical axis, we get $+\hbar/2$. You need to just abandon trying to visualize the internal structure.

but then, what is the difference between the 1/2 spin of a quark and the 1 spin of a gauge boson or the 0 spin of a Higgs boson?
Does this mean that the 1 spin is twice as "intense" as the 1/2 spin, and that the Higgs boson doesn't have a spin at all?

 

[Khashishi]

spin 0 means that particle doesn't have any intrinsic angular momentum. Spin 1 means if we make a measurement, we get one of the values $-\hbar, 0, \hbar$. We don't use the terms spin up/spin down for anything except spin 1/2 particles.

 

[saboo_tage]

spin 0 means that particle doesn't have any intrinsic angular momentum. Spin 1 means if we make a measurement, we get one of the values $-\hbar, 0, \hbar$. We don't use the terms spin up/spin down for anything except spin 1/2 particles.

I give up for today
Should never have gotten myself ENTANGLED in all of this
pun intended

 

[nashed]

I want to try and give it a go, so here goes: classically a rigid body can rotate around it's own axis (think of a ball rotating in place) this is it's spin, the rigid body can also perform some rotational movement in space (think of the Earth rotating around the sun), both types of rotations can be quantified using angular momentum.

Now here's a seemingly unrelated concept, a current loop ( literally a loop of some conductor with a current running through) will feel a force under the influence of an external magnetic field, the thing is, if you put an electron in an external magnetic field it will have the same kind of behavior! So an initial model was to imagine the electron as being a sort of charged ball spinning around it's own axis and that's where the name spin comes from, this model is inconsistent with other physical theories and is wrong but the name stuck, nevertheless the electron still has the same kind of behavior under an external magnetic field as a current loop and so we attribute to it some built in angular momentum that causes this interaction with magnetic fields, so that's what spin is, some attribute of a particle that allows it to interact with external magnetic fields. (There maybe other interactions that spin is part of but this is the concept of spin pretty much).

P.S. Spin arises from the mathematics quite naturally when you merge Special Relativity with Quantum Mechanics, so there are ways to predict this property of particles from theory instead of adding it in after observing that it interacts with a magnetic field, in addition, the spin of a particle determines if this type of particle is allowed to bunch up in the same state or if there can be only one particle in each state at a time.

 

[vanhees71]

The most simple definition of spin is the true definition of spin in theoretical physics, which is based on the behavior of the mathematical elements of quantum theory (Hilbert-space vectors and self-adjoint operators representing observables) under the symmetry transformations of spacetime. The operator algebra is the key, and it is determined by this behavior under symmetry transformations. It's a pretty abstract formalism called representation theory of the space-time symmetry group on a projective Hilbert space. What, however, turns out is pretty intuitive. A particle is specified by its mass and spin. A complete set of generalized states is, e.g., given by the momentum eigenvectors, which except for spin 0 are always degenerate. Spin is defined by the representation of the rotation group on the states of a particle at rest. Thus, for a particle at rest, for any eigenstate of momentum $\vec{p}$ you have $(2s+1)$ orthonormal eigenstates corresponding to the spin-z component in the reference frame, where the particle is at rest.

The case of massless particles is more complicated. There for a particle of spin s with $s >0$ you have always 2 helicity eigenstates in a reference frame, where the particle has a momentum in $z$-direction, the possible values for the helicity are $\pm s$.

 

[stevendaryl]

Really? I watched some youtube videos on the topic, they claimed that electrons having angular momentum was ruled out because of that it had to be rotating at the speed of light or something. There was another point against it that had something to do with that if electrons had it, then neutrons have to have had it too, which isn't possible or something. (not quite sure on the last one, it wasn't really explained clearly)

I think that they were saying that, despite the name, spin can't be understood as being due to an electron spinning on its axis. It is still angular momentum, though.

 

[nettleton]

Can somebody tell me whether an electron is aware of its spin? I feel it must be; otherwise how can the law that an atomic orbit must be occupied by electrons of opposing spin be obeyed.

 

[Khashishi]

No, for multiple reasons. Electrons are not "aware", whatever that means. They cannot be treated as individuals which can be distinguished. Rather, they are excitations of the same electron field. An oversimplified bad analogy is this: if you shake a rope attached to a wall, you can get multiple nodes to appear. If you do, the antinodes always alternate (in space): crest-trough-crest. How do the antinodes know to alternate? Well, they aren't independent objects, but part of the same rope.

 

[nettleton]

] 543/.

No, for multiple reasons. Electrons are not "aware", whatever that means. They cannot be treated as individuals which can be distinguished. Rather, they are excitations of the same electron field. An oversimplified bad analogy is this: if you shake a rope attached to a wall, you can get multiple nodes to appear. If you do, the antinodes always alternate (in space): crest-trough-crest. How do the antinodes know to alternate? Well, they aren't independent objects, but part of the same rope.

Consider the approach of two hydrogen atoms to form a hydrogen molecule, I find it difficult to apply a rope analogy. I could visualise a force field between the electrons which has a minimum value when the electrons have opposing spins.

 

[Khashishi]

The point of the rope analogy was not to visualize electrons but rather to move you away from thinking of electrons as classical objects. I did say it was a bad analogy. Your force field idea is wrong. Pauli exclusion principle isn't a force. No amount of energy can make two electrons share the same quantum numbers.

 

[mikeyork]

Let me offer a different description of spin. Spin is an intrinsic SU(2) "charge". When an observer imposes a space-time frame it is observed as intrinsic angular momentum and couples to orbital angular momentum.

 

[ken schatten]

I looked through a number of the previous answers. I think i have a different view, although i think the conventional
ones made may not be so broad as my view...

To me, although one can think of spin, as the type of property one gets from a classical object spinning
(so, it might be thought of as so many revolutions per second),
yet there may be another way to consider spin..

To me, spin can also be viewed as a property of an electron, that we cannot really fathom.
I shall try to explain, and i hope my view, as expressed by me, is not way off the mark.
Spin put simply be a name with a property of having two inherent states (like the baryons and quarks, etc. have:
e.g. that can have a quantiized property, with two choices of the variable,or any combination of this property..
In this view, the "spin" of one half, means that the property can have two properties (yes or no, or up or down, or any other name,
as spin is like the other quantum properties, unfathomable, but
we can work with it, as having two choices (up or down), or a combination of these.
The spin,like other quantum properties can be in a superposition of the variables:eg.
rather than just being up or down, the electron can also be 1/2 up and 1/2 down, etc...
So, the electron's spin is more than the simple spin of classical objects.

Also, the spin # denotes the number of possible states the object can have: so the number
of states, if the spin state has a number say s, then the object can have 2s+1 states, so for
s=1/2, then there 2x1/2 +1 (2 states), so sping up or down. For a larger #, say g, the number
of different states would be denoted by 2g+1..

I looked at what i wrote, and my writings are not as well expressed as i would wish,
but not sure how would make them better.. If this view is 'wrong', I would be happy to
know how, so i can have this (above) view corrected..

 

[Khashishi]

ken, you've lost all of the geometric aspects of the spin. Up and down aren't just arbitrary labels for two states and shouldn't be replaced with blue state and green state. The spin is described by a geometric object called a spinor (for spin 1/2). If an electron is spin up, and you turn your head upside down, it will be spin down. (If you turn your head again a full 360, it will be spin up, but with an extra negative sign compared to the original.)

 

[nettleton]

I think that I can visualise the classical approach to the recombination of hydrogen atoms; only three body collisions between hydrogen atoms and a third body to absorb the heat of combination are successful in forming the molecule when the the electron spins are in opposition. When the spins are similar the 3 entities fly apart.
Consider now the case of an electron attempting via Coulomb attraction to join an unfilled orbit of an ion. What prevents it from violating the Pauli principle?

 

[Khashishi]

If it's an unfilled orbit, then Pauli exclusion principle doesn't apply. If it's a filled orbit, then an extra electron will have to go into a different orbit.

 

[nettleton]

I liked Ken's suggestion of a mysterious property of an electron.
Can you please explain to my simplistic way of thinking why the Pauli principle fails in this case.

 

[Nugatory]

I liked Ken's suggestion of a mysterious property of an electron.
Can you please explain to my simplistic way of thinking why the Pauli principle fails in this case.

It does not "fail". The Pauli principle says that two fermions may not have identical quantum numbers, so it says that you can have two electrons in different orbitals, or two electrons in the same orbital with different spins, but not two electrons in the same orbital with the same spins.

 

[Nugatory]

I think that I can visualise the classical approach to the recombination of hydrogen atoms; only three body collisions between hydrogen atoms and a third body to absorb the heat of combination are successful in forming the molecule when the the electron spins are in opposition. When the spins are similar the 3 entities fly apart.

That's not right. There's no third body required or involved, the energy released by the reaction is not heat (although it may end up as heat eventually, and generally will if our reacting atoms are surrounded by matter). Most important, no matter what the initial state of the electrons we end up with the lowest orbital filled and the electrons having opposite spins - there is no "flying apart" if the spin are in opposition, they just change to allow the interaction to proceed.

Consider now the case of an electron attempting via Coulomb attraction to join an unfilled orbit of an ion. What prevents it from violating the Pauli principle?

You are trying to visualize this with classical thinking, imagining that the electron is a little object that moves around and can approach an ion, or that we could in principle try to force an electron with the wrong spin into an orbital.

However, from a quantum mechanical point of view, the two electrons are not separate particles. They are a single quantum system with a single quantum state, and none of the possible states have two electrons in the same orbital with the same spin. It's like the top and bottom of a rolling wheel; the entire wheel is moving and no matter how it moves the top and bottom will be opposite. It makes no sense to ask if we could make the top of the wheel be at one side while leaving the bottom at the bottom.

 

[nettleton]

'Staff mentor' I am still puzzled by the idea ' that they just change to allow the interaction to proceed'. If that is the action what is the cause?

 

[Nugatory]

'Staff mentor' I am still puzzled by the idea ' that they just change to allow the interaction to proceed'. If that is the action what is the cause?

You are still trying to think of the two electrons as two separate things each with their own spin, so that something has to "cause" one of them to change its spin before the two of them can settle into the same orbital.

I know of no good classical analogies for multi-particle quantum systems (even the phrase "multi-particle" doesn't mean quite what it sounds like, because the word "particle" doesn't mean what it does in ordinary language). The closest I've been able to come up with is the example of a rotating wheel: If you think of two opposite sides of the wheel as two independent objects, it is very mysterious that somehow they are always moving in opposite directions. Once you realize that there is really just one thing there, the wheel, it makes more sense; if the two sides didn't always move in opposite directions it wouldn't be a wheel.

 

[vanhees71]

In other words a many-electron system is always entangled due to the fact that they are indistinguishable fermions and the state must be antisymmetric under interchanging any pair of the electrons (which defines what a fermion is). So it doesn't make sense to talk about any individual electron but you have to consider the entire system of many electrons as a whole.

 

[Khashishi]

It might be useful to look at orthohelium and parahelium. Orthohelium is helium in a state where both electrons have the same spin. Parahelium is helium in a state where electrons have opposite spin. (Normal ground state helium is parahelium.)
There are useful Grotrian diagrams here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.html

If electrons with the same spin were repelling each other with a "force", we'd expect the orthohelium states to have higher energies. Actually they have lower energies. There simply is no state of orthohelium where both electrons are in the 1s state. It's just not a state.

 

[nettleton]

I am beginning to think that I am entering a Zeno paradox. Thus, at what distances does the system of wave functions begin their interaction and how close is this to entanglement?

 

[Khashishi]

Wavefunction, not wavefunctions. There is one wavefunction to describe both electrons.

 

[houlahound]

I believe the frustration emerges from the pioneers choosing the only language they had available to hook new concepts to.

Spin implies something spinning.

Now we know more a new language could be adopted to better reflect our understanding. It would be very productive IMO.

 

[Nugatory]

I believe the frustration emerges from the pioneers choosing the only language they had available to hook new concepts to.

Yes, and we have similar problems with the words "particle" and "observation" - both came into general use before the non-classical nature of the phenomena they attached to was fully understood.

It's a source of never-ending misery for the explainers as well as the explainees

 

[houlahound]

Make a good Insights article, a lexicon of nonclassical objects and phenomenon.

 

[nettleton]

Thanks for all the help offered. However, I am still puzzled by the distance over which two electrons can share a single wave function.

 

[Khashishi]

Basically, if the wavefunctions of the individual electrons don't overlap at all (or negligibly), you can treat them as separate wavefunctions. But if they interact at all, then you have to redo the calculation with a single wavefunction.

 

[akvadrako]

Yes, and we have similar problems with the words "particle" and "observation" - both came into general use before the non-classical nature of the phenomena they attached to was fully understood.

It's a source of never-ending misery for the explainers as well as the explainees

Then why not start coming up with a better language? Seems like you are in the perfect position to ignite such an endeavour. I've been lurking here for a while and it does get annoying to see the same endless arguments over unclear language and the misunderstanding it introduces. Just a suggestion, maybe a kind of moderated wiki of definitions would help.

 

[houlahound]

It's not a simple matter as writing a glossary. It more like writing a functional programming language from scratch. Albeit a most unnatural language to boot.