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.