# B Simple definition of spin?

1. Sep 13, 2016

### 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 explaination 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?

2. Sep 13, 2016

### 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.

3. Sep 13, 2016

### drvrm

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.

4. Sep 13, 2016

### 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).

5. Sep 13, 2016

### 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?

6. Sep 13, 2016

### 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.

7. Sep 13, 2016

### saboo_tage

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)

8. Sep 13, 2016

### 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.

9. Sep 13, 2016

### 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.?

10. Sep 13, 2016

### drvrm

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,

11. Sep 13, 2016

### 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.

12. Sep 13, 2016

### saboo_tage

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?

13. Sep 13, 2016

### 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).

14. Sep 13, 2016

### 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.

15. Sep 13, 2016

### 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.

16. Sep 13, 2016

### 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

Last edited: Sep 13, 2016
17. Sep 13, 2016

### 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

18. Sep 13, 2016

### 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?

19. Sep 13, 2016

### 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.

20. Sep 13, 2016

### saboo_tage

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