What exactly does spin mean when talking about quantum physics?

[A.I.]

I've been reading a bit about electrons and quarks, and each has been, at one time or another, described as having a certain amount of 'spin'; when I think of spin, I imagine a spherical object rotating around some central axis--this can't be correct, can it? Can an electron really... move in any sort of way? What exactly does spin mean when talking about quantum physics?

 

[rohanprabhu]

well.. yes.. some particles do have something we call 'intrinsic angular momentum'. In classical mechanics, 'Angular momentum' is associated with rotation along an axis [as u said]. In quantum physics, a 'rotation' is not asserted. It is just that the 'intrinsic angular momentum' is a property of that particle.

It is because, in quantum physics, particles like 'electrons' are true point particles. They cannot be made up of smaller particles which revolve around an axis and constitute an electron.

 

[Marco_84]

I've been reading a bit about electrons and quarks, and each has been, at one time or another, described as having a certain amount of 'spin'; when I think of spin, I imagine a spherical object rotating around some central axis--this can't be correct, can it? Can an electron really... move in any sort of way? What exactly does spin mean when talking about quantum physics?

To think about it in a naively way it is fine...
But to better get the meaning of what spins is u should read abou stern and gerlach experiment...
Thinking about an elctron as a spinning little ball is missleading... because until now there are no experimental proves that electrons have volums. IN our theory they are dots.
Making experiments the first sperimentalist understood that electrons have one more degree of freedom besides the translations ones...
and to figure that out they imagined a a spinning ball.

But being rigorous an electron Spin is just a two dimensional Rapresentation of the SU(2) group since the value of the spin for that kind of fermion is S=1/2.

In fact whene you diagonalize along Lz/Lx/Ly you get two states (say up or down,+,-) which are the two basis vectors of C.

Finally you can say that an Hilbert space for a particle is L2(R^3)XC^(2s+1).

I hope that helped you.

im sorry 4 my english.

 

[Tanja]

You can also regard the spin of an electron as the magnetization vector. An particle like an electron has many properties and one is, that it can lead to magnetism in solids. The spin is responsible for this specific property. In a magnetic field the magnetization vector begins to oscillate around the axis of the magnetic field. In classicle physics it is known as "Bloch equation" which is a set of 3 differential equation, one for each space coordinate (real space!). But there's no way to describe e.g. spin-spin coupling classicle. You have to turn to quantum physics.

In quantum mechanics the spin is represented with Pauli Matrices (Spin matrices) and these matrices rotate in the so called Bloch sphere (complex space!).

So, it's not the electron that rotates, it's the spin.

The spin in quarks ... I'v know idea what they are doing, but the mathematics should be similar as explained above: representations of SU(2) groups and I can remember that they obey the Lie Algebra.

 

[A.I.]

Ahhh, that makes sense, all but the formulaes in your response, Marco. Thank you for the help!

 

[Edgardo]

Hi A.I.,

in an older thread here I tried to explain what spin is (see my post #7). Maybe you will find it useful.