As you all know that Quantum Mechanics tells us that all particles are in fact waves, and that higher the energy of a particle, the smaller the wavelength of the corresponding wave. Everything in the universe, including light and gravity, can be described in terms of particles. These particles have a property called spin.

This is my question: Why does the elemtary particles has the property of spin...

I know that it has spin 0, 1, 2, and 1/2....and I know what it all means....

But I do not know why they have such property....and I don't quiet get what it does....

::snip:: But I do not know why they have such property....and I don't quiet get what it does....

I think that makes the rest of us as well. I'm not aware of any extant theory that explains why spin exists. It is only quantified, not explained at present.

Same goes for charge as well. We know it exists, not why it exists.

all particles live in an irrep of the Poincare group. The allowable irreps of the poincare group are parametrized by two numbers, mass and spin.

What does this mean in layman's terms? The Poincare group is the set of allowable intertial coordinate transformations, and saying that a particle lives in a particular irrep just means that you want particles to be well behaved under coordinate transformations (i.e., if it looks like a particle in one coordinate system, it should look like the same particle in all coordinate systems, though certain quantities may change)

essentially spin simply labels how the particles behave under rotations, which are a subset of allowable coordinate transformations. nothing more mysterious than that.

likewise, mass is simply a number that describes how the particles transform under boosts.

the fact that the spin quantum number takes only discrete values is a consequence of the the compactness of the universal cover of the rotation group in three dimensions. It doesn't happen in, say, 2 dimensions, where the universal cover of the rotation group is noncompact.

Hum,
which is basically saying that those properties are hidden in the tiny fuzzy nature of space-time...

and at the scale of about 10^-35 metres... the apparently smooth fabric of space and time degenerate into a kind of 'foam', a multi-dimensional foam, whos topology, some say, give rise to the all the constants and particle properties in the large four-dimensional Universe we see around us, as described by Einstein's theory of relativity.

hmmm...i thought that Quantum Mechanics stats that particles do not have a axis.....if it doesn't....how does it rotate?


hmm~??~?~?

The quantum spin property does not equate to rotation. "Spin" is just a convenient word... it could as easily have been called "Spix".

The quantum spin property does not equate to rotation. "Spin" is just a convenient word... it could as easily have been called "Spix".
of course spin is related to rotation. spin describes how the particle changes under rotations (as i said above). also, the particle's angular momentum is given by its spin. angular momentum is the conjugate coordinate to angle

hmmm...i thought that Quantum Mechanics stats that particles do not have a axis.....if it doesn't....how does it rotate?


hmm~??~?~?
quantum mechanics makes no such claim. in fact, most particles do have a preferred axis.

Oh!

I've been misinformed.
My apologies.

Oh!

I've been misinformed.
My apologies.
people often say that spin isn't really spin in the classical sense. In other words, it is false to think of the particle as a little spinning sphere. That's true, the electron is not a little sphere which is spinning.

However, spin is called spin for a reason. Besides the fact that you can't treat the particle as if it is actually rotating, it is very much like a spinning top. All the notions that apply to spinning tops also apply to spinning particles, except for the idea that it is rotating. So don't asign its rotation an angular velocity, don't pretend that the surface velocity at the radius is given by r*ω. But do assign it a magnetic dipole moment just like a spinning charge. Do assign it a gyroscopic precession, just like a spinning top. Do assign it some angular momentum, just like a spinning top.

In short, particle spin is very much like the spin of a spinning top. That's why it's called spin and not spix.

It is sometimes also said that spin is a purely quantum mechanical property. This is not true. Classical field configurations also have spin, although since classical fields do not have particles, the analogy with the spinning top is a bit more tenuous.

what is true is that half integer spin is purely quantum mechanical

hum,
anything that has to `<i>spin/spix</i>` round <b>twice</b> to get back to the same position, has to be difficult to envisage (in one's mind).

Whatever it is, The Quantum Spin property cannot be modeled by objects which can be visualized by our classically conditioned minds. Most (all?) of what happens at the Quantum level is counterintuitive.

Whatever it is, The Quantum Spin property cannot be modeled by objects which can be visualized by our classically conditioned minds. Most (all?) of what happens at the Quantum level is counterintuitive.

actually, i think spin is pretty easy to visualize. just imagine an angular momentum vector pointing along some axis of the particle, with all the associated properties of normal angular momentum.

what's hard about that to visualize?