Undergrad Need Help on Particle Spin

[LarryS]

TL;DR

Why do particles spin all the time?

All elementary particles have an intrinsic spin/angular momentum. The fact that particles spin at all is due to Special Relativity. How MUCH they spin, half-integer multiples of reduced Planck's Constant, is due to Quantum Mechanics. Right?

Apparently, the reason particles spin at all is because two non-colinear Lorentz Boosts are the same as one Lorentz Boost followed by a rotation. How do you go from that to all particles spin all the time?

Thanks in advance.

 

[PeterDonis]

All elementary particles have an intrinsic spin/angular momentum.

Except those that don't, such as the Higgs. Unless you're counting spin zero as having "intrinsic spin/angular momentum".

The fact that particles spin at all is due to Special Relativity.

Why do you think this?

How MUCH they spin, half-integer multiples of reduced Planck's Constant, is due to Quantum Mechanics. Right?

There is a spin-statistics connection which is believed to be due to quantum field theory, that particles with integer spin are bosons and particles with half-integer spin are fermions.

Apparently, the reason particles spin at all is because two non-colinear Lorentz Boosts are the same as one Lorentz Boost followed by a rotation.

Where are you getting this from? Do you have a reference?

 

[JimWhoKnew]

TL;DR Summary: Why do particles spin all the time?

All elementary particles have an intrinsic spin/angular momentum. The fact that particles spin at all is due to Special Relativity.

In addition to #2:
Elementary particles don't spin. Many of them have non-classical degrees of freedom which are named "spin", because their quantum behavior under application of Lorentz transformations (especially spatial rotations) resembles that of angular momentum. The polarizations of light are a well known example of spin. They readily appear in the classical treatment when we regard light as EM waves. You know that a linear polarization of an EM plan-wave in vacuum doesn't "spin", right?

Apparently, the reason particles spin at all is because two non-colinear Lorentz Boosts are the same as one Lorentz Boost followed by a rotation.

Could it be that you are confused between spin and Thomas Precession?

 

[pines-demon]

How do you go from that to all particles spin all the time?

This question looks like if you were asking for why are particles spinning, do not confuse spin (intrinsic quantum property) with spatial rotation, particles cannot rotate.

 

[DEvens]

Spin is angular momentum. Electrons in atoms can change their quantum states by flipping from up to down and at the same time changing their orbital quantum state and emitting or absorbing a photon.

The unit of half-h-bar arises from representations of the symmetry group involved. Specifically the rotational part of the Poincaré group. (Brace yourself. I'm linking a wiki page.)

https://en.wikipedia.org/wiki/Poincaré_group.

Group theory is a lovely but very large subject. But, in extremely shortened form, a particle sits in a representation of the group. It changes into a symmetry related version of itself under rotations. Under rotation, an electron changes into an electron with spin pointing differently. If it didn't sit in a rep then rotations would split up the parts that did sit in reps.

Electrons, being spin half, require 720 degrees of rotation to get back to their original configuration. Photons only require 360 degrees. This is related to the Pauli exclusion principle. But, as I said, this is a very large and very lovely subject. Group theory is one way to deal with a large category of symmetries. And symmetry is one of the more powerful means of understanding things.