# Why do all elementary particles spin?

1. Feb 1, 2009

### samsara15

Any ideas here? For that matter, why should the spin of each particle always be the same? Or can we do no better than to say they do, and that its spin is a fundamental property of what defines each particle?

2. Feb 1, 2009

### Fredrik

Staff Emeritus
It's a fundamental part of the definition of each particle species. It's a consequence of the postulates of QM and the rotational invariance of space. The rotational invariance is usually imposed by postulating that spacetime is Minkowski space (although this isn't necessary if we're only interested in the spin; we could consider the non-relativistic spacetime as well). This forces us to consider representations of the covering group of the Poincaré group on Hilbert spaces, and it turns out that it's natural to identify each irreducible representation with a possible particle species. ("Possible" because not all of them correspond to particles that exist in the real world). Within each irreducible representation, the spin is the same.

Chapter 2 of Weinberg's QFT book describes this stuff pretty well, but it's not really easy. I still don't fully understand this stuff myself.

3. Feb 2, 2009

### samsara15

Thanks for the references. Not sure I fully understand, but the general drift of your argument is comprehensible enough to give me something to reference.

4. Feb 7, 2009

### Sideways

Figure that out, and you'll win a Nobel Prize.

5. Feb 27, 2009

### abbottsys

"Why do all elementary particles spin?"

If only we knew. The property we call spin is derived from some very deep interaction with spacetime at the quantum level (for which we currently have no physical theory). By the time this interaction is transmitted all the way back up to our macroscopic version of spacetime (for which we do have a physical theory) we see an effect we call "spin".

Spin is a reminder of just how much we don't know.

6. Feb 28, 2009

### alxm

abbotsys: I thought Dirac had explained spin pretty well?

7. Feb 28, 2009

### Bob S

The pion, otherwise called the pi meson, has no spin. The pion is the lightest particle with no spin. There are actually 3 pions, one with zero charge, and two with charge equal to + or - 1 electron (or proton) charge. Their masses are about 1/7 the mass of a proton. They are all unstable (radioactive), and decay into two photons (pi zero) or a muon and a neutrino (pi plus and pi minus).

8. Feb 28, 2009

### malawi_glenn

but pion is no elementary particle..

9. Feb 28, 2009

### humanino

The spin is a symmetry property under rotation. The pion does have spin, it just happens to be zero, and it's quite an important property !

10. Feb 28, 2009

### Bob S

. What about the pi zero, which is its own antiparticle?

11. Feb 28, 2009

### humanino

The pion isospin triplet has one given Lorentz spin of course, the same for the 3 members of the isotriplet. They are pseudoscalars. I don't understand the subtlety here.

12. Mar 1, 2009

### Atakor

The spin is basically a "number" that labels the way the mathematical entities describing a particle (function, vector field,...) transform under a "rotation"..

However to understand why half-integer spins are also possible one has to know a bit of group theory (the fact that we must use SU(2) as a rotational group and not the normal SO(3) )

13. Mar 2, 2009

### Bob S

The lowest mass particle that has isospin I= 0 is the eta particle at mass = 547 MeV. Does the eta have spin, even if its isospin equals zero? Or is isospin = 0 equivalent to having no spin? Is the eta particle an elementary particle?

14. Mar 2, 2009

### malawi_glenn

it is a pseudoscalar meson, isosinglet state.

The physical eta meson is a mixture of the octet and singlet eta-meson.

the singlet eta meson has quark-wavefunction:
(1/sqrt 3) (u,u-bar + d,d-bar + s,sbar)

The octed eta meson has quark-wavefunction:
(1/sqrt 6) (u,u-bar + d,d-bar - 2s,sbar)

So no, the eta is a meson, a composite particle.

And don't mix isospin with spin....

15. Mar 7, 2009

### dangerbird

are all these things figured out in bubble chambers?and by spin are physicists refering to the spiraling patterns left in bubble chambers? lots of questions because im uneducated

16. Mar 7, 2009

### malawi_glenn

NO. LOL.

The reason for why particle make spirals is that charge particles spiral in electric and magnetic fields, it is called the Lorentz Force.

Spin is related to transformation properties under rotation groups.

17. Mar 8, 2009

### dangerbird

dunno half of what you just said but hmm ok. thanks

18. Mar 8, 2009

### malawi_glenn

19. Mar 9, 2009

### cragar

spin is the angular momentum when the particle interacts with other matter.

20. Mar 9, 2009

### malawi_glenn

no not accurate, spin is the rotation transformation property. An non interacting particle also have spin.