Integer Spin and Half Spin: What's the Difference? (Bosons vs. Fermions)

[lamba89]

bosons have integer spin, fermions have half spin, what does that mean? why bosons (integer spin) is able to avoid pauli's exclusion principle?

 

[SpectraCat]

bosons have integer spin, fermions have half spin, what does that mean? why bosons (integer spin) is able to avoid pauli's exclusion principle?

In non-relativistic QM, spin is [STRIKE]just[/STRIKE] an [STRIKE]arbitrary[/STRIKE] "intrinsic" angular momentum that is added via an additional postulate in order to make the theory consistent with experiment. Furthermore, experiment tells us that some particles have half-integer spin, and others have integer spin, and the two sets (integer and half-integer spins) cannot be inter-converted, because angular momentum is quantized and can only be added to or subtracted from a quantum system in units of hbar.

So in that context, fermions are just *defined* as particles with half-integer spin.

and bosons are just *defined* as particles with integer spins.

Dirac showed that the concept of spin emerges naturally from first principles in the fully relativistic treatment of QM, so it is more fundamental than its original context, which was as a phenomenological "patch" that was applied to fix agreement with experiment.

Regarding your second question, it has to do with the different statistics that are required to handle permutations of indistinguishable particles in bosonic and fermionic systems. In a fermionic system, the overall wavefunction must be antisymmetric with respect to exchange of any two indistinguishable particles ... this gives rise to the Pauli exclusion principle. In bosonic systems, the overall wavefunction must be symmetric with respect to exchange of any two indistinguishable particles ... for spin-0 bosons, this allows all of the particles to collect in the ground state at very low temperatures .. this is the known as a "Bose-Enistein condensate" or BEC. You can read more about it http://en.wikipedia.org/wiki/Bose-Einstein_statistics" .

 

[dextercioby]

In non-relativistic QM, spin is just an arbitrary "intrinsic" angular momentum that is added via an additional postulate in order to make the theory consistent with experiment.[...]

First of all, spin is not arbitrary, it's precise, while the whole <theory> (definitions & axioms) can be reformulated consistently, so that the concept of spin appears naturally.

[...]Dirac showed that the concept of spin emerges naturally from first principles in the fully relativistic treatment of QM, so it is more fundamental than its original context, which was as a phenomenological "patch" that was applied to fix agreement with experiment.[...]

Over the years one has learned that any <first principles of the fully relativistic treatment of QM> lead to insurmountable problems whose only resolution is a quantum theory of fields. In no way is the spin a <phenomenological patch> in non-relativistic QM, but rather a necesary concept to explain some non-classical angular momentum appearing from some properly written equations & axioms.

 

[ZealScience]

I think spins only matter while dealing with more than one particles. It is added by Pauli himself, simply to solve the dilema of Bohr's model. It is the fourth quantum number added to the principal QN and other two angular QNs, in Schrodinger's Equation. I think it has something to do with the geometry of the particle (not the old geometry, but quantumnized geometry, I don't understand either).

If you wnt to know the fundamental idea, then wait until string theory or other super unified theories are completed. Those theories are invented just to explain the difference between particles and explain the interaction between them.

 

[SpectraCat]

First of all, spin is not arbitrary, it's precise, while the whole <theory> (definitions & axioms) can be reformulated consistently, so that the concept of spin appears naturally.

You are right, it was incorrect to describe it as arbitrary. I have edited my post accordingly.

Over the years one has learned that any <first principles of the fully relativistic treatment of QM> lead to insurmountable problems whose only resolution is a quantum theory of fields. In no way is the spin a <phenomenological patch> in non-relativistic QM, but rather a necesary concept to explain some non-classical angular momentum appearing from some properly written equations & axioms.

Please note that I only claimed that it was originally included as a phenomenological patch to explain the observed anti-symmetric properties of electronic wavefunctions. I believe that is historically accurate, but perhaps it is only anecdotal.