Tuesday, March 15, 2016

spin Since swapping two identical particles of the same energy makes no physical difference to the overall state, you have to add up the two different cases (swapped and unswapped) when calculating the actual real probability of a physical state occurring

Since swapping two identical particles of the same energy makes no physical difference to the overall state, you have to add up the two different cases (swapped and unswapped) when calculating the actual real probability of a physical state occurring. Adding the plus and the minus in the fermion case gives zero, but in the boson case they really do add up. This means any state containing two identical fermions of the same energy has zero probability of occurring*. Whereas a state with two identical bosons of the same energy has an enhanced probability.


Bosons and Fermions

The difference between bosons and fermions is just spin. But in physics, this is a fundamental difference. Bosuns and bosoms are of course completely different again

The word boson causes no end of trouble when people report about the search for the Higgs boson. It regularly gets spelled or pronounced "bosun", and once while being interviewed on TV and reading the autocue over the presenter's shoulder, I saw it spelled as bosom. The presenter, however, said boson without blinking.
Decorated pigtails
 Jon Butterworth/JMB

Boson is the name for a generic class of particles. The Higgs boson is one (if it exists) but so are many other particles. All the particles which carry forces (gluons, the W and the Z and the photon. Also the graviton, if there is one.) are bosons.

Quarks, electrons and neutrinos, on the other hand, are fermions.
Advertisement
The difference between them is just spin. But in this context, spin is a quantum number of angular momentum. It is a bit like the particle is spinning, but that is really just an analogy, since point-like fundamental particles could not spin, and anyway fermions have a spin such that in a classical analogy they would have to go round twice to get back where they started. Quantum mechanics is full of semi-misleading analogies like this.
Regardless, spin is important.
Bosons have, by definition, integer spin. The Higgs has zero, the gluon, photon, W and Z all have one, and the graviton is postulated to have two units of spin. Quarks, electrons and neutrinos are fermions, and all have a half unit of spin.
This causes a huge difference in their behaviour.
The best way we have of understanding fundamental particles is quantum field theory. In quantum field theory a "state" is a configuration describing all the particles in a system (say a hydrogen atom). The maths is such that if you swap over two identical fermions with identical energies (say, two electrons) then you introduce a negative sign in the state. If you swap two bosons, there is no negative sign.
Since swapping two identical particles of the same energy makes no physical difference to the overall state, you have to add up the two different cases (swapped and unswapped) when calculating the actual real probability of a physical state occurring. Adding the plus and the minus in the fermion case gives zero, but in the boson case they really do add up. This means any state containing two identical fermions of the same energy has zero probability of occurring*. Whereas a state with two identical bosons of the same energy has an enhanced probability.
Advertisement
This fairly simple bit of maths is responsible for the periodic table and the behaviour of all the elements.
Chemical elements consist of an atomic nucleus surrounded by electrons. Because electrons are fermions, not all the electrons can be sucked into the lowest energy level around the nucleus. If they were, the probability of that "state" happening would be zero, by the argument above. So as more electrons are added around a nucleus, they have to sit in higher and higher energy levels - less and less tightly bound to the nucleus, in general. The behaviour of a chemical element - how it reacts with other elements and binds to form molecules, and where it sits in the periodic table - is driven by how tightly bound its outermost electrons really are.
When bosons clump together they do some fascinating stuff too, but it's hard to beat being responsible for the whole of chemistry, and therefore biology.
Still, it's only spin.

* This is known as the Pauli exclusion principle.

No comments:

Post a Comment