Why some particles are fractional spin?

If you want to divide particles which are rather known as elementary particles you would want to divide them into two types. The Fermionic or Bosonic particles. These are also called matter particles (Fermionic) and Force Carrier particles (Bosonic). The matter particles always exist as half-integral particles. That is, our favorite electrons, protons etc {proton is strictly not elementary, it is built from more elementary constituents called quarks} are spin-1/2 or multiples of spin-1/2 in characteristics. That means some of these particles will be 1/2, some will be 3/2 and so on. {Their spin would be 1/2, 3/2, 5/2 etc} The other kinds of particles called Force carriers would be spin 1, spin 2, spin 3 etc.

Why spin-1/2? Why a fractional spin? Its perhaps also related mathematically at-least that particles could have fractional charges. But for spin, particles are often defined by many properties, among them, mass, spin, charge and quark content and polarization of quantum states, strangeness and other quantum numbers. So particles can share a spin space.

What would be a spin space like? Whats a simple space like? Its like a football field. If there are 11 players in the field, then the field is divided between 11 players. Its shared by 11 players. You can have various regions carved out for various players who are sharing the region in a dynamical way. Its similar with the particles. If 3 people live in a house then they share 1/3rd of the house. If a bunch of particles are available in a spin-space, a spin space is a part of a Phase-space, ( phase space is defined here) then the particles will have either integral or fractional spins. Turns out that all particles we know are therefore categorized into these two ways: 1/2, 3/2, 5/2 … and 0, 1, 2, 3 .. and so on. Example: electrons are spin 1/2, photons are spin 1. (spin 0 is called scalar particles and spin 1 is called vector particles)

When particles are going into a “crammed” spin-space they can only share the amount of spin available. Much like two people fitting into a piece of cloth, if not many clothes are available. But only when more spin-space is available they can go into “open or free” spin-space. So perhaps a particle with fractional spin is like one part of the spin-space and another particle covers the other part of the spin-space. Then the other particle may or may not cover an integral amount of the spin-space. This is due to how mathematics and Physics have defined their units. Elementary particles are studied in terms of h-cross. If that is redefined then the spin-value will be altered. Then spin-1/2 can become spin 1 and as a result spin 1 will become spin 2 but spin 3/2 will become 3. What if h-cross is redefined to be 1/4, then spin-1/2 will be spin 2. But if h-cross is redefined as h-cross / 2 then spin 1 will become a spin 1/2 particle. But that would entail changing everything and on top of that such a scheme may not be warranted.

So spin 1/2 or spin-3/2 particles are clumped together. Which is why this behavior. Because the other types of particles which are only less in number have integral spins, they carry the force over large and un-clumped distances in spin-space. The spin angles in the phase space is integrally divided and these particles are free enough to be seen in those free windows. But for fractional spins, they have to share the spin, simply because there are too many particles. In terms of spin their head and tail are not free from each other. Much like in prison.

Perhaps when particles are produced we see them while the spin is still being customized. So they come out in half spins much like you can go to a drama in half-patloons.