Seonglae ChoThe spin state of an electron up down of a superposition of the two is not a direction in space but an abstract direction in a mathematical space invented to describe the particle. Quantum mechanics does not use real numbers but complex numbers to describe quantum states.
The probabilities are the same whether we consider one state or its opposite. It means that the two opposite states actually represent the same reality and it is impossible to differentiate them with any experiment. It is this subtlety that will finally allow us to understand spin one half. If the object is quantum, the opposite of a quantum state is physically equivalent to it although mathematically different. The idea of a spin half object is therefore allowed within quantum physics. We call the mathematical tool that models it a spinner which is an abstract entity which requires two rotations of space to return to its starting point in the state space.
Electron have spin number one half which means that they can be modeled by a field of Spinners. If we pick an electron at random it will have a state pointing in one direction of its abstract state space. We call this electron’s spin state and physicists have named the axes of this space up and own because electrons in these states are deflected upwards or downwards in the Stern & Gerlach experiment in 1922.
1928 Paul Dirac became interested in the behavior of spinners when we add the dimension of time in the context of relativity. When we change our reference frame which amounts to rotating Spacetime, a spinner rotates accordingly within its abstract space. However it turns out there are two possible behaviors it can react either in one direction or the other. Mathematically, a spinner somewhat behaves like a square root there are two of them one positive and one negative. In the same way, there are two different types of spinners reacting in opposite ways in the direction of time. they correspond to particles and antiparticles. In this way, Dirac predicted the existence of Antimatter.