Elementary particles such as the electron have the peculiar property that they only become identical to themselves after two complete rotations. Is there any clear explanation for this phenomenon?
All elementary particles have a property that physicists call "spin". Spin can be thought of as the internal angular momentum of a particle. Remarkably, all elementary particles have a spin whose value is a multiple of ħ. The symbol ħ stands for Planck's constant h dived by 2π, whose experimentally measured value is 1,055 · 10-34 Js.
Elementary particles and composite particles whose spin is an odd multiple of ½ħ are called "Fermi particles" or "Fermions". They are named after the Italian nuclear physicist Enrico Fermi (1901-1954). This group includes all the elementary particles that make up the material world, such as electrons and quarks. Fermi particles of the same type cannot have the same properties - this leads to the exclusion principle, named after Wolfgang Pauli (1900-1958), according to which two electrons in the shell of an atom must differ in at least one quantum number.
Particles, on the other hand, named after the Indian physicist Satyendranath Bose (1894-1974) and referred to as “Bosons”, have a spin that is an even multiple of ½ħ. Bosons can match in all quantum numbers. Therefore, light particles (photons) with identical oscillation properties can be superimposed, which is utilized in lasers. In addition to photons, other interacting particles associated with the basic physical forces such as the strong and weak interaction also belong to the bosons.
Fermions and bosons differ in another remarkable way, which the famous physicist Stephen Hawking (1942-2018) illustrated in his book A Brief History of Time with an analogy: 'A particle with spin 0 is a dot: it looks the same from all directions. A particle with spin 1, on the other hand, is like an arrow: it looks different from different directions. Only after a complete rotation (360 degrees) does the particle look the same again. [In addition, there are] particles [...] that do not look the same after one rotation: Two rotations are required! The spin of such particles is given as ½'.
Is there a clear explanation for why fermions with spin ½ħ are identical to themselves only after a rotation of 720°, while bosons with spin ħ have to rotate only 360°?
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