The third physical property attributed to fundamental particles is spin.
Spin is defined as a phenomenon in quantum physics. Let us first examine the history.
Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924 Wolfgang Pauli introduced what he called a “two-valued quantum degree of freedom” associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can share the same quantum state at the same time.
The physical interpretation of Pauli’s “degree of freedom” was initially unknown. Ralph Kronig, one of Landé‘s assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron’s hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity. Largely due to Pauli’s criticism, Kronig decided not to publish his idea.
In the autumn of 1925, the same thought came to two Dutch physicists, George Uhlenbeck and Samuel Goudsmit. Under the advice of Paul Ehrenfest, they published their results. It met a favorable response, especially after Llewellyn Thomas managed to resolve a factor-of-two discrepancy between experimental results and Uhlenbeck and Goudsmit’s calculations (and Kronig’s unpublished ones). This discrepancy was due to the orientation of the electron’s tangent frame, in addition to its position.
Mathematically speaking, a fiber bundle description is needed. The tangent bundle effect is additive and relativistic; that is, it vanishes if c goes to infinity. It is one half of the value obtained without regard for the tangent space orientation, but with opposite sign. Thus the combined effect differs from the latter by a factor two (Thomas precession).
Despite his initial objections, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics invented by Schrödinger and Heisenberg. He pioneered the use of Pauli matrices as a representation of the spin operators, and introduced a two-component spinor wave-function.
Pauli’s theory of spin was non-relativistic. However, in 1928, Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a “Dirac spinor“) was used for the electron wave-function. In 1940, Pauli proved the spin-statistics theorem, which states that fermions have half-integer spin and bosons integer spin.
In retrospect, the first direct experimental evidence of the electron spin was the Stern–Gerlach experiment of 1922. However, the correct explanation of this experiment was only given in 1927.
It is noticeable that the physical property of spin was first attributed to an exclusion principle that determined that no two electrons can share the same quantum state at the same time. This so-called Pauli exclusion principle is a statement of what has been observed. There is no theory available to back up this principle. In this respect spin is a quantum mechanics property, though it has been attributed as being non-relativistic. Spin was also assumed to be a magnetic momentum that was related to a fundamental particle. The true cause of this spin was (and still is) unclear, but this property has proven to be affected by a magnetic field outside the particle; and the magnetic field generated by the particle itself is shown to be measurable. This possibility is used in MRI apparatus, for example.
There is a lot of theoretical work currently being done on spin and there is not a great deal of value in describing this work in the framework of what will be discussed here. As a result, we take notice of this theoretical work, including the property of spin quantum numbers as described below.
As the name suggests, spin was originally conceived as the rotation of a particle around an axis. This picture is correct, so far as spin obeys the same mathematical laws as quantized angular momenta. On the other hand, spin has some peculiar properties that distinguishes it from orbital angular momenta:
- Spin quantum numbers may take half-integer values.
- Although the direction of spin can be changed, an elementary particle cannot be made to spin faster or slower.
- The spin of a charged particle is associated with a magnetic dipole moment with a g-factor that differs from 1. This could classically if the internal charge of the particle was distributed differently from its mass.
The conventional definition of the spin quantum number s is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 0, 1/2, 1, 3/2, 2, etc. The value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum S of any physical system is quantized. The allowed values of S are:
Based on this spin quantum number, a split is made towards fermions and bosons.
- Fermions have spin of 1/2, 3/2, 5/2 …. ,called half integer spin and are assumed to be matter constituents. They obey Fermi-Dirac statistics.
- Bosons have spin of 0,1,2,…. called integer spin and are assumed to be force carriers. They obey Bose-Einstein statistics.
Spin can be seen as the quantum mechanics notation for the Pauli exclusion principle. If a spin quantum number is 1/2, 3/2, and so on, then the Pauli exclusion principle states spatial restrictions for fermions, and when the spin is 1, 2,… and so, these restrictions are not applicable, as in the case of bosons.
The Dutch Paradigm will clarify the impact of spin on a neutrino and an electron. The history of the discovery of spin behavior is related to measurements on electrons in the outermost shell of an atom. This was translated into the so-called Pauli exclusion principle, stating that no two electrons can share the same quantum state at the same time, but there is no theory as a back-up.
It will be clarified that spin in an electron in the outer shell of an atom induces spinor behavior, while spin in a naked neutrino is responsible for asymmetry in chirality, preferable being left handed. Both phenomena interrelate with the wave/particle duality of neutrinos and photons.