The third physical property attributed to fundamental particles is spin.
Spin is a phenomenon in quantum physics. Let’s start by exploring its history.
Wikipedia:
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a factor-of-two discrepancy between experimental results and Uhlenbeck and Goudsmit’s calculations (and Kronig’s unpublished ones).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 is initially linked to an exclusion principle that states that no two electrons can share the same quantum state at the same time. This so-called Pauli exclusion principle is a statement on what is observed. There is no theory available to back up this principle. In this respect, spin is a quantum mechanics property and is assumed to be non-relativistic. Spin was also assumed to be a magnetic momentum related to a fundamental particle. In the prevailing paradigm, the actual cause of this spin was (and still is) unclear. Still, this property has proven to be affected by a magnetic field outside the particle, and the magnetic field generated by the spin-carrying particle itself is shown to be measurable. MRI apparatus uses this phenomenon.
Much theoretical work is currently being done on spin, and there is not a great deal of value in describing this work in the framework of The Dutch Paradigm. As a result, we take notice of this theoretical work, including the property of spin quantum numbers as described below.
Wikipedia:
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:
where h is the Planck constant. In contrast, orbital angular momentum can only take on integer values of s, even values of n.
Based on this spin quantum number, fermions and bosons are different types of fundamental particles.
- 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 is 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 explains how spin affects neutrinos and electrons. The discovery of spin behavior is linked to observations of electrons in an atom’s outer shell. This behavior led to the Pauli exclusion principle, which states that no two electrons can simultaneously occupy the same quantum state. However, there is currently no supporting theory for this.
The spin of an electron in the outer shell of an atom leads to spinor behavior, while the spin of a neutrino without its partner is responsible for left-handed chirality asymmetry. Both of these phenomena are related to the wave/particle behavior of neutrinos and photons.