Spin is one of the fundamental properties of elementary particles. Electron and its antiparticle positron have spin=1/2. Photon which has no antiparticle has spin 1.

The elementary particles known as fermions and their antiparticles (constituents of matter) have spin=1/2 and the elementary particles known as gauge bosons (the particles that facilitate interaction among fermions) have spin=1. The Higgs boson is special, it has spin=0.

A fermion will impart units of spin angular momentum when it interacts with other particles or fields. The absolute value of the spin angular momentum in units of is used as a short hand notation to indicate fermion nature. We say that fermions are spin=1/2 particles.

A gauge boson will impart units of spin angular momentum when it interacts with other particles or fields. Again, the absolute value of the spin angular momentum in units of is used as a short hand notation to indicate gauge boson nature. We say that gauge bosons are spin=1 particles.

The is not a variable. The is a constant of nature. It is a constant number.

**We do not understand the intrinsic properties**

We classify and categorize the elementary particles in a system labeled by intrinsic properties such as spin and electric charge but we do not really understand these intrinsic properties. The use of group theory for the classification purposes is only the first step towards a complete understanding.

It would be delusional to think that the group theoretic approach to elementary particle theory represents an explanation. Group theory gives us insights but it does not explain the intrinsic properties of particles such as spin and electric charge.

**Non-classical rotation**

Quantum physics teaches us that it is wrong to think of the intrinsic spin as rotation. According to Standard Model of particles electron is a point particle, it has no extension, therefore it cannot rotate in the classical sense, yet it has a magnetic dipole moment. Even though the electron spins in a non-classical way, it still generates a magnetic dipole moment because the charge of the electron is involved in this non-classical rotation.

**Spin of Antiparticles**

The magnetic dipole moment direction of the antiparticle will be the opposite of that of the particle. Let’s place an electron and its antiparticle positron in the same magnetic field. Electron and positron magnetic dipole moments will be aligned in opposite directions. The spin for both, however, is 1/2. In other words, they will both impart units of spin angular momentum when they interact with other particles and fields.

**Chirality**

The handedness or chirality of elementary particles is another fundamental property which is poorly understood. Better understanding of this property will be key to new advances in particle theory.

Electron, muon, tau and the quarks which have spin 1/2 can have left-handed chirality or right-handed chirality but the (electron, muon, tau) neutrinos which also have spin 1/2 exhibit left-handed chirality only. The successful follower of the Standard Model has to explain this phenomenon.

Photons (and spin=1 particles in general) have chirality (handedness) too. The circular polarization of the photon can be either left-handed or right-handed.

Spin and chirality must be intimately related but we do not have a unifying theory yet. When we understand chirality we will know more about the connection between neutrino, electron and photon. We will most probably discover that neutrino, electron and photon are essentially the same. I speculate that they become different when this unknown symmetry is broken. We need to discover this unifying symmetry that relates chirality to spin.

**Chirality and Helicity
**

In the earlier version of this article I tried to explain the concepts of chirality and helicity in more detail. I removed that earlier treatment because there is already an excellent article for general audience. It is hard to beat Tanedo’s version in terms of clarity and entertainment value.

### “Helicity, Chirality, Mass, and the Higgs” by Flip Tanedo

http://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/

**Pauli Exclusion Principle and Bose-Einstein Condensation**

The Pauli exclusion principle states that no two spin=1/2 particles can occupy the same quantum state. The Bose-Einstein condensation refers to the fact that multiple bosons can occupy the same quantum state. Both principles have been experimentally verified.

The nature of the spin=1/2 particle as expressed by the Pauli exclusion principle is intimately related to the creation of space. This principle expresses the space occupying nature of fermions. This is the starting point of some of the modern theories of Quantum Gravity (spin-networks, etc.)

Multiple bosons (photons), on the other hand, can occupy the same space, therefore the force-carrying (spin=1) particles have a non-spatial characteristic at the fundamental level. This has implications for non-locality and the constancy of the speed of light in vacuum.

**Measurements of Chirality and Entanglement**

Speaking of non-locality, let’s discuss the quantum entanglement which is said to exhibit non-locality. Quoting from Wikipedia:

“A positron and an electron are emitted from a source, by pion decay, so that their spins are opposite; one particle’s spin about any axis is the negative of the other’s. Also, due to uncertainty, making a measurement of a particle’s spin about one axis disturbs the particle so you now can’t measure its spin about any other axis. Now say you measure one particle’s spin about the x-axis. This automatically tells you the other particle’s spin about the x-axis. Since you’ve done the measurement without disturbing the other particle in any way, it can’t be that the other particle “only came to have that state when you measured it”, because you didn’t measure it! It must have had that spin all along. Also (although you can’t actually do it now that you’ve disturbed the particle), you could have taken the measurement about any other axis. So it follows that the other particle also had a definite spin about any other axis – much more information than the particle is capable of holding, and a ‘hidden variable’ according to EPR.”

To repeat for emphasis, it is possible to prepare an electron-positron pair occupying a quantum state called a **spin singlet**. The “singlet” state can be thought of as a composite particle that has spin=0. The “singlet” state is also the “zero-chirality” state by definition. The experimental observation is that a pair of particles prepared as a “zero-chirality composite” exhibit “quantum entanglement” and “non-locality”. The “zero-chirality composite” behaves like a spin=0 particle.

What makes quantum reality so different from classical reality? Is it the uncertainty principle? Is it the wave/particle duality? Or, is it the quantum entanglement? The modern view is that quantum entanglement is the quintessential feature of quantum reality. I simply wanted to remind you that “spin” plays a key role in quantum entanglement.

**Non-locality at a Deeper Level**

The key to understanding “non-locality” is the “singlet” state or the “zero-chirality” state. In addition to the entangled electron-positron and entagled photon pairs we have another example. Remember that Higgs particle is a singlet state of the Higgs field. This implies that the Higgs particles which pervade the entire universe make the whole universe connected in a “non-local” way. This is profound!

**Hints for the Physicists**

The spin of a quantum is the fundamental property of the physical existence. The mystery of the spin is profound. The mystery is not limited to the discussion above. There is much more to contemplate.

I hope to inspire physicists to consider the following:

- Spin and electric charge are connected.
- Electric charge and “time” are simultaneous manifestations of a more fundamental process.
- Therefore, spin and “time” are deeply connected.
- Spin may be a manifestation of “mixed-duality”.
- Think about the relationship between spin=1/2 and the square-root of 2. In other words, revisit Dirac’s arguments in a new light.
- Zero-chirality state effectively eliminates the “time effect”, because “time effect” is an objectivation which requires localization/binding which is chirality. When chirality is neutralized “time effect” disappears.

My recent work titled “Golden Biquaternions, 3 Generations, and Spin” provides yet another perspective on the mystery of spin. I show that a particular solution of the golden condition (g – 1/g = 1) for biquaternions and its physical interpretation as the fermion predicts exactly 3 generations and 1/2, 3/2, 2 as the only possibilities for particle spin and hints at the composite nature of bosons. The “golden biquaternion as fermion” idea works if there are 3 fundamental variables that are coupled in a pairwise fashion.

**History of Spin**

For a complete and authoritative history of “spin” property of elementary particles I recommend Sin-itiro Tomonoga’s book titled “The Story of Spin” [1].

Sin-itiro Tomonaga shared the Nobel Prize in physics in 1965 for his work in the development of Quantum Electrodynamics with Richard Feynman and Julian Schwinger. His Nobel lecture is also very interesting.

**References**

[1] Sin-itiro Tomonoga, “The Story of Spin” (“Spin Wa Meguru” copyright 1974, translated by Takeshi Oka), The University of Chicago Press (1997), ISBN 0-226-80794-0