Leptons (electron, muon, tau and their corresponding neutrinos and their anti-particle versions) and quarks (u, d, c, s, b, t quarks and their anti-quarks) belong to a category known as **fermions**. Members of this category are the constituents of matter.

Photons, gluons and W, Z belong to a category known as **gauge bosons**. Members of this category are the force carriers. Gauge bosons facilitate interaction. Photons facilitate the electromagnetic force. Gluons facilitate the strong nuclear force. W and Z facilitate the weak nuclear force.

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.

The 2-valuedness (positive or negative ) of spin angular momentum is not a consequence of the spin=1/2 property. The spin=1 particles can be 2-valued too. Photon is the perfect example. Photon is a spin=1 particle therefore a gauge boson. The polarization (helicity) of photon can be right-handed or left-handed. This is the 2-valuedness of the photon.

The spin=1/2 or spin=1 refers to the amount of spin angular momentum imparted by the particle. The 2-valuedness refers to the rotational sense of the imparted momentum.

After this introduction, let’s now state the mystery. The mass-energies of the particles mentioned above are vastly different. They can have vastly different kinetic energies as well.

- fermions impart the exact same amount of spin angular momentum () irrespective of their energy.
- gauge bosons impart the exact same amount of spin angular momentum () irrespective of their energy.

This is a profound mystery. My dear young physicist, add this to your list.

The newly discovered Higgs particle is a spin=0 particle which makes it very special. Higgs particle is the **only known spin=0 elementary particle** so far. There are theorized particles with spin=0 but they have not been experimentally discovered yet. There are composite particles with zero total spin but we are not talking about composite particles here. On the other hand, one could argue that perhaps there are no truly spin=0 elementary particles in nature. One could argue that the Higgs particle is a composite. We will find out in few years whether the Higgs particle is truly elementary or composite.

I did not mention gravitation and its hypothetical force carrier graviton because the gravitational force cannot be explained by the force carrier paradigm, in my opinion .

Stating the mystery, or appreciating the mystery is half-enlightenment, right? No. Unfortunately, no!

In a previous post, I said, always approach formal/mathematical explanations with caution. If anyone claims that they can explain the mystery mentioned in this post (constancy of spin angular momentum irrespective of energy) as a consequence of a mathematical formalism (geometry of space-time, mathematics of rotations, relativistic quantum mechanics, etc.) does not appreciate the mystery. Yes, the explanation will necessarily involve mathematics but the physicist has to demonstrate that this mystery is a consequence of deeper principles of nature. You start with the deeper more general principles and then invent the most fitting mathematical formalism around those principles. The formalism will have logical consequences. Those are your predictions. This is different from saying that there is no deeper principle, it is just a technical consequence of the existing formalisms. I don’t think so! We need new principles to explain this mystery.

Well…I tried in the my “golden biquaternion as fermion” paper (link given below)

Golden Biquaternions, 3 Generations, and Spin

The central idea of the paper is that the mathematical object ‘golden biquaternion’ may represent the physical object fermion. The ‘golden biquaternion’ is the most fitting mathematical object to follow the consequences of the the new principles mentioned in that paper.

- There are 3 fundamental variables internal to the elementary particle.
- The 3 fundamental variables cannot be expressed in terms of each other.
- The 3 fundamental variables are coupled pairwise.
- There is a conservation law for the 3 fundamental variables.
- The golden condition (g – 1/g = 1) is the primordial generator.

These new principles lead to a particular mathematical formalism (much simpler than quantum mechanics, String Theory or Quantum Field Theory) and the consequences of the new formalism are:

- There are exactly 3 generations (families) for fermions.
- In addition to fermions (Spin=1/2) there may be Spin=3/2 and Spin=2 particles in nature.
- The Spin=1 particles (gauge bosons) and Spin=0 particles (Higgs particle) are composites. They are constructed from Spin=1/2, Spin=3/2 and Spin=2 particles.

**Spin=3/2 and Spin=2 particles have not been discovered yet**. The Spin=3/2 particle is mentioned in theories involving Supersymmetry. The Spin=2 particle is mentioned in the String/M Theory.

The ‘**golden biquaternion as fermion**‘ idea is not a catch-all idea. It has many limitations but it explains the “number of fermion generations” and the constancy of spin angular momentum (irrespective of energy) based on the principles mentioned above.