What is Spin?

A fermion will impart \frac{1}{2} \hbar units of spin angular momentum irrespective of its energy when it interacts with other particles or fields. In physics jargon  \hbar is sometimes dropped, we say that fermions are spin=1/2 particles.

A gauge boson will impart 1 \hbar units of spin angular momentum irrespective of its energy when it interacts with fermions. We say that gauge bosons are spin=1 particles.

The \hbar is not a variable. The \hbar 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.  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 charge.

Non-classical rotation

Quantum physics teaches us that it is wrong to think of the intrinsic spin as rotation. According to SM (Standard Model) of particles electron is a point particle, it has no extension, therefore it cannot rotate in the classical sense, yet this non-classical rotation generates a magnetic dipole moment in the case of charged fermions.

Spin direction of charged antifermions

Let’s place an electron and a positron in the same magnetic field. Electron and positron magnetic dipole moments will be aligned in opposite directions. The spin angular momentum magnitude for both, however, is the same which is \frac{1}{2} \hbar.

Spin direction of neutrinos and antineutrinos

All fermions have antifermions. Being fermions, neutrinos have antineutrinos as well. One big difference: neutrinos are mass-less and charge-less.  The spin angular momentum vector of a neutrino points in the opposite direction of its direction of motion. The spin angular momentum vector of an antineutrino points in the same direction as its direction of its motion. The spin angular momentum magnitude for both neutrinos and antineutrinos, however, is the same which is \frac{1}{2} \hbar.

More on spin direction

Do not confuse spin direction with spin magnitude.

Chirality

Quantum mechanical chirality of elementary particles is another fundamental property which is poorly understood. Massive fermions (electron, muon, tau and the quarks) can have either left-handed or right-handed chirality but massless fermions (neutrinos)  can have left-handed chirality only.

Chirality and Helicity

In an earlier version of this article I tried to explain the concepts of chirality and helicity. 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 fermions 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.

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.

Hints for the Physicists

I hope to inspire physicists to consider the following:

  • Spin and electric charge are connected.
  • Electric charge and “time effect” are simultaneous manifestations of a more fundamental process.
  • Therefore, spin and “time effect” are deeply connected.
  • Zero-chirality state effectively eliminates the “time effect”.

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

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