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Internal Quantum Numbers: Spin (Article)

The History of Spin:

When was spin discovered?

The first observation of spin came about in the form of the results of the Stern-Gerlach experiment. Conceptualized in by Otto Stern in 1921, and carried out by Walther Gerlach in 1922, it consisted of sending a beam of atoms of silver through a varying magnetic field, and observing the nature of their deflection based on how they impacted a detector screen on the other end of the magnetic field.

Silver atoms were chosen because they are electrically neutral, and thus wouldn't interact with the magnetic field in the same manner that a charged object would. However, silver atoms also possess a single electron in their valence (outermost) shell, which is necessarily charged, and since charged objects in motion produce magnetic fields: in the event that there is angular momentum intrinsic to electrons, there would have a resulting magnetic field, along the direction of the spin, which would then have to be the source of any observed interaction between the greater silver atom, and the magnetic field of the apparatus.

The variation of the magnetic field is necessary, because if the field was of uniform strength, the force of the field would be even on either pole of the magnetic field, and no deflection could be observed. Due to this variation, the field acts on the dipole of the electron, aligning it with the direction of the stronger field, such that the atom is then pulled toward, or away from the stronger field, according to the value of the spin of the electron.

The realization that spin was quantized, was due to the fact that the result of the experiment presented a contradiction of classical physics. Rather than seeing a continuous distribution of impacts on the detector screen, which would result from continuous values for spin, there were two separate lines, indicating that the magnetic field had split the beam into two distinct ones.

The logical explanation for this was that the values for the angular momentum of the electron are non-continuous, or quantized: constrained to a discrete set of values.

Who (theoretically) discovered spin?

Pauli was the first to propose an additional quantum number (the fourth), in order to explain the behavior of atomic orbitals, which seemed to indicate that they could contain, at most, two electrons, suggesting that electrons could only reside within the same orbital, if their respective values for this quantum number was different: this is the exclusion principle.

The issue now was giving physical meaning to this value. There was a general idea that the electron may possess some sort of rotation, around its own axis, with Dirac finally suggesting that if electrons are constrained to one of two possible values, perhaps this explains why orbitals have a "max occupancy" of two electrons.

What were the implications of spin on the rest of quantum physics?

Do all particles have spin?

Yes.

What is spin?

In concise and technical terms, spin is an internal quantum number, of integer or fractional value, representing the internal angular momentum of fundamental and composite particles (as well as), and is a conserved quantity.

It is known from experiment, that this property can be observed by subjecting electrons to magnetic fields, with their spin being inferred from how they are deflected by the magnetic field.

We refer to these various values as +12+\frac{1}{2}, or −12-\frac{1}{2}, due to a peculiar property of the class of particles with half-integral spin, or fermions (to save one that mouthful): these particles are not invariant under 360 degrees of rotation around their axes, as one might expect from our experience of the macroscopic world, but rather require an additional 360 degrees of rotation, for a total of 720 degrees, in order to return to their original position.

Hence, the halving of the spin value relates to the fact that the rotational transformation that we would expect to yield a system that is symmetric to its pre-image, is only half of the transformation required to actually do so.

This observed aspect of nature is highly contradictory to our physical intuition; it serves as a forceful exemplar of the stark difference between quantum and macroscopic reality, and evokes the words of Feynman, that we should "accept nature as She is - absurd", lest we find our mind in tangles trying to impress our daily experiences on aspects of reality that differ from it greatly.

So, now that we have our starting point, we can begin to break down the meaning of terms like conserved quantity, and internal quantum number.

What is the meaning/source of spin?

Referenced in

Internal Quantum Numbers: Spin (Article)