Physics Lournal

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The Wave Equation

From Page 158

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.

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.

Referenced in

The Wave Equation