My Final Post EVER On Electron-Spin (Dear God Let It Be So!)

rep electr

So, from about 1916 to 1926, spectral lines were explained by a combination of three or four Quantum Numbers — specifying: 1) Electron orbit size, 2) Electron orbit angle, 3) Electron orbit shape [or possibly Total Angular Momentum], and 4) some other atomic configuration characteristic, which Pauli insisted was a variable which could only be one of two values and which was solely a property of Valence Electrons.

In 1926, however, theorists attempting to imagine what this fourth Quantum Number could be, began to reinterpret it, not as an orbital property, but as a physical property of the Electron, itself– namely, the rotation of the Electron about its own axis… called from the start its “Spin.”

I think our author Arabatzis makes one of the best unintentional puns in physics-writing when he says that the proposal of Spin “was a turning point in the history of the Electron’s representation.” Before Spin, the Electron could be thought of as “point particle.” It could move up-or-down, side-to-side, or back-and-forth– three degrees of freedom. However, by suggesting that the Electron had enough corporeality to spin about its own axis, theorists bestowed upon the Electron an additional, fourth, degree of freedom, and this helped to explain some of the magnetic splitting of spectral lines which scientists were toying around with at the time in their incredibly expensive playrooms.

I won’t go deeply into the history of Spin here, as I’ve covered it in other posts. You may, however, wish to remember, as a bit of conversational trivia, that the first guy to propose Spin (Ralph Kronig, 1925) was ridiculed so badly by Wolfgang Pauli that he backed away from the idea and did not publish. The next year, a two-man team (Goudsmit and Uhlenbeck) published the same idea, having come up with the notion independently from Kronig. As a footnote to this trivia– and perhaps being a case of sour grapes– the original inventer of Spin, Kronig, latter renounced the idea and tried to poke holes in the theory.

One tiny problem with the addition of Spin into the physicists’ evermore complicated and exotic Wonderland of the atom, is that, well, it doesn’t work. You see, physicists like Bohr, desperately seeking patches to cover the gaping holes in their frentic, ad hoc theory-making, had already accepted the validity of the theory of Relativity and inserted it into the world of atom. Once Relativity was accepted as applicable to the sub-atomic world, everything (supposedly) in the atom now had to come to terms with it– everything must be interpreted or reinterpreted in light of Relativistic effects (actually, it’s not uncommon to find physicists ignoring Relativity when dealing with simplified models).

Spin came late to the atomic story-telling game and had to fit into the formulas and equations already accepted by the atom-imagining clique. When physicists attempted to drop a tincture of Spin into their cauldron of guesses, they found that the runes of their complicated equations predicted that, if an Electron actually rotated in reality, then its surface would have to move faster than the speed of light.  Yikes– this is not allowed by the theory of Relativity which the theorists had already invited behind the Looking Glass and into their atom.

Also, when Goudsmit and Uhlenbeck (not to be confused with Rosencrantz and Guildenstern) sought a critique of their theory from the venerated Lorentz, the old sage patted them on the foreheads (figuratively) and informed them that the magnetic energy created by a rotating Electron would be so large that the Electron would have to have a mass larger than the proton.  This was a bit of a problem since one of the playing-cards in the towering atomic house built by quantum physicists states that the electron is hundreds and hundreds of times smaller than the proton.

Arabatzis tells us that these problems were “solved” when physicists later denied “that Spin represented a literal rotation of the Electron.” Well, except when the idea of a spinning Electron helps to explain certain magnetic phenomenon… Talk about having your cake and wearing it like a schmuck, too.

One situation in which the split-personality of the spinning/not-spinning Electron is in evidence is in the work of Heisenberg. Heisenberg had found, in his calculations of Spin effects, that the incorporation of Spin into the atom model predicted spectral line-splitting which was perfect– except for the fact the Spin-model produced values twice as large as the spectral line-splitting actually being observed in laboratories.

To put a patch over this latest problem, both Kronig and Einstein, independently it appears, suggested that, in the frame of reference of the rotating Electron, the atomic Core appeared to be moving to the Electron– as the Sun appears to us to move around the rotating Earth. And since moving charges create a magnetic field, this would give the Core lodged in the center of the atom (but moving, Relativistically speaking, around each Electron!) a magnetic field. This magnetic field would interplay with the magnetic field generated by the spinning Electron… 

L.H. Thomas said– hello!– all this magnetic interaction between the revolving-but-not-revolving Core and a spinning-but-not-spinning Electron will create a “Relativist precession” of the Electron’s orbit.  And –obviously!– “the conjunction of this Relativistic effect with the Spin-field interaction” will eliminate “the unwanted factor of two” by which the Spin-math was off. Duh.

Arabatzis says that these Relativistic and magnetic interpretations of the Electron’s rotation proved “crucial for the reception of Spin”— even convincing Pauli that his fourth Quantum Number could be allowed to become synonymous with Spin. I guess no one had the guts to explain to the caustic Pauli that the Electron was not really, you know… spinning.

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