= Stern-Gerlach historical and modern interpretations
{c}
The 1922 interpretation concerned <space quantization> of atomic <magnetic moments> in the old <quantum theory>. The modern electron <spin> proposal came in 1925; the original observers did not identify intrinsic electron <spin> as the cause of their splitting. An orbital interpretation then seemed plausible, but the later <spin> explanation gives a different account of the same two-component evidence.<The Stern-Gerlach Experiment and the Electron Spin by Sandip Pakvasa>[Pakvasa, pp. 1–3: original orbital interpretation, 1925 spin proposals and later reinterpretation]{ref}
Modern atomic data assign neutral <silver> the <ground state> <electron configuration> $[\mathrm{Kr}]4d^{10}5s$ and electronic term ${}^2S_{1/2}$. The filled <electron shells> contribute zero net electronic <angular momentum>; the outer <unpaired electron> has <orbital angular momentum> $L=0$, <spin> $S=1/2$, and electronic total <angular momentum> $J=1/2$. The <magnetic quantum number> has two values $m_J=\pm1/2$.<Handbook of Basic Atomic Spectroscopic Data by Jean E. Sansonetti and William C. Martin/Atomic Data for Silver (Ag)>[Handbook of Basic Atomic Spectroscopic Data by Jean E. Sansonetti and William C. Martin; Ag I ground-state configuration and term; electronic J, distinct from isotope nuclear-spin rows]{ref}
In the effective electronic description,
$$
\mu_z=-g_J\mu_B\frac{J_z}{\hbar},\qquad
J_z|J,m_J\rangle=\hbar m_J|J,m_J\rangle,\qquad
\mu_z\simeq\mp\mu_B\quad(g_J\simeq2).
$$
The minus sign matters: for positive $G$, the component with $m_J=+1/2$ has negative electronic <magnetic moment> and deflects toward negative $z$ in our coordinates. Calling the upper spot “spin up” without specifying the <magnetic field> and channel calibration can therefore reverse the assignment. The <total angular momentum operator> here sums electronic <orbital angular momentum> and electronic <spin>; $J$ is not a claim that the <atomic nucleus> has no <spin>. <Hyperfine structure> and nuclear <magnetic moments> can require additional internal levels, so a two-channel electronic approximation must be justified for the field and resolution being used.
This is a neutral <atomic beam>, not a beam of free <Electrons>. The deflected <mass> in the flight equations is the entire <silver> <chemical atom>; its dominant electronic <magnetic moment> supplies the state-dependent <force>. Replacing that atom by a free <Electron> would also introduce the charged particle's <Lorentz force> and a different preparation problem. The ideal two-state model is useful because it isolates the connection between discrete internal components and spatially resolved outputs; it does not retroactively turn the 1922 deposit into a direct contemporary identification of intrinsic electron <spin>.
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