The Left-Handed Universe

How Feynman and Gell-Mann Overturned the Broken Mirror of Beta Decay

Inside a low-temperature cryostat at the National Bureau of Standards in Washington, D.C., in December 1956, Columbia University physicist Chien-Shiung Wu cooled radioactive Cobalt-60 nuclei to 0.003 Kelvin inside a strong magnetic field. According to the law of parity conservation, any physical process and its mirror image must occur at identical rates. Physicists had assumed that symmetry since the birth of quantum mechanics. Yet Wu's anthracene scintillation counters recorded a stark asymmetry. The spinning Cobalt-60 nuclei spat out beta-decay electrons overwhelmingly in the direction opposite to their nuclear spin axis. Following the theoretical proposal of Tsung-Dao Lee and Chen-Ning Yang, Wu had proved that the weak nuclear force distinguishes left from right.

By the summer of 1957, however, weak-interaction physics remained a confusing tangle of contradictory experiments. In nuclear beta decay, a neutron transforms into a proton, an electron, and an antineutrino. Mathematically, that process could proceed through five distinct relativistic combinations of Dirac spinor currents: Scalar ($S$), Vector ($V$), Tensor ($T$), Axial-Vector ($A$), and Pseudoscalar ($P$). For three years, flagship angular-correlation experiments on the decay of Helium-6 had convinced the physics community that beta decay was governed by Scalar and Tensor ($S$ and $T$) couplings.

Returning to Pasadena from a visit to Brazil in the summer of 1957, Feynman teamed up with his Caltech theoretical colleague Murray Gell-Mann to clean up the mess. At the same time, Robert Marshak and his graduate student E. C. G. Sudarshan at the University of Rochester were attacking the same puzzle. Feynman had rewritten the four-component Dirac equation for a spinning electron in a simpler two-component form using the chiral projection operator $\frac{1}{2}(1 - \gamma^5)$. That operator projects out only the left-handed helical component of every fermion spinor.

When Feynman and Gell-Mann required that every weak-interaction wave function enter the coupling solely through that left-handed two-component projection, the mathematics simplified at a stroke. In three spatial dimensions and one time dimension, multiplying two left-handed spinor currents forces the Scalar, Tensor, and Pseudoscalar terms to vanish identically. Only Vector ($V$) and Axial-Vector ($A$) currents survive, locked together in the universal subtraction $V - A$:

Furthermore, they coupled this left-handed lepton current to the corresponding neutron-proton current. That calculation predicted the lifetime of the muon from the beta-decay constant of the neutron to within two percent. They achieved that match by proposing a conserved vector current analogous to electric charge.

There was only one obstacle: the $V - A$ equation flatly contradicted the published textbook experiments on Helium-6 recoil and neutron decay. Feynman and Gell-Mann read the original experimental papers in the Caltech library and consulted Caltech nuclear experimentalist Felix Boehm. Then they took a bold epistemic stand. They declared in print that three years of flagship nuclear measurements were wrong. Electrons scattering inside overly thick radioactive sources had distorted the recoil angles.

Seeing how a single two-component spinor rule unified neutron decay, pion decay, and muon decay across nature, Feynman felt a rare rush of triumph. He later recalled that night in Pasadena as the single moment when he felt he had glimpsed a newly revealed law of nature in all its elegance and simplicity.

Why had the experimental community stayed stuck on $S$ and $T$ for years? Once an early faulty Helium-6 experiment pointed toward Tensor coupling, succeeding experimenters stopped looking for apparatus errors whenever their data agreed with the expected Tensor curve. When experimentalists at Argonne and Columbia repeated the beta-decay measurements with thinner radioactive sources in 1958, every prior anomaly vanished and confirmed the left-handed V-minus-A current.