Pauli's Missing Arrow — the Neutrino
In 1930, beta decay seemed to break two of the best-tested laws in physics. Here a nucleus at rest decays once inside a spherical detector lined with light sensors, which sees only charged particles: an electron runs to the wall while the nucleus recoils the other way. Added tip to tail, their measured momentum arrows do not return to the start, and the electron never takes all of the energy released. A histogram of 2 000 electrons from the same source shows a continuous spread instead of one sharp line. A switch tests Wolfgang Pauli's idea: add one unseen, neutral particle and see whether both laws hold again.
How to use this simulation
- Energy the decay releases Q — 0.30 to 3.00 MeV, starting at 1.16 MeV (bismuth-210). The decay shown always gives its electron the median energy, so a larger Q means a faster electron and longer arrows, and the histogram rescales with Q. A change redraws the decay at the same moment without starting it.
- Pauli's unseen particle — a two-way switch, without or with. It changes only the bookkeeping: the tracks, the measurements and the histogram stay exactly the same. With it, a dashed arrow closes the momentum triangle, the energy bar fills up to Q and the predicted curve appears on the histogram.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion, on top of the scene's own slowing: 1 ns of the decay takes 1 s.
- Drag anywhere on the scene to look around.
What to look for
- Before you press play, the nucleus sits at rest in the centre: the total momentum is 0 and nothing has left yet.
- The electron is measured when it reaches the wall, 3.9 ns after the decay, and the sensors around the hit light up.
- Without the particle, the electron's and the nucleus's arrows, added tip to tail, stop short of the start: a red gap of 0.71 MeV/c, and the two tracks are 133° apart instead of 180°.
- The electron carries 0.45 of the 1.16 MeV released; the 2 000 recorded electrons spread continuously from 0 to Q, and almost none reach Q, where the dashed two-body line puts them all.
- Switch the particle on: its dashed arrow runs from the tip of the nucleus's arrow straight back to the start, the total reads 0.00 MeV/c and the energy bar fills to 1.16 MeV. The missing momentum, 0.71 MeV/c, and the missing energy, 0.71 MeV, are the same number, as they must be for a particle with no mass.
- Raise Q to 3 MeV: the electron is faster and every arrow longer, yet the gap still opens without the particle and still closes with it.
The physics behind it
Before the decay the nucleus is at rest, so the total momentum is 0, and the decay releases an energy Q, 1.16 MeV for bismuth-210. The electron's kinetic energy T follows the allowed spectrum N(T) ∝ pE(Q − T)², a continuous spread from 0 to Q that peaks near 0.4 MeV. The decay shown gives its electron the median energy, 0.45 MeV, so it leaves at 85% of the speed of light with a momentum of 0.82 MeV/c and reaches the wall, just under 1 m away, after 3.9 ns. If the electron and the nucleus were the only products, momentum conservation would send them apart exactly back-to-back with equal momenta, and every electron would carry T = Q: one sharp line. Instead the measured p_e + p_N is 0.71 MeV/c, not 0, the two tracks are 133° apart, and T is less than Q. Pauli's particle, neutral and massless, takes the rest: an energy Q − T = 0.71 MeV and a momentum of the same size, 0.71 MeV/c, in its own direction. The nucleus recoils with p_N = −(p_e + p_ν), at only about 1.4 km/s because it is so heavy, and the three arrows close: 0 before, 0 after. Pauli proposed the particle in 1930; Enrico Fermi named it the neutrino, and in 1956 Clyde Cowan and Frederick Reines detected it.