This page offers an accessible introduction to the mystery of particle lifetimes.
Every elementary particle has its own characteristic mass and lifetime. Electrons appear to be essentially stable, and their mass is about 0.5 MeV. Protons are also extremely long-lived; if they decay, their lifetime has not yet been measured. Their mass is about 940 MeV. If we imagine the electron’s mass as 0.5 g, the proton’s mass would correspond to about 940 g.
High-speed protons travel through space as cosmic rays. When these protons collide with atoms in Earth’s atmosphere, they produce many other particles, including tau leptons and muons.
The tau lepton behaves somewhat like a heavy electron, but its mass is about 1800 MeV. In the everyday mass analogy above, that would be about 1800 g. Its average lifetime is only about 300 femtoseconds (1 fs = one quadrillionth of a second). Tau leptons decay into electrons and neutrinos.
Muons also resemble electrons. A muon’s mass is about 100 MeV, or about 100 g in the same everyday analogy. Its average lifetime is about 2 microseconds (1 μs = one millionth of a second). If the tau lifetime were scaled up to 1000 years, the muon lifetime would be about 700 million years. Muons also decay into electrons and neutrinos.
Light travels about 600 m in 2 μs. Since a muon’s lifetime is also about 2 μs, it seems at first that a muon should not be able to travel much farther than 600 m. In reality, however, muons produced high in the atmosphere can travel more than 6000 m and still reach the ground. This is explained by special relativity: for a fast-moving muon, time is dilated, so it survives longer as seen from Earth.
| Particle | Mass | Lifetime |
|---|---|---|
| Electron | 0.5 MeV (0.5 g) | Stable |
| Proton | 940 MeV (940 g) | Unknown |
| Tau | 1800 MeV (1800 g) | 300 fs (1000 years) |
| Muon | 100 MeV (100 g) | 2 μs (700 million years) |
The fact that particles have finite lifetimes is itself remarkable. A candle’s lifetime is determined by the amount of wax it contains, but a particle’s lifetime is not fixed in advance. A particle that has existed for 1000 years looks exactly the same as one that has existed for 700 million years. In that sense, a particle has no memory of its age.
Instead, each unstable particle decays with a fixed probability per unit time. We can picture the particle as “rolling a die” once every second:
Of course, the die is only a metaphor. How does the particle actually “roll the die,” and how short is the interval between one chance of decay and the next? I suspect that the interval is extremely short—perhaps as short as the smallest possible tick of time.
Clearly, there is still much we do not understand about particle decay.
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