Particle physics (intro)
The idea
Zoom in past nuclei and a compact inventory emerges: matter is built from quarks (which bind in threes into baryons like the proton, or quark-antiquark pairs called mesons) and leptons (the electron, muon, tau, and their neutrinos). Forces are carried by exchange bosons — photons for electromagnetism, gluons for the strong force, W and Z for the weak force — and the Higgs boson reflects the field that gives fundamental particles mass. Every particle has an antiparticle with identical mass and opposite charge.
What makes the subject tractable is that reactions are governed by conservation laws. Energy, momentum, and charge are always conserved, and so are quantum numbers like baryon number and lepton number; a proposed reaction that violates any of them simply does not occur. Because E = mc² lets energy become mass and back, collisions can create particles that were not present before — provided every conservation law is honored, which is why high energies are needed to make heavy particles.
Annihilation does not mean the disappearance of stuff: when an electron meets a positron, their entire rest energy is converted to photons, with nothing lost from the total energy-momentum ledger. And a single photon can never carry off an annihilation at rest — momentum conservation demands at least two photons flying apart back to back.
Worked example
An electron and a positron, each with rest energy 0.511 MeV, annihilate essentially at rest into two photons. Verify which conservation laws permit this, and find each photon's energy and wavelength (use hc ≈ 1240 eV·nm).
- Audit the conservation laws: charge goes from (−1) + (+1) = 0 to 0 — fine; lepton number goes from (+1) + (−1) = 0 to 0 — fine; photons carry no baryon or lepton number, so the reaction is allowed.
- Apply momentum conservation: the initial momentum is essentially zero, so a single photon (which always carries momentum E/c) is forbidden — there must be at least two photons, emitted in opposite directions with equal momenta.
- Apply energy conservation: the available energy is the total rest energy, 2 × 0.511 = 1.022 MeV, shared equally by symmetry, so each photon carries 0.511 MeV.
- Convert to wavelength: λ = hc/E = 1240 eV·nm/511000 eV ≈ 2.4 × 10⁻³ nm, about 2.4 picometers — gamma rays, far more energetic than visible light's hundreds of nanometers.
- Interpret: this back-to-back pair of 511 keV photons is so characteristic that PET scanners detect exactly these pairs to pinpoint where positrons annihilate inside the body — conservation laws turned into medical imaging.
Answer. The annihilation is allowed and must produce at least two photons; each carries 0.511 MeV with wavelength about 2.4 pm, emitted back to back.
Check your understanding
- Why does momentum conservation forbid one-photon annihilation of a pair at rest, but allow it near a heavy nucleus?
- How do conservation laws let physicists rule out reactions without calculating any dynamics?
- Why are higher and higher collision energies needed to discover heavier particles?
- What would running the annihilation backwards (pair production) require, and where does the threshold energy come from?
Build the foundations first
Particle physics (intro) builds on these concepts. If any feel shaky, start there.