From one vertex to a whole world of events
In the last guides you met QED as a theory built from a single elementary move: the [[electron-photon-vertex|electron-photon vertex]], where a charged particle emits or absorbs one photon. That is lovely as a slogan, but a theory earns its keep by predicting things that actually happen in a lab. So this guide cashes the slogan in. We take that one vertex and watch it generate four of the most famous processes in all of physics — and you will see, again and again, that the *only* thing changing is how a handful of identical dots are wired together.
The four headliners are Compton scattering (light bouncing off an electron), electron-positron annihilation (matter turning into light), pair production (light turning into matter), and bremsstrahlung (an electron radiating light as it is deflected). They sound like four separate chapters of a physics textbook. They are not. Each is just two electron-photon vertices joined by an internal line — the same two bricks, snapped together in a different shape. Learn to read the shape and you can read the process.
Compton scattering: light bounces, and reddens
Start with the gentlest case: a photon hits a loose electron and bounces off. Classically you might expect the light to keep its color, the way a ball keeps its size after a bounce. It does not. The scattered light comes back with a slightly *longer* wavelength — slightly redder — and the redder it is, the sharper the bounce. This is [[compton-scattering|Compton scattering]], and when Arthur Compton measured it in 1923 it was decisive proof that light really arrives in particle-like packets, not just smooth waves.
The picture is just a billiard-ball collision, but between a photon and an electron. A photon carries both energy and momentum, so when it strikes a resting electron it knocks the electron forward, handing over a slice of each. Having given energy away, the photon leaves with less — and for light, less energy means longer wavelength. Apply nothing fancier than conservation of energy and momentum to the collision, treating the photon with its full energy and momentum, and the exact reddening-versus-angle falls right out. It matches experiment beautifully and is gibberish if light is only a wave.
Now read it in QED's alphabet. The electron absorbs the incoming photon at one vertex, travels briefly as a virtual electron, then emits the outgoing photon at a second vertex. Two vertices, one internal electron line — done. Computing its probability, the Compton cross-section, was an early triumph of the theory. And this is not academic: Compton scattering is exactly how X-rays and gamma rays lose energy plowing through matter, which is why it governs radiation shielding, medical imaging, and how light from the hot early universe jostled against electrons.
Matter into light, and light into matter
Compton scattering shuffled particles around; the next pair *transforms* them. In electron-positron annihilation, an electron meets its antimatter twin, the positron, and the two destroy each other — their entire mass converting into pure energy that flies off as photons. In [[pair-production-and-annihilation|pair production]], the reverse: an energetic photon vanishes and an electron-positron pair appears in its place. These are the most vivid demonstrations anywhere of mass-energy equivalence — Einstein's E = mc-squared playing out one particle at a time.
But nature charges admission, and conservation laws set the price. To make an electron-positron pair you must supply at least both particles' rest energy. Each weighs about 0.511 MeV in rest energy, so the photon needs at least about 1.022 MeV — that is the threshold energy for the process. Below it, no amount of trying produces a pair; above it, the surplus becomes the new particles' motion. Annihilation runs the budget the other way: the released energy must reappear as photons, and conservation of momentum is why an electron and positron at rest annihilate into *two* photons flying off back-to-back, not one.
Read these in QED's alphabet and an astonishment appears. Annihilation is two vertices: the electron and positron lines meet, vanish, and two photon lines emerge. Pair production is the *same drawing*, just with which lines are incoming and which are outgoing swapped around. In fact, Compton scattering, annihilation, and pair production are all the *one* diagram viewed from different angles — flip an incoming electron into an outgoing positron, rotate which lines are 'before' and which are 'after,' and one process becomes another. Physicists call this [[s-t-u-channel-processes|crossing]], and it means these are not three theories but one, seen from three sides.
Bremsstrahlung: braking radiation
The fourth headliner has the best name. [[bremsstrahlung|Bremsstrahlung]] is German for 'braking radiation,' and the name says it all: when a fast charged particle is suddenly slowed or deflected, it gives off light. Slam the brakes in a car and the kinetic energy becomes heat in the pads; do the analogous thing to a speeding electron — bend its path hard as it whips past a heavy nucleus — and a slice of its energy is shed as a photon. The deflection is the braking; the emitted photon is the radiation.
Underneath, it is again the one vertex. As the electron is yanked off course by the nucleus's electric field, it accelerates sideways, and an accelerating charge radiates — in the quantum picture, it emits a photon at a vertex. There is one telling difference from the processes above. In Compton scattering or annihilation the photon energies are pinned down by the geometry, but a braking electron can shed *almost any* amount of energy, from a feeble nudge up to its entire kinetic energy. So bremsstrahlung produces a smooth, *continuous* spread of photon energies rather than sharp lines.
rest energy of electron or positron: m c^2 ~ 0.511 MeV
pair-production threshold (photon): E_gamma >= 2 m c^2 ~ 1.022 MeV
bremsstrahlung photon energy: 0 < E_gamma <= electron kinetic energy
(a continuous spread, not a single line)Bremsstrahlung is everywhere in practice. It makes the broad continuous background in every medical and dental X-ray tube, where electrons are fired into a metal target and braked hard. It is the dominant way high-energy electrons bleed off energy as they cross matter, which shapes how detectors and calorimeters work. And it lights up the X-ray and gamma-ray glow of hot cosmic regions, from the Sun's corona to clusters of galaxies. The dentist's X-ray and the X-rays from a galaxy cluster are, at the level of the diagram, the very same little dot doing the very same job.
One vertex, many faces — and what it teaches
Step back and look at the family portrait. Four famous processes, four different photographs, but every one of them is the [[electron-photon-vertex|electron-photon vertex]] repeated and rewired. Compton: absorb a photon, emit a photon. Annihilation: two matter lines meet and become photons. Pair production: that picture run backward. Bremsstrahlung: emit a photon while a nucleus bends your path. The grand variety of electromagnetism is not a long list of separate rules — it is one rule, drawn in different arrangements.
- Sketch the external lines — the real particles going in and the real particles coming out.
- Connect them using only electron-photon vertices, with a virtual line bridging the vertices.
- Check the bookkeeping: charge in equals charge out, and total energy and momentum are conserved.
- Each vertex costs a factor near sqrt(alpha), so more vertices means a smaller, finer correction.
There is a deeper lesson hiding here, and it is the whole reason this rung matters. The fact that you can *draw* a process before you compute it — that a tidy picture made of vertices and lines is a literal instruction for a calculation — is the gift of the [[feynman-diagram|Feynman diagram]], and QED is where it was born. Crossing symmetry, the threshold-energy rule, the continuous-versus-line spectra, all of it falls out of reading those diagrams honestly. This is the template that the strong and weak forces inherited: same vertices-and-lines grammar, richer vocabulary.
One honest closing note, in the spirit of this whole ladder. These diagrams are extraordinarily powerful, but a Feynman diagram is a calculational tool, not a snapshot of reality — the virtual electron in Compton scattering and the recoiling nucleus in pair production are pieces of the math, not little balls you could film. What is real, and tested to staggering precision, are the *answers*: the reddened X-ray, the back-to-back gamma rays of a PET scan, the continuous glow of an X-ray tube. QED earns its reputation not because the pictures are pretty, but because the numbers they yield keep coming out right.