Illustrated Physics
physics, drawn
Concept

Pair production — where it appears

The creation of a particle and its antiparticle, most often an electron and a positron, from energy — a photon near a nucleus, or two photons colliding. It needs at least twice the particle's rest energy in the centre-of-momentum frame.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The stiffness that falls below four-thirds. The first adiabatic exponent Γ₁ — how steeply pressure rises when a gas is squeezed without heat escaping — of hot oxygen with its radiation and its equilibrium electron–positron pairs, against temperature, at densities of 10³, 10⁴, 10⁵, 10⁶ g/cm³. At 10³ g/cm³ its least value is 1.222, near 1.2 billion kelvin; at 10⁴ g/cm³ its least value is 1.235, near 1.3 billion kelvin; at 10⁵ g/cm³ its least value is 1.285, near 1.8 billion kelvin; at 10⁶ g/cm³ its least value is 1.339, near 3.1 billion kelvin. A star can hold itself up only if its core's Γ₁ averages above 4/3, the value for a gas of light alone; a core that dips below it has no stable size, and the pair production that pulls it below is strongest where the gas is hot and thin — the cores of the most massive stars.

The heat that turns into matter

Thermodynamics counts particles and relativity lets them be made. Heat a gas to a billion kelvin and its light carries enough energy to create electrons and positrons, which the gas then holds in equilibrium like any other ingredient. The heat spent making them raises neither the temperature nor the pressure, so the gas grows soft — softer, in the cores of the most massive stars, than a star can survive. Those stars collapse, ignite their oxygen all at once and blow themselves entirely apart; and the same pairs, vanishing a few seconds after the Big Bang, left the universe's light hotter than its neutrinos by a factor that is the cube root of eleven over four.

relativity · Relativistic thermodynamics The photon a fast electron throws back. The highest energy of a laser photon scattered straight back by an electron it meets head-on, against the electron's energy, for a carbon-dioxide laser, an infrared and a green one, on logarithmic axes: dashed, 4γ² times the laser photon's energy, the double Doppler shift of a mirror moving at the electron's speed; solid, the exact edge with the electron's recoil, E·x/(1 + x) with x = 4γε/mc²; dotted, the electron's own energy, which no scattered photon reaches. A 1 GeV electron turns 1.17-eV infrared photons into gamma rays of 17.6 MeV, within 1.8 per cent of the mirror's figure. At 46.6 GeV and 2.35 eV the mirror's figure is 78.2 GeV, more than the electron has to give; the photon actually comes back with 29.2 GeV.

The photon a fast electron throws back

Shine an infrared laser at a beam of gigaelectronvolt electrons and gamma rays come back out of the collision, each carrying seventeen million times the energy of the laser photon it started as. The electron acts as a mirror moving at nearly the speed of light, and a moving mirror multiplies the energy of light by two Doppler factors. Push the electron's energy far enough and the mirror arithmetic promises photons more energetic than the electron itself — and the photon's own momentum, which the mirror ignored, steps in to stop it.

relativity · Length contraction

Named alongside it

The objects these essays reach for when they reach for this one.

Adiabatic indexChemical potentialCompton scatteringCosmic neutrino backgroundDoppler effectEquation of stateInverse compton scatteringKlein nishinaThe Lorentz factorMass-energyStellar stabilitySupernova

All concepts