Illustrated Physics
physics, drawn
Concept

Lorentz boost — where it appears

A change between two frames of reference in uniform relative motion, mixing space and time as special relativity requires. Boosts along one direction compose by adding their rapidities, which is why distributions measured along a collider's beam merely shift from one frame to another.

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

The neutrino's energy against the pion's, at four angles. The energy of the neutrino from a pion's decay against the pion's energy, for neutrinos going exactly forward and at 1°, 2.5° and 4° to the pion's line of flight. Straight ahead the neutrino takes a fixed share, 0.427, of the pion's energy, so pions of every energy give neutrinos of every energy. Off axis the curve rises, flattens and falls: at 2.5° it peaks at 0.683 GeV for a pion of 3.2 GeV, and every pion between 2 and 10 GeV gives a neutrino between 0.61 and 0.68 GeV. The flat top is where γθ = 1. Its height, p*/θ, depends on the angle alone — the rest-frame momentum of the decay, 29.8 MeV/c, divided by the angle in radians.

The neutrino energy an angle fixes

A pion breaks into a muon and a neutrino, and the neutrino carries off a fixed 29.8 MeV in the pion's own frame. In the laboratory, straight along the pion's path, it carries a fixed share of whatever energy the pion had, so a beam of pions of every energy makes neutrinos of every energy. Two and a half degrees to one side, something else happens. The neutrino's energy, as a function of the pion's, rises to a maximum and falls again, and around the maximum pions from two to ten GeV all give neutrinos within a tenth of a GeV of each other. An experiment in Japan builds its detector deliberately off the axis of its own beam for that reason — trading most of its neutrinos for the ones at the energy it needs.

relativity · Relativistic dynamics One spray of particles, seen from two frames. Massless particles sprayed evenly in every direction from a source, as distributions in two variables. Left: against the cosine of the angle from the beam axis, for the source at rest (flat) and the same source moving along the axis at 0.8c (peaked forward), which crowds the particles forward until 81 times as many go straight ahead as straight back. Right: the same two sprays against pseudorapidity, η = −ln tan(θ/2). In η the moving spray is the resting one moved over by 1.099, the rapidity of 0.8c, with its shape — ½ sech² η, a peak of 0.5 and a width of 1.76 at half height — unchanged. A boost along the beam that distorts every distribution in angle or velocity only translates a distribution in rapidity.

The angle a collider counts in logarithms

The two proton beams of the Large Hadron Collider meet head on with equal energies, so the collisions ought to happen at rest in the laboratory. They do not. Each collision is really between two fragments of protons carrying unknown, unequal shares of the momentum, and every one is moving along the beam at a different speed. Particle physicists therefore describe what comes out in a variable that a boost along the beam simply shifts: rapidity, the quantity in which speeds add. A detector cannot measure rapidity directly. It measures an angle, and converts it to a logarithm.

relativity · Velocity addition

Named alongside it

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

Centre of mass frameDoppler factorJacobianJacobian peakNeutrino beamNeutrino oscillationParticle colliderPionPseudorapidityRapidityRelativistic kinematicsTransverse momentum

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