Illustrated Physics
physics, drawn
Concept

Cosmic rays — where it appears

Charged particles arriving from space with energies from a million to a hundred thousand million million electronvolts. Their spectrum is a power law over twelve decades, most are protons, and the highest-energy ones cannot have travelled far because the microwave background stops them.

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

A wall pulled away fast leaves the energy behind. The energy of a ball bouncing in a box whose wall is moved, against the length of the box, for 3 wall speeds — each a fraction of the ball's own starting speed — with the adiabatic prediction drawn dashed. Every collision is solved for exactly rather than stepped, so nothing here assumes the wall is slow. Moved slowly, the wall takes energy from the ball at the adiabatic rate, and the energy falls as the inverse square of the length. Moved as fast as the ball is moving, it takes almost nothing: the ball cannot catch a wall retreating faster than it travels, so the collisions stop and the energy stops falling. That is the difference between a gas pushing a piston and a gas expanding into a vacuum, and it is drawn here for one particle. At the end of the range the slowest wall leaves the energy at 0.058 of its starting value and the fastest at 1.000, against an adiabatic 0.065.

The wall that moves while the ball is in flight

Energy is conserved because the rules do not depend on the time. Move the walls of a box and the rules do depend on the time, so what is inside gains or loses without limit — and how much depends entirely on how fast. Moved slowly, a wall takes energy at exactly the rate the adiabatic law says; moved faster than the ball travels, it takes none at all, and the same box is a piston or a vacuum according to a speed.

mechanics · Energy The bath does push back, by an unmeasurable amount. The retarding force on a perfectly absorbing body moving through isotropic radiation at 2.725 kelvin, against its speed, for three areas. Moving through a bath of radiation is not free: the radiation arriving from ahead is blue-shifted and more intense and the radiation from behind is red-shifted and weaker, so the body absorbs more momentum from the front than from the back and decelerates. A square metre at half the speed of light feels 3.7e-14 newtons. That is the reason a preferred frame exists without relativity being violated: the laws are the same in every frame and the radiation is not — it is a physical system with a state, and its state picks out the frame in which it is isotropic, exactly as a body of water does.

The bath that pushes back

Moving through a bath of radiation is not free. The light arriving from ahead is blue-shifted and more intense and the light from behind is weaker, so a body absorbs more momentum from the front than from the back and slows down. That drag picks out the frame in which the radiation is isotropic — without violating relativity, because the laws are the same in every frame and the radiation is not.

relativity · Relativistic thermodynamics

Named alongside it

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

ActionAdiabatic invariantBlackbodyCollisionCompton scatteringConservation of energyCoolingCosmic microwave backgroundDissipationDragEnergyIrreversibility

All concepts