Illustrated Physics
physics, drawn
Concept

Arrow of time — where it appears

The asymmetry between past and future in a world whose microscopic equations have none. It is always traceable to a condition rather than to a law — an initial state in thermodynamics, a boundary at infinity in electromagnetism — which is why finding which condition is the whole of the question.

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

Runs that break the second law, and how often. The work done in a process repeated many times, and the same for the process run in reverse with its work reflected, for a free-energy change of 4 kT and a dissipation of 3 kT. The average work exceeds the free-energy change, which is the second law, and individual runs do not have to: the shaded tail is the fraction of runs that do less work than the free energy — trajectories in which the entropy of the universe went down — and it is 11.03% here. The two curves cross exactly at the free-energy change, whatever the dissipation, which is what makes an irreversible measurement able to report an equilibrium quantity.

The second law, with a probability attached

Entropy increases, on average. For a small system pulled quickly, individual runs go the other way — and how often is not a matter of taste but an exact number, fixed by a relation with no adjustable constant in it and no requirement that anything be near equilibrium.

thermodynamics · Entropy Two solutions, and nothing in the equations to choose between them. A spherical pulse leaving a point and a spherical pulse arriving at one, each drawn at three times 0.35, 0.6, 0.85 in units where the speed is one. Both are exact solutions of the same wave equation, which is checked here by differencing the drawn samples twice in space and twice in time and requiring the residual to vanish for each. The one on the left is what is always used; the one on the right is discarded, and the equations do not do the discarding. The incoming pulse grows as it converges for the same reason the outgoing one decays as it spreads — the same energy through a smaller sphere — and it is as consistent with conservation as its mirror image is.

The solution that is thrown away

Maxwell's equations admit a field that converges on a charge exactly as readily as one that leaves it, and nothing in them prefers either. Retardation is a boundary condition rather than a law. Which boundary condition is right has been argued about for a century, one of the answers makes the arrow of time a property of there being absorbers, and the laboratory version of the question — whether an atom emits at all — has a measured answer that depends on what is listening.

electromagnetism · Retardation

Named alongside it

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

IrreversibilityAdvanced solutionBoundary conditionCausalityDetailed balanceDipole radiationEntropyFluctuationsFree energyPurcell effectRadiationRetardation

All concepts