Now imagine there is a very small demon who is waiting at the partition next to a small trap door. He can open and close the door with negligible work. Let's say he opens the door to allow a fast-moving molecule to travel from the left side to the right, or for a slow-moving molecule to travel from the right side to the left, and keeps it closed for all other molecules. The net effect would be a flow of heat -- from the left side to the right -- even though the container was in thermal equilibrium. This is clearly a violation of the second law of thermodynamics.

So where did we go wrong? It turns out that information has to do with entropy as well. In order to sort out the molecules according to speeds, the demon would be having to keep a memory of them -- and it turns out that increase in entropy of the maintenance of this simple memory would more than make up for the decrease in entropy due to the heat flow.

Gauss' law

The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface; in differential form,

div E = rho,

where rho is the charge density.

Gauss' law for magnetic fields

The magnetic flux through a closed surface is zero; no magnetic charges exist. In differential form,

div B = 0.

Faraday's law

The line integral of the electric field around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve; in differential form,

curl E = -dB/dt,

where d/dt here represents partial differentation.

Ampere's law, modified form

The line integral of the magnetic field around a closed curve is proportional to the sum of two terms: first, the algebraic sum of electric currents flowing through that closed curve; and second, the instantaneous time rate of change of the electric flux through a surface bounded by that closed curve; in differential form,

curl H = J + dD/dt,

where d/dt here represents partial differentiation.

In addition to describing electromagnetism, his equations also predict that waves can propagate through the electromagnetic field, and would always propagate at the same speed -- these are electromagnetic waves; the speed can be found by computing (epsilon₀ mu₀)^-1/2, which is c, the speed of light in vacuum.

The experiment showed absolutely no aether shift whatsoever, where one should have been quite detectable. Thus the aether concept was discredited as was the idea that one measures the velocity of light as being added vectorially to the velocity of the emitter.

See constancy principle.