How the Movement of Water Molecules Corresponds to Ripples in Spacetime
There is an interesting connection between two of the best-studied nonlinear partial differential equations in physics: the equations of hydrodynamics and the field equations of gravity.
Let’s start with a brief review of hydrodynamics. At the microscopic level a tank of water is a collection of, say, 1025 molecules that constantly collide with one another. The methods of physics may be used to model this collection of water molecules as follows: we set up equations that track the position and momentum of each of the water molecules and predict their time evolution. These conceptually complete equations have of order 1025 variables and so are clearly too difficult to handle in practice.
Does it then follow that tanks of water cannot be usefully studied using the methods of physics? As every plumber knows, this conclusion is false: a useful description of water is obtained by keeping track of average properties of water molecules, rather than each individual molecule.