Fine Structure

Imperfect Equations and Singularites

Here's the kind of beyond-the-formula thinking about science that I wished students saw more of in school: Stefan from Backreaction explains the basics of a singularity in your very own kitchen (or bathroom)! Navier-Stokes equations are typically used for predicting the flow of liquids but they assume that liquids are fluid on an infinitely small scale (i.e. that there are no fluid molecules at a certain small limit but that a fluid is simply fluids all the way down). In accordance with that assumption, the equations predict an infinitely reducing radius of water as a droplet falls from your kitchen tap. Clearly, the droplet separates from the tap at some point in time so the equation, while a decent estimate, doesn't fully predict fluid behavior. These kinds of problems really show the necessity of knowing the limits (pun) of your formulas and the reality of what's going on!