# Maxwell's Wave Equation (Discovery) ### Commentary Calculus effectively helps us *know where to probe*; it is a probing device, a thinking tool to interact with the world around us *thoughtfully* and *logically*. ### Excerpt A beautiful example between the interplay of experiment and theoretical science is at play here. > Take the story of wireless communication. It began with the discovery of the laws of electricity and magnetism by scientists like Michael Faraday and Andre-Marie Ampere. Without their observations and tinkering, the crucial facts about magnets, electrical currents and their invisible force fields would have remained unknown, and wireless communication would never have been possible. So clearly experimental physics is indispensable here. > > But so was *calculus*. In the 1860's Maxwell recast the experimental laws of electricity and magnetism into a *symbolic form* that could be fed in the maw of calculus. After some churning, the maw disgorged an equation that didn't make sense. Apparently something was missing in the physics. Maxwell suspected that Ampere's law was the culprit. He tried patching it up by including a new term in his equation-a hypothetical current that would resolve the contradiction-and then let calculus *churn* again. This time it spat out a sensible result, a simply, elegant wave equation much like the equation the describes the spread of ripples on a pond. Except Maxwell's result was predicting a new kind of wave, with electric and magnetic fields dancing together in a pas de deux. *A changing electric field would generate a changing magnetic field, which in turn would regenerate the electric field, and so on, each field bootstrapping the other forward, propagating together as a wave of traveling energy*. And when Maxwell calculated the speed of this wave, he found-in what must have been one of the greatest Aha! moments in history-that it moved at the speed of light. So he used calculus not only to predict the existence of electromagnetic waves but also to solve an age-old mystery: What was the nature of light? Light, he realized, was an electromagnetic wave. --- Date: 20210815 Links to: [Physics](notes/Physics.md) [Infinite-Powers](Infinite-Powers.md) [Calculus MOC](Calculus%20MOC) Tags: #review References: * Infinite Powers, Strogatz, Pg xi