ljudskija7s

2022-08-13

Why are electromagnetic waves called waves even though they don't travel through a medium?

Clare Chung

Expert

The definition of a wave is not that it is the oscillation of a medium. Waves are called waves because they are solutions to a wave equation, which is, for a generic "excitation" $A\left(t,x\right)$ depending on the time t and some spatial coordinate $x\in {\mathbb{R}}^{n}$, of the general form
$\frac{{\mathrm{\partial }}^{2}A}{\mathrm{\partial }{t}^{2}}={c}^{2}\mathrm{\Delta }A$
where $\mathrm{\Delta }$ is the Laplacian for the spatial coordinate. The wave equation, in turn, is called a wave equation because it is precisely the equation that governs the archetypical system where a wave occurs - that of masses linearly connected by springs.
While a wave equation may arise from considering a medium, a medium is not necessary for a wave equation to occur, as Maxwell's equations and the disproof of almost all luminiferous aether theories show.

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