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Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.

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Couldn't understand the reasoning on the propagation of the electromagnetic wave in the vacuum?

The solution of the wave function in vacuum gives two progressive plane waves $f(x-ct)+g(x+ct)$, which both represent solutions to the wave equation. … Since $E$ is static, the wave is not propagating, but it is still transverse, as the two progressive plane waves are perpendicular to each other. …
Khadim Hussain Rasooli's user avatar