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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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Why don't constant motion charges produce waves?

I'm a little confused about the origin of electromagnetic waves. Although I can understand their origin mathematically, I get a little confused about the physical intuition of... … How then does constant motion not produce EM waves, but also disturb a local field and not violate the speed limit on field propagation? …
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