The Aether drag hypothesis is a concept from historical physics that emerged in the 19th century, associated with the aether theory. This theory posited that a "luminiferous aether" filled space and was the medium through which light waves propagated, similar to how sound waves travel through air. The aether drag hypothesis specifically dealt with the behavior of this aether in relation to moving objects.
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Given experiments such as the Fizeau experiment and the Michelson-Morley experiment that couldn't really detect the Earth's movement across aether, people started to wonder if the Earth wasn't dragging the luminiferous aether.