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In page Luminiferous aether:

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The key difficulty with Fresnel's aether hypothesis arose from the juxtaposition of the two well-established theories of Newtonian dynamics and Maxwell's electromagnetism. Under a Galilean transformation the equations of Newtonian dynamics are invariant, whereas those of electromagnetism are not. Basically this means that while physics should remain the same in non-accelerated experiments, light would not follow the same rules because it is travelling in the universal "aether frame". Some effect caused by this difference should be detectable.[citation needed]