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What If Light Had No Speed Limit?

What if light had no Speed Limit? It might appear like a pointless question, as the speed of light clearly isn’t infinite, but questions like these are a good way to see how different aspects of a physical model are interrelated.
Such that, in our universe light is an electromagnetic wave. It not only has a speed, but a wavelength. If you think of a wave as an oscillation, then at boundless speed light would have no time to oscillate. So infinite light can’t be a wave. Since the wavelength of light defines its color that would also mean it has no color. But it gets worse as in classical physics light is made when electromagnetic waves cause the charges in atoms and molecules to oscillate. Deprived of waves, atoms can’t be persuaded to emit light; the universe would be a sea of darkness.