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In the latter part of the 19th century, scientists believed that light must be transmitted through a medium. Since it had been shown that light (all electo-magnetism, really, but light in particular) moves as a wave, it was supposed that there must be some medium through which it traveled. Think about the kinds of waves we usually encounter -- sound waves travel through the medium of air, ocean waves through the medium of water. Without the medium, the wave does not exist. Light was a wave, so it should have a medium. This medium was called "ether" (sometimes spelled "aether.")
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Their experiment, pictured at the left, was ingenious, and became one of the most well-known experiments in history.
Because it failed.
The experiment clearly showed that the Earth was not moving, relative to the ether, and so science was faced with a (seeming) contradiction. It was proven that the Earth was not at rest with respect to the ether, and it was also proven that the Earth was not in motion with respect to the ether. How could this be?
Einstein would give the answer with his theory of special relativity in 1905, and one of the results would be the (now obvious) answer: there is no such thing as "ether" - no "medium" which transmits electro-magnetic waves such as light.
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No scientist ever gets "the final answer" because no theory has yet explained everything. But throughout history, science has gotten closer and closer to being able to describe more and more of reality by constantly looking for contradictions, anomalies and points of divergence and trying to find theories which explain them all -- or at least more than the theories which are known at the time.
It's a darn good thing Michelson and Morley were willing to show that they were wrong. Great scientists.
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