Kennedy-Thorndike experiment
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The Kennedy-Thorndike experiment, first conducted in 1932, is a modified form of the Michelson-Morley experimental procedure. The modification is to make one arm of the classical MM apperatus much larger than the other, in an attempt to detect phase shifts due to the rotation of the Earth. The experiment had the null result.
The original Michelson-Morley experiment was useful for testing only the first postulate; movement relative to a fixed or linearly moving aether. If the aether was being dragged by large masses, a common hypothesis at the time, the experiment would give the null result because the aether would be moving along with the Earth, as would the experiment.
Kennedy had already made several increasingly sophisticated versions of the MM experiment through the 1920s when he struck upon a way to test aether drag as well. By making one arm of the experiment much longer than the other, differences in rotational speed between one end and the other (relative to the Earth) would cause a fringe shift to occur.
Another common attempt to "rescue" classic mechanics was the Fitzgerald-Lorentz contraction hypothesis, in which objects moving against the aether would contract. This would nullify any measurement that relied on the speeds relative to an aether, as the experiment itself was being contracted exactly the amount to cancel out the measurement. However the Kennedy-Thorndike experiment also ruled out any simple explanations here as well, as the two ends of the experiment had different rotational speeds, and thus should have different length contractions.
Current (as of 2003) Michelson-Morley experiments' precision is higher than the current Kennedy-Thorndike experiments' precisions.