Michelson-Gale-Pearson experiment
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The Michelson-Gale-Pearson experiment is a modified version of the Michelson-Morley experiment which tests the aether drag along the rotating frame of Earth. That is, if aether is dragged rotationally by the Earth, as was assumed by many, the Michelson-Gale-Pearson experiment would be able to detect this effect.
Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source after travelling in two directions. The major change was to replace the two "arms" of the original MM version with two rectangles, one much larger than the other. Light was sent into the rectangles, reflecting off mirrors at the corners, and returned to the starting point. Light exiting the two rectangles was compared on a screen just as the light returning from the two arms would be in a standard MM experiment.
This seemingly small modification to the original MM experiment actually has a very useful side-effect. If aether is dragged rotationally by the Earth, light travelling in the longer rectangle will see a different amount of drift than in the smaller one, because the two arms of the longer rectangle are spinning at different speeds. This is due to the Earth being a sphere, the "northernmost" arm is moving slower than the "southernmost" one. The experiment was deliberately set up such that the long axis of the rectangle was aligned east-west, at 612 meters long, while the north-south "legs" were 339 m.
Interestingly the experiment was expected to generate a positive result both for an entrained aether as well as due to relativistic effects. The main difference would be the magnitude of the effect. It was thus a surprise to everyone when the MGP experiment also returned what appeared to be a null result, or at least a rather inconclusive one. The results consisted of 269 measurements that showed an effect of -0.04 to +0.55 fringes, which could be seen as evidence of the rotational effects, but at the same time they were not statistically significant.
Einstein himself attempted an explanation, but it was confusing and less than convincing. Explanations using general relativity have also been offered.