Richard Feynman: "Suppose we are riding in a car that is going at a speed u, and light from the rear is going past the car with speed c. [...] ...according to the Galilean transformation the apparent speed of the passing light, as we measure it in the car, should not be c but should be c-u. For instance, if the car is going 100,000 mi/sec, and the light is going 186,000 mi/sec, then apparently the light going past the car should go 86,000 mi/sec. In any case, by measuring the speed of the light going past the car (if the Galilean transformation is correct for light), one could determine the speed of the car. A number of experiments based on this general idea were performed to determine the velocity of the earth, but they all failed - they gave no velocity at all. [...] As mentioned above, attempts were made to determine the absolute velocity of the earth through the hypothetical “ether” that was supposed to pervade all space. The most famous of these experiments is one performed by Michelson and Morley in 1887."
http://www.feynmanlectures.caltech.edu/I_15.html
The Michelson-Morley experiment "gave no velocity at all" because the principle of relativity was operative in that case - all parts of the experiment, including the emission and the detection of the light, occurred WITHIN the moving system.
In the car case the light comes "from the rear" - the experiment is not entirely performed within the moving system and the principle of relativity is irrelevant. Nothing prevents people in the car from measuring the speed of light as c-u.
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