Michelson-Morley Experiment

The aberration of stellar light can be thought of as an indirect measurement of the velocity of the Earth with respect to the aether. In 1887, Albert Michelson and Edward Morley attempted to measure this velocity directly in the laboratory. Their apparatus was an optical version of the hypothetical sound-wave experiment shown in Figure 3.2. The apparatus sends light through a half-silvered mirror that is used to split it into two beams that travel at right angles to one another. The two beams travel out to the ends of long arms of equal length where they are reflected back into the middle by small mirrors. The beams then recombine on the far side of the splitter in an eyepiece, producing a pattern of interference fringes whose transverse displacement depends on the difference in time it takes light to transit the longitudinal and the transverse arms of the apparatus. By analogy with Equation (3.9), this time difference is

$${\mit\Delta t} = \frac{l_0\,v_e^{\,2}}{c^3},$$ (3.59)

where $l_0$ is the length of the arms, $v_e$ the orbital velocity of the Earth, and $c$ the velocity of light in vacuum. (Henceforth, $c$ refers exclusively to the velocity of light in vacuum.) By turning their apparatus through $90^\circ$, the experimentalists expected to reverse the time difference, and, thus, to generate a shift in the interference fringes. The magnitude of this shift is $2\,c\,{\mit\Delta t}/\lambda$ fringes, where $\lambda = 5\times 10^{-7}\,{\rm m}$ is a typical wavelength of light. Thus, given that the lengths of the arms in the experiment were (effectively) $10\,{\rm m}$, the expected shift is $0.39$ fringes. Such a shift should have been easily measurable. However, no such shift was observed. One possible explanation for this null result is that the Earth completely drags the aether in its immediate vicinity. However, this explanation is in conflict with Bradley and Airy's observations of stellar aberration, as well as Fizeau's experiment.