### The Michelson-Morley Experiment

Newton’s laws and Maxwell’s equations had proven so successful in explaining and predicting nearly everything, that by the turn of the twentieth century many physicists were doubtful that much was left to be discovered. In a book published 1903, physicist Albert Michelson brashly proclaimed:

The more important fundamental laws and facts of physical science have all been discovered, and these are so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote.Albert A. Michelson, Light Waves and Their Uses (Chicago: University of Chicago Press, 1903), 23-24.

Was he in for a surprise! The irony is that one of Michelson’s own discoveries—made a few years earlier in collaboration with his colleague Edward Morley—would soon lead to a conceptual revolution unprecedented in the history of modern physics.

Michelson and Morley were trying to measure the speed at which Earth moves through aether, the unknown substance in which light waves were supposed to propagate. If the sun is at rest relative to the aether, then in order to make our annual journey around the sun (a distance of 94 million kilometers), Earth would be whisking through the aether at a constant speed of nearly 30 km/s. On the other hand, if the sun is moving relative to the aether, then our planet’s speed must vary from less than 30 km/s to more than 30 km/s depending on the time of year, as illustrated in the animation to the right. Either way, we’ll be rushing through aether at least some of the time, if not all year long. Measuring our speed relative to aether would not be easy, however, because aether doesn’t seem to affect matter. The earth isn’t slowed by friction, and we feel no “aether wind.” Since aether doesn’t exert any forces on matter, the only way to determine how fast we’re moving through it would be to measure our speed relative to a beam of light!

According to the aether theory, light travels through aether at a speed of 300,000,000 m/s. So, if we are moving through the aether too, then from our perspective the speed of light should vary depending on which direction the light is going. Light traveling the same direction as the earth should be slower, in our reference frame, than light going the other way. Perhaps the speed at which we are moving through aether could be measured by sending beams of light in different directions. The measurement would have to be extraordinarily precise, though. The speed of light is about 10,000 times faster than Earth’s speed around the sun; so unless our entire solar system is racing through the aether at a tremendous clip, we’re moving at a snail’s pace compared to the speed of light. Assuming the sun is at rest in the aether, a beam of light traveling the same direction as Earth would be only 1/10000th slower in our reference frame, compared to a beam traveling orthogonally. Could this tiny discrepancy be detected? In 1887, Michelson and Morley devised an experiment to find out.

In the famous Michelson-Morley experiment, a beam of light shone upon a half-silvered mirror—a mirror which reflected 50% of the light and allowed the other 50% to pass through. The half-silvered mirror was oriented at a 45-degree angle from the incoming beam, so that the reflected beam would travel at a right angle compared to the light that passed straight through the mirror. In the paths of each of these two beams, fully reflecting mirrors (not half-silvered ones) were positioned to reflect the light back to the half-silvered mirror. Upon striking the half-silvered mirror the second time, 50% of each returning beam would be reflected; the other 50% would pass through. Thus, 50% of each returning beam (and therefore 50% of the total light) would end up traveling back toward the original light source. The other 50% would go toward a small telescope, which was positioned near the half-silvered mirror. The simple setup I’ve just described captures the essential idea, but the actual design of the experiment was a bit more complicated. The device used additional mirrors to increase the distance light had to travel, lenses to focus the light, and thin sheets of glass to compensate for the refraction of light that had passed through the half-silvered mirror. For details, you can download a copy of the original report, which includes a description and numerous diagrams of the experimental setup.

The fully reflecting mirrors were positioned at equal distances from the half-silvered mirror, so that the two beams of light would have to travel the same distance to reach the telescope—if we are at rest relative to the aether. However, if Earth is moving through aether in the same direction as one of the beams, that beam would travel more slowly in Earth’s frame of reference (because it has farther to go in the aether’s frame) before reaching the telescope, and thus would arrive slightly later than the other beam. The difference would be minuscule, of course. In the fraction of a millisecond that it takes for light to travel back and forth between the mirrors, Earth moves only a tiny distance. Nevertheless, Michelson and Morley thought of a clever way to detect this motion by exploiting the phenomenon of wave interference.

Recall from Chapter 2 that interference occurs whenever two waves meet. If the waves are in phase—that is, if their peaks and troughs are aligned—the waves will constructively interfere, resulting in a larger wave (a wave with greater amplitude). On the other hand, if the peaks and troughs are out of phase (misaligned), the two waves will destructively interfere, resulting in a smaller wave.

The waves of light in the Michelson-Morley experiment would be in phase initially, because they originated from a single beam that was split by the half-silvered mirror. Provided the earth is at rest in the aether, these two waves would travel the same distance and arrive at the telescope simultaneously, so they would still be in phase. But if Earth is moving through the aether, Michelson and Morley reasoned, one beam of light would arrive at the telescope slightly (ever so slightly!) behind the other. In that case, the waves would be out of phase, causing some destructive interference. This destructive interference should make the light appear dimmer than it would otherwise, when viewed through the telescope.

Michelson and Morley predicted that the amount of destructive interference would vary depending on the wavelength of the light: colors with shorter wavelengths (blue, violet) should be affected more dramatically than colors with longer wavelengths (orange, red). By observing the patterns of interference produced by different colors of light, they hoped to measure the phase shift—that is, the amount by which one light wave was ahead of the other. Knowing the phase shift would allow them to calculate the speed at which Earth was moving through aether.

That was the plan, anyway. But when they actually conducted the experiment, Michelson and Morley found no phase shift at all. Apparently, the two beams of light had traveled exactly the same distance and arrived at the telescope simultaneously. This meant that the experimental apparatus wasn’t moving through aether, or at least, it wasn’t moving in the same direction as either beam of light. The scientists rotated the entire apparatus at various angles and repeated the experiment numerous times, to see whether the earth was moving in a different direction than they had expected. Same result. The two beams of light always stayed in phase, no matter which way the device was oriented.

Perhaps they had chosen the wrong time of year. If the sun is moving through the aether, then Earth’s speed relative to aether will vary as it orbits the sun. (See the animation above.) In fact, it is possible that the earth could be completely at rest in the aether at a certain time each year. The earth orbits the sun at 30 km/s, so if the sun itself is moving at 30 km/s, then Earth will be at rest in the aether when the sun’s motion (relative to aether) and our motion (relative to the sun) go in opposite directions. Were Michelson and Morley unlucky enough to conduct their experiment at precisely that time of year? To rule out this possibility, they waited a few months and tried again. And again a few months after that. Still no luck.

To their astonishment, Michelson and Morley found that no matter what time of year the experiment was performed, and no matter which way the apparatus was oriented, they always got a null result: no phase shift. How could that be? Surely the earth had to be moving through aether at least some of the time, they thought, since the direction of our motion is constantly changing as we circle the sun. Yet no “aether wind” (flow of aether) could be detected. What in the world was going on? The truth, as we’ll see, is even more surprising than the unexpected result of their experiment.