A famous experiment with a null result

Michelson & Morley

In 1878, the New York Times announced, “It would seem that the scientific world of America is destined to be adorned with a new and brilliant name,” predicting that light would soon be measured “with almost as much accuracy as the velocity of an ordinary projectile.” The new, brilliant name was Albert A Michelson, who went on to win the Nobel Prize in 1907, for his pioneering efforts in measuring and analyzing light, the first Nobel prize in science awarded to an American.

Measuring the speed of light had been a concern of scientists ever since the time of Galileo. Kepler and Descartes had imagined light to have infinite speed. Galileo had suggested in Two New Sciences, standing on a hilltop, an experimenter would flash a bright light toward a distant hill, where an assistant would answer back by flashing. Of course, no hills on earth are far enough to measure the delay, if any.

The first scientist to prove to the world that indeed, light travelled at a finite speed was Ole Roemer in 1676. He got an idea about the speed of light by studying the apparent speed of Jupiter’s moon Io. According to his calculations, light had a speed of 140,000 miles or 225,000 Kilometers per second.

In 1849, a French physicist Louis Fizeau designed a self-contained terrestrial experiment for measuring the speed of light. From a house in the Western suburbs of Paris, he projected a light beam toward a mirror atop Montmartre, which reflected it back again. Interposed in the path was a rapidly spinning cog wheel with 720 precisely machined teeth. The rotational speed of this cog wheel could be accurately adjusted so that the light, going and coming, would pass through a gap between the teeth and appear in Fizeau’s eye piece as “a luminous point like a star”. Spin the wheel a little faster or slower, and the beam would be eclipsed. From the length of the light path and the speed of the wheel, Fizeau estimated the speed of light at about 196, 000 miles or 315, 400 Kilometers per second.

Almost 30 years later, Michelson got a grant of $2000 from his father in-law and began planning his first big experiment. He began by placing two mirrors, one revolving and one stationary, about 2000 feet apart, along the north sea wall of the campus of the Naval Academy at Annapolis. To measure the separation precisely, he used a steel tape. Holding the tape along the pier with lead weights, and taking the pains to ensure that it was stretched at a constant tension, he made several readings. Correcting for the effects of expansion and contraction of the tape, the distance between the mirrors came out to be 1,986,23 feet. One mirror would be stationary and the other rotating. On the two legs of its journey, the ray of light would strike the mirror at slightly different points in its rotation.

Michelson planned to calculate the speed of light by measuring the tiny displacement.

To clock the speed of the revolving mirror, he used an electric tuning fork. He used a steam powered blower to spin the mirror at 256 revolutions per second. Using sunlight focused through a lens, he measured the deflection at the end of the light’s journey at 133 millimetres. A few calculations yielded a speed of 186, 380 miles or 299, 940 kilometres per second.

Michelson was confident about the precision of his experimental setup and the result it yielded. But one thing kept bothering him – it was the drag of the ‘luminiferous aether’, an ineffable fluid that pervaded everything, even the spaces between atoms. It had become necessary to invent the concept of aether after Thomas Young’s experiment asserted the nature of light as ‘waves’ and not particles, as Newton had erroneously believed. If light is a wave, it needs a medium for propagation. Scientists called that hypothetical all pervading medium ‘aether’.

Michelson asked himself whether the speed of light he had measured was affected by the earth’s motion through aether. He planned to measure the motion of the earth against the aether. In his new experimental design, he planned to split a beam of light using a half silvered mirror and send one beam along the direction of the earth’s revolution around the sun and the other beam perpendicular to it. Travelling along two finely machined brass arms, each a metre long, the two beams would repeatedly bounce off four mirrors and come back together again to form an interference pattern.

Michelson argued that if the instrument was turned 90 degrees, changing its orientation to the aetheral river, the fringes should move.

In Michelson’s interferometer, the beam splitter is a partially silvered mirror kept at an angle of 45° to the narrow beam of light. The beam splitter reflects part of the light at an angle of 90° and allows part of the light to pass through. Both the light beams intercept a mirror placed at right angles to their path and they are reflected back. Presuming that the setup is moving through an aether, one beam will first move downstream and then upstream. It will take time l/(c+v) + l/(c-v) to come back to the beam splitter. The other beam will travel cross stream, but its path, as seen from the aether fame, will be at an angle. Since the paths of the two beams are different, when they finally unite at the beam splitter, they will be slightly out of phase and form an interference pattern.

When the instrument is rotated through 90°, the first beam moves cross stream and the second beam moves up and down stream. Michelson had set the optical path length for the two beams at 22 metres. So according to his calculations, there should be a fringe shift of 0.4 when the instrument is turned through an angle of 90°.

But there was no observable fringe shift. In fact, in his first attempt he obtained a much higher fringe shift, which he later realized to be caused by extraneous vibration like passing traffic.

In so delicate an experiment, the slightest vibration would throw off the path lengths and spoil the results. Day after day he measured, turning the brass arm this way and that, in different seasons of the year, but he could find no more than the tiniest shift.

Michelson reported the negative result to his benefactor Bell, stating that this should not be taken as disproving the existence of
aether. There was a possibility that some of the aether in the vicinity of the earth was dragged along in its journey round the sun. Later, Morley joined Michelson in his experiments; they increased the length of the brass tubes to 36 metres. They mounted the interferometer on a massive stone slab for stability and floated the apparatus on mercury so that it could be rotated smoothly around a central pin. The fringes were observed under a continuous rotation of the apparatus. And yet there was no shift in the interference pattern. Δ N = 0

Michelson eventually spoke of aether as “one of the grandest generalizations of modern science, of which we are tempted to say that it ought to be true, even if it is not.”

Michelson’s experiment remains important in physics as an experiment that reluctantly disproved a grand hypothesis. It is also an
exemplary case of precision measurements, through which we get the value of one of the fundamental constants of the universe.

Reference
George Johnson, The Ten Most Beautiful Experiments, The Bodley Head, London;
Wikipedia; www.lib.uchicago.edu/projects/centcat/centcats/fac/facch07_01.html