Michelson–Morley experiment

"Maxwell... was one of the scientific editors of the Encyclopedia Britannica (1878-89)... contributing a number [of articles] himself, most famously those of 'atom' and 'ether'. ...'Ether' contained a suggestion for detecting the Earth's motion through the ether that inspired the Michelson–Morley experiment."

"[L]et us look at what primarily motivated Michelson (and Morley) into performing these experiments. One of the clear motivations was a letter written by Maxwell titled, "On a Possible Mode of Detecting a Motion of the Solar System through the Luminiferous Ether", that was published in Nature, shortly after he died. Michelson and Lorentz refer to this letter in their respective papers about the Michelson Morley experiment, in 1887 and 1892, respectively. ...Michelson read this... letter and thought he could prove Maxwell and his mathematics wrong... and failed to detect anything meaningful in the form of an interference shift."

"But the changes of dimension and mass due velocity are not conventions but realities; so I urge, on the basis of the electrical theory of matter. The Fitzgerald-Lorentz hypothesis I have an affection for. I was present at its birth. Indeed, I assisted at its birth for it was in my study... with Fitzgerald in an armchair, and I was enlarging on the difficulty of reconciling the then new Michelson experiment with the theory of astronomical aberration and with other known facts, that he made his brilliant surmise:—"Perhaps the stone slab was affected by the motion." I rejoined that it was a 45° shear that was needed. To which he replied, "Well, that's all right—a simple distortion." And very soon he said, "And I believe it occurs, and that the Michelson experiment demonstrates it." A shortening long-ways, or a lengthening cross-ways would do what was wanted. And is such a hypothesis gratuitous? Not at all: in the light of the electrical theory of matter such an effect ought to occur. The amount required by the experiment, and given by the theory, is equivalent to a shrinkage of the earth's diameter by rather less than three inches, in the line of its orbital motion through the aether of space. An oblate spheroid with the proper eccentricity has all the simple geometrical properties of a stationary sphere; the eccentricity depends in a definite way on speed, and becomes considerable as the velocity of light is approached. All this Profs Lorentz and Larmor very soon after and quite independently perceived..."

"We have... to speak of a celebrated experiment made by Michelson in 1881, and repeated by him on a larger scale with the cooperation of Morley in 1887. It was a very bold one, two rays of light having been made to interfere after having travelled over paths of considerable length in directions at right angles to each other. Fig 9. shows the general arrangement of the apparatus. The rays of light coming from the source L are divided by the glass plate P, which is placed at an angle of 45°, into a transmitted part PA and a reflected one PB. After having been reflected by the mirrors A and B, these beams return to the plate P, and now the part of the first that is reflected and the transmitted part of the second produce by their interference a system of bright and dark fringes that is observed in a telescope placed on the line PC. The fundamental idea... is, that, if the ether remains at rest, a translation given to the apparatus must of necessity produce a change in the differences of phase, though one of the second order. Thus, if the translation takes place in the direction of PA or AP, and if the length of PA is denoted by L [denoting speed of light c and earth's speed \left\vert w \right\vert (the absolute value of its velocity w)], a ray of light will take a time \frac{L}{c + \left\vert w \right\vert} for travelling along this path in one direction, and a time \frac{L}{c - \left\vert w \right\vert} for going in the inverse direction. The total time is\frac{2Lc}{c^2 - w^2},or up to quantities of the second order [by multiplying numerator and denominator by \frac{1}{c^2} to obtain \frac{2L}{c}\frac{1}{(1 - \frac{ w^2}{c^2})}, then multiplying this numerator and denominator by (1 + \frac{ w^2}{c^2}) and dropping the resulting denominator's negligibly small fraction \frac{ w^4}{c^4}, giving]\frac{2L}{c}(1 + \frac{ w^2}{c^2}),so that for the rays that have gone forward and back along PA there will be a retardation of phase measured by \frac{2Lw^2}{c^3}.There is a similar retardation, though of smaller amount, for the other beam. ...a ray of this beam, even if it returns, as I shall suppose..., to exactly the same point of the plate P, does not come back to the same point of the ether, the point... having moved with the velocity W of the earth's translation over a certain distance say from P to P' while the light went from P to B and back. If Q is the point in the ether where the ray reaches the mirror B, ...with sufficient approximation...the points P, Q, P' are the angles of an isoscele triangle, whose height is L (since the distances PA and PB in the apparatus were equal) and whose base [the total distance traveled by mirror B resulting from the motion of the earth] is \frac{2L\left\vert w \right\vert}{c} [where \frac{2L}{c} is the time for light to travel distance L twice]. The sum of the sides PQ and QP' is2\sqrt{L^2 + \frac{L^2w^2}{c^2}},so that we may write\frac{2L}{c}(1 + \frac{w^2}{2c^2})for the time required by the second beam. It appears from this that the motion produces a difference of phase between the two beams to the extent of\frac{Lw^2}{c^3},and this may be a sensible fraction of the period of vibration, if L has the length of some metres."

"Relative motion of the aether.—We must therefore consider the aether within dense bodies as somewhat loosely connected with the dense bodies, and we have next to inquire whether, when these dense bodies are in motion through the great ocean of aether, they carry along with them the aether they contain, or whether the aether passes through them as the water of the sea passes through the meshes of a net when it is towed along by a boat. If it were possible to determine the velocity of light by observing the time it takes to travel between one station and another on the earth's surface, we might, by comparing the observed velocities in opposite directions, determine the velocity of the aether with respect to these terrestrial stations. All methods, however, by which it is practicable to determine the velocity of light from terrestrial experiments depend on the measurement of the time required for the double journey from one station to the other and back again, and the increase of this time on account of a relative velocity of the aether equal to that of the earth in its orbit would be only about one hundred millionth part of the whole time of transmission, and would therefore be quite insensible. The theory of the motion of the aether is hardly sufficiently developed to enable us to form a strict mathematical theory of the , taking into account the motion of the aether. Professor Stokes, however, has shown that, on a very probable hypothesis with respect to the motion of the aether, the amount of aberration would not be sensibly affected by that motion. The only practicable method of determining directly the relative velocity of the æther with respect to the solar system is to compare the values of the velocity of light deduced from the observation of the eclipses of Jupiter's satellites when Jupiter is seen from the earth at nearly opposite points of the ecliptic."

"Sir, I have received with much pleasure the tables of the satellites of Jupiter which you have been so kind as to send me, and I am encouraged by your interest in the Jovial system to ask you if you have made any special study of the apparent retardation of the eclipses as affected by the geocentric position of Jupiter. I am told that observations of this kind have been somewhat put out of fashion by other methods of determining quantities related to the velocity of light, but they afford the only method, so far as I know, of getting any estimate of the direction and magnitude of the velocity of the sun with respect to the luminiferous medium. Even if we were sure of the theory of aberration, we can only get differences of position of stars, and in the terrestrial methods of determining the velocity of light, the light comes back along the same path again, so that the velocity of the earth with respect to the ether would alter the time of the double passage by a quantity depending on the square of the ratio of the earth's velocity to that of light, and this is quite too small to be observed."

"If... an apparatus is so constructed as to permit two pencils of light, which have travelled over paths at right angles to each other, to interfere, the pencil which has traveled in the direction of the earth's motion, will in reality travel 4/100 of a wave-length farther than it would have done, were the earth at rest. The other pencil being at right angles to the motion would not be affected. If, now, the apparatus be revolved through 90° so that the second pencil is brought into the direction of the earth's motion, its path would have lengthened 4/100 wave-lengths. The total change in position of the interference bands would be 8/100 of the distance between the bands, a quantity easily measurable."

"In 1880 Michelson was at Berlin in the laboratory of Helmholtz. There he started the experiment, which was later completed at Cleveland in collaboration with Professor E. W. Morley, of attempting to measure the motion of the earth with respect to the ether. Astronomers had found that the sun with its retinue of planets is moving toward the stars in the constellation Hercules at the rate of twelve miles per second, or four hundred million miles per year. This would be the motion of the sun if the stars were at rest, but as they are not at rest, the real problem of determining the motion of the sun remained unsolved. Michelson undertook to measure the motion of the sun with respect to that all-pervading medium, known as ether, which fills interstellar space."

"If the ether is stationary, as postulated by Fresnel, the optically important phenomenon of aberration is completely explained, but the Michelson Morley experiment appeared to show that this hypothesis was untenable, and left aberration without the shadow of an explanation. ...Fitzgerald... and Lorentz... nearly at the same time made the same suggestion as a possible way out of the difficulty. ...Fitzgerald and Lorentz suggested that the dimensions of the block of sandstone [on which the interferometer mirrors were mounted] were altered by its drift through the ether, that... the stone was shorter... in the direction of the earth's motion in space than when it lay at right angles to this motion. ...All substances might experience such a deformation... but it was conceivable that they might not be all deformed alike, that a soft and yielding substance like wood might suffer a different amount of shortening from that of stone or iron. In 1904 Morley and Miller repeated the experiment of 1887, using a lvery much larger apparatus, the path of each of the interfering beams of light being now 32 metres instead of about 11... The mirrors were separated by rods of pine instead of sandstone... But the effects were the same. No effect could be discovered... to show that the earth drifts or moves through the ether. ...The mathematicians now took the matter up, and under the leadership of Einstein and Minkowski put forward the principle of relativity in all measurements of space and time..."