# On the Relative Motion of the Earth and the Luminiferous Ether **Albert A. Michelson** and **Edward W. Morley** *American Journal of Science*, Third Series, Vol. XXXIV, No. 203, November 1887, pp. 333-345. --- ## Summary This is the most famous null result in physics. Michelson and Morley attempted to detect Earth's motion through the luminiferous ether using an interferometer floating on mercury. The predicted fringe shift (0.4 of a fringe for Earth's orbital velocity) was not observed. The actual displacement was "certainly less than the twentieth part" of the expected value, "and probably less than the fortieth part." What makes this paper essential for the Airy project is not the interferometer result itself, but: 1. **The opening paragraph** directly references Airy's experiment as the motivation for the entire investigation 2. **The remarkable footnote on page 333** where Michelson notes the absurdity of the emission theory requiring "the motion of the water in the telescope carries the ray of light in the opposite direction!" 3. **The conclusion on page 341** where Michelson states that if the values are taken at face value, "the relative velocity of the earth and the ether is probably less than one sixth the earth's orbital velocity, and certainly less than one fourth" 4. **The devastating final paragraph on page 341** where Michelson shows that Lorentz's own theory is internally inconsistent: Lorentz shows Stokes's conditions are incompatible, then proposes a modification using Fresnel's coefficient, but if the ether is at rest on the surface (as the null result suggests), "there could not be a velocity potential, and his own theory also fails" --- ## Page-by-Page Breakdown # Page 1 (p. 333) ![[Attachments/page-01.png]] **Opening paragraph**: "THE discovery of the aberration of light was soon followed by an explanation according to the emission theory. The effect was attributed to a simple composition of the velocity of light with the velocity of the earth in its orbit. The difficulties in this apparently sufficient explanation were overlooked until after an explanation on the undulatory theory of light was proposed. This new explanation was at first almost as simple as the former. **But it failed to account for the fact proved by experiment that the aberration was unchanged when observations were made with a telescope filled with water.** For if the tangent of the angle of aberration is the ratio of the velocity of the earth to the velocity of light, then, since the latter velocity in water is three-fourths its velocity in a vacuum, the aberration observed with a water telescope should be four-thirds of its true value." > [!danger] Michelson Opens With Airy (p. 333) > The very first paragraph of the most famous physics paper of the 19th century cites Airy's water telescope experiment as the foundational problem. The wave theory predicted aberration should increase by 4/3 in water. It didn't. This is the problem that motivated Fresnel's drag hypothesis, which motivated the entire Michelson-Morley experiment. **Footnote †** (bottom of p. 333): "It may be noticed that most writers admit the sufficiency of the explanation according to the emission theory of light; while in fact the difficulty is even greater than according to the undulatory theory. For on the emission theory the velocity of light must be *greater* in the water telescope, and therefore the angle of aberration should be *less*; hence, in order to reduce it to its true value, we must make the absurd hypothesis that **the motion of the water in the telescope carries the ray of light in the opposite direction!**" > [!danger] Michelson's Devastating Footnote (p. 333) > Michelson points out that the emission theory is even WORSE than the wave theory for explaining Airy: under emission theory, light is faster in water, so aberration should decrease. To recover the observed (unchanged) value, you'd have to assume the water carries the light backward. He calls this "absurd." Neither theory (emission or wave) can explain Airy's null result without an ad hoc rescue. # Page 2 (p. 334) ![[Attachments/page-02.png]] **Fresnel's two hypotheses**: (1) the ether is at rest except inside transparent media, (2) inside such media it moves with the medium at a velocity proportional to $(n^2 - 1)/n^2$, where $n$ is the index of refraction. These two hypotheses give a "complete and satisfactory explanation of aberration." The second hypothesis is confirmed by Fizeau's experiment and "by the ample confirmation of our own work." The experimental trial of the FIRST hypothesis (ether at rest outside transparent bodies) is the subject of the present paper. **Lorentz's barometer tube argument**: If the earth were a transparent body, the intermolecular ether might be at rest. But Earth is opaque, and "there can hardly be question that the ether can and does pass through metals." Lorentz cites the metallic barometer tube: when inclined, the mercury is forced out, proving the space above is connected to the exterior. The ether in the tube must be free to move. "But again we have no right to assume that it makes its escape with perfect freedom." **Lorentz's own remark** (quoted in French): "quoi qu'il en soit, on fera bien, à mon avis, de ne pas se laisser guider, dans une question aussi importante, par des considérations sur le degré de probabilité ou de simplicité de l'une ou de l'autre hypothèse, mais de s'addresser à l'expérience pour apprendre à connaître l'état, de repos ou de mouvement, dans lequel se trouve l'éther à la surface terrestre." Translation: "Whatever the case, one would do well, in my opinion, not to let oneself be guided, in so important a question, by considerations of the probability or simplicity of one or other hypothesis, but to address oneself to experiment to learn the state, of rest or of motion, in which the ether is found at the terrestrial surface." # Page 3 (p. 335) ![[Attachments/page-03.png]] **Lorentz's analysis of the first experiment**: H. A. Lorentz "finds that this effect can by no means be disregarded." The quantity to be measured was "in fact but one-half the value supposed," and since it was already barely beyond experimental error, "the conclusion drawn from the result of the experiment might well be questioned." This motivated repeating the experiment with modifications to make the theoretical result "much too large to be masked by experimental errors." **Theory of the method**: Fig. 1 and Fig. 2 diagrams. A ray $sa$ is partly reflected along $ab$ and partly transmitted along $ac$, returned by mirrors $b$ and $c$, and recombined at $a$. If the apparatus moves at velocity $v$ in the direction $sc$, the path lengths change. # Page 4 (p. 336) ![[Attachments/page-04.png]] **The key derivation.** Let: - $V$ = velocity of light - $v$ = velocity of earth in orbit - $D$ = distance $ab$ or $ac$ (Fig. 1) Time for light to travel from $a$ to $c$ and back: $T + T_1 = \frac{D}{V-v} + \frac{D}{V+v} = \frac{2D}{V} \cdot \frac{V}{V^2-v^2} = 2D\frac{V}{V^2-v^2}$ Distance traveled: $2D\left(1 + \frac{v^2}{V^2}\right)$, neglecting fourth order terms. Length of other path: $2D\sqrt{1+\frac{v^2}{V^2}}$, or to the same accuracy, $2D\left(1+\frac{v^2}{2V^2}\right)$. **The difference is $D\frac{v^2}{V^2}$.** Rotating the apparatus 90° doubles this, so the **displacement of interference fringes should be $2D\frac{v^2}{V^2}$.** For $D \approx 11$ meters (after multiple reflections), $D = 2 \times 10^7$ wavelengths of yellow light: expected displacement = **0.4 fringe**. # Page 5 (p. 337) ![[Attachments/page-05.png]] **The apparatus.** A massive stone 1.5 m square, 0.3 m thick, floating on an annular wooden float in a cast iron trough filled with mercury. The float rests on mercury, and a pin guided by arms keeps it concentric. A lever can withdraw the pin. The annular iron trough rests on a bed of cement on a low brick pier. Fig. 3: perspective view of the apparatus. # Page 6 (p. 338) ![[Attachments/page-06.png]] **Mirror arrangement.** Four mirrors $dd$, $ee$ at each corner. A plane-parallel glass $b$ at center. Light from an argand burner $a$ passes through a lens, falls on $b$, is partly reflected and partly transmitted. The two pencils follow paths $bdedbf$ and $bde_1d_1bf$ respectively, observed through telescope $f$. Both $f$ and $a$ revolve with the stone. Fig. 4: plan view of the optical layout (the famous X-pattern of the interferometer arms). Mirrors of speculum metal, 5 cm diameter. Glasses $b$ and $c$ are plane-parallel, 1.25 cm thick. # Page 7 (p. 339) ![[Attachments/page-07.png]] **Observation procedure.** Sixteen equidistant marks around the cast iron trough. Apparatus revolved very slowly (one turn in six minutes). Micrometer cross wire set on the clearest interference fringe. Reading taken at each mark. Very slight gradual impulse to keep motion going. Results more consistent during slow uniform motion than when the stone was brought to rest (strains took half a minute to settle, temperature effects also). Fig. 5: cross-section of the float and trough assembly. **Data tables**: Noon observations and PM observations for July 8, 9, 11, 12. Width of fringes varied from 40 to 60 divisions, mean ~50. One division = 0.02 wavelength. # Page 8 (p. 340) ![[Attachments/page-08.png]] **Noon and PM observation tables** (complete data). **Fig. 6**: The results plotted graphically. Upper curve = noon, lower = evening. **The dotted curves represent one-eighth of the theoretical displacements.** > [!danger] One-Eighth of Theory (p. 340, Fig. 6) > The dotted theoretical curves are already scaled down to ONE-EIGHTH of the predicted displacement. The observed curves still don't match them. The actual displacement is far smaller than even 1/8 of the prediction. "Considering the motion of the earth in its orbit only, this displacement should be $2D\frac{v^2}{V^2} = 2D \times 10^{-8}$." # Page 9 (p. 341) ![[Attachments/page-09.png]] **THE KEY CONCLUSION PAGE.** "The distance D was about eleven meters, or $2 \times 10^7$ wave-lengths of yellow light; hence the displacement to be expected was 0.4 fringe. **The actual displacement was certainly less than the twentieth part of this, and probably less than the fortieth part.**" "**But since the displacement is proportional to the square of the velocity, the relative velocity of the earth and the ether is probably less than one sixth the earth's orbital velocity, and certainly less than one fourth.**" > [!danger] Michelson's Quantitative Conclusion (p. 341) > The observed displacement is < 1/20 of 0.4 fringe = < 0.02 fringe. Since displacement $\propto v^2$, the implied velocity is lt; v_{\text{orbit}}/\sqrt{20} \approx v_{\text{orbit}}/4.5$, i.e., less than ~7 km/s. Michelson rounds this to "less than one sixth" (5 km/s) and "certainly less than one fourth" (7.5 km/s). > > This is NOT a clean null. It is a result too large for Fresnel/Lorentz/Stokes to explain (they predict zero) but also too small for Earth's full orbital velocity (30 km/s). It sits in a no-man's land that is uncomfortable for EVERYONE. **Stokes's theory**: requires the ether at Earth's surface to be at rest, and the relative velocity to have a potential. "But **Lorentz shows that these conditions are incompatible.** Lorentz then proposes a modification which combines some ideas of Stokes and Fresnel, and assumes the existence of a potential, together with Fresnel's coefficient." "**If now it were legitimate to conclude from the present work that the ether is at rest with regard to the earth's surface, according to Lorentz there could not be a velocity potential, and his own theory also fails.**" > [!danger] Michelson Kills Lorentz's Theory Too (p. 341) > Michelson shows that Lorentz's own framework is self-contradictory: > 1. Lorentz proves Stokes's conditions (ether at rest + velocity potential) are incompatible > 2. Lorentz proposes a hybrid using Fresnel's coefficient > 3. But if the ether IS at rest at Earth's surface (as Michelson's null result suggests), Lorentz's own requirement for a velocity potential fails > 4. "His own theory also fails" > > This is the "rather involved arguments" that Pauli later dismissed as unnecessary from the relativistic viewpoint. But Michelson himself saw them as failures, not successes. # Page 10 (p. 342) ![[Attachments/page-10.png]] **Supplement.** "It is obvious from what has gone before that it would be hopeless to attempt to solve the question of the motion of the solar system by observations of optical phenomena *at the surface of the earth.*" Proposes alternative methods: (1) experiments at mountain peaks where relative motion might be perceptible, (2) multiplying the square of aberration to bring it within range. Derives formulae for reflection from moving surfaces. For a mirror moving at velocity $\omega$ making angle $\alpha$ with the normal: $\theta = r + \frac{r^2}{2} = \frac{\sqrt{2}\omega\cos\alpha}{V} + \frac{\omega^2}{V^2}\cos^2\alpha$ Total deviation $\theta + \theta_1 = 2\rho^2\cos^2\alpha$, where $\rho$ is the angle of aberration. # Page 11 (p. 343) ![[Attachments/page-11.png]] **Figures 1-4** for the supplement. Diagrams showing the optical arrangements for the proposed new methods of detecting solar system motion. # Page 12 (p. 344) ![[Attachments/page-12.png]] Proposes using two mirrors revolving with equal velocity in opposite directions (Fig. 3) with selenium cells and a telephone to detect phase differences. Also proposes three astronomical methods: 1. Telescopic observation of proper motions of stars (direction only, not amount) 2. Spectroscopic observation of stellar motions along line of sight 3. Determination of velocity of light by eclipses of Jupiter's satellites (difference between nearest and farthest positions) # Page 13 (p. 345) ![[Attachments/page-13.png]] Final paragraph on method 3 (Jupiter's satellites). "If the improved photometric methods practiced at the Harvard observatory make it possible to observe these with sufficient accuracy, the difference in the results found for the velocity of light when Jupiter is nearest to and farthest from the line of motion will give, not merely the motion of the solar system with reference to the stars, but with reference to the luminiferous ether itself." --- ## See Also - [[1871_Airy_Supposed_Alteration_Aberration|Airy 1871]] — The experiment cited in Michelson's opening paragraph as motivation - [[1810_Arago_Memoir_Speed_of_Light|Arago 1810]] — Arago's prism experiment, referenced alongside Airy on p. 333 - [[1895_Lorentz_Versuch_Airy_Sections|Lorentz 1895]] — Lorentz's theory that Michelson critiques on p. 341; the "searching analysis" referenced on p. 335 - [[1921_Pauli_Theory_of_Relativity|Pauli 1921]] — SR resolution that makes the question "meaningless" - [[1972_Jones_Fresnel_Aether_Drag_Transverse|Jones 1972]] — Direct measurement of the Fresnel drag that Michelson confirmed via Fizeau - [[1988_VanDerKamp_De_Labore_Solis|Van der Kamp 1988]] — Epistemological analysis of this result (pp. 34-38, "The 1887 Cleveland Disenchantment") - [[Aberration_in_Air_vs_Water|Null Hypothesis]] — Listed in the table of attempted differentiators ## Critical Notes for the Airy Argument > [!danger] Michelson Opens and Closes With Airy > The paper begins with Airy's null result as the foundational problem that motivated the entire investigation. Michelson traces the chain: aberration discovered → emission theory explained it → wave theory tried → Airy's water telescope disproved the naive wave theory → Fresnel drag proposed → Fresnel's drag confirmed by Fizeau → but is the ether at rest? That's what the interferometer tests. Airy is the reason this experiment exists. > [!danger] The Result Is NOT a Clean Null > Michelson does not say "zero." He says "less than one twentieth" of 0.4 fringe, implying a relative velocity of "less than one sixth" Earth's orbital velocity (~5 km/s) and "certainly less than one fourth" (~7.5 km/s). This is too small for Earth's orbital velocity (30 km/s) but NOT zero. It is too large for Fresnel/Lorentz (who predict zero for first-order effects) and too small for the full orbital velocity. Every theory has a problem with this result. > [!danger] Michelson Kills Three Theories on One Page (p. 341) > In three paragraphs, Michelson shows: > 1. **Stokes** (ether dragged): conditions are incompatible (per Lorentz) > 2. **Lorentz** (hybrid Stokes-Fresnel): if ether is at rest at surface, velocity potential fails, "his own theory also fails" > 3. **Fresnel** (ether at rest, drag coefficient): the result is too small to match orbital velocity, so either Earth doesn't move at 30 km/s, or the ether IS partially dragged (contradicting Fresnel's first hypothesis) > > None of the three major theories survive the result as stated. SR later "resolves" this by declaring the question meaningless and saying they measured c = c. > [!important] The Footnote About Emission Theory and Airy (p. 333) > Michelson's footnote is devastating: under emission theory, light is FASTER in water, so aberration should DECREASE. To recover the unchanged value, you'd need the water to carry light BACKWARD. "We must make the absurd hypothesis that the motion of the water in the telescope carries the ray of light in the opposite direction!" Both theories (emission and wave) fail on Airy without ad hoc rescues. > [!note] Proposed But Never Executed Methods > Michelson proposes mountain-top experiments, revolving mirror methods, spectroscopic stellar observations, and Jupiter satellite timing. These represent the unfulfilled experimental program that could, in principle, distinguish absolute from relative motion. As of 1887, the question remained open.