Arago’s Inadvertent Test of Relativity

Greg Gbur

Nearly 100 years before Einstein’s special theory of relativity, François Arago unknowingly found the first experimental evidence for it.



lighttouch-img1.jpgPortrait of Arago.

Wikimedia Commons/Engraving by A.V. Sixdeniers/Painting by H. Scheffer

The year 2010 marked an unusual and little known milestone in the history of physics: the 200-year anniversary of the first experimental evidence for Einstein’s special relativity. In 1810, French physicist François Arago (1786-1853) attempted and failed to measure expected variations in the speed of light coming from distant stars. Of course, Einstein’s theory of special relativity, which postulates the constancy of the vacuum speed of light, would not be proposed until 1905. Arago didn’t discover relativity, but his experiment nevertheless had a remarkable influence on 19th century physics and a role in the acceptance of the wave theory of light.

The years leading up to Arago’s experiment were trying ones for the young researcher. In 1806, at age 20, he undertook a trip to Spain with Jean-Baptiste Biot on behalf of the Académie des Sciences to perform mountaintop triangulation measurements of the curvature of the Earth. Things went so smoothly that Biot soon returned to France and left Arago in charge. In late 1807, Napoleon invaded Spain, and angry Spanish locals assumed that the Frenchman shining mysterious lights at the mountain’s peak was signaling the French army.

What followed was a dangerous odyssey that lasted nearly two years. Arago first allowed himself to be imprisoned on the island of Ibiza for his own protection. However, when he was presented news accounts of his own execution, he read between the lines and escaped, heading to Algiers and then catching a ship back towards safety in Marseilles. The Algerian ship was intercepted by the Spanish, though, and Arago was imprisoned a second time on the Spanish coast. When the Algierian government forced the prisoners’ release, the ship made again for Marseilles, only to be blown by an intense windstorm further down the African coast. In 1809, after a dangerous overland trip back to Algiers, Arago finally returned to France—where he then spent weeks in quarantine.

Arago’s adventures—and the fact that he held on to his research notes in spite of them—led him to a prestigious membership in the Académie des Sciences. With this new position, Arago turned to answering a question that had been troubling astronomers: Is the speed of light from all stars constant? In 1725, James Bradley showed that the observed angular positions of stars shift seasonally, in a phenomenon now known as stellar aberration. This aberration is a consequence of the Earth’s motion and the finite speed of light, just as vertically falling rain appears to fall at an angle to an observer moving through it. However, the aberration is strongly dependent on the speed of light, and astronomers were divided on whether this speed was the same for all starlight. According to Newton’s corpuscular theory of light, it was thought that light escaping a star’s gravitational well would be slowed, and larger stars would consequently emit slower corpuscles.

Stars of different sizes would therefore have different aberrations; unfortunately, direct telescope aberration measurements were not sensitive enough to observe the predicted variations. Under the corpuscular theory, however, the refraction of light was interpreted as an increase in the normal component of the corpuscle’s speed. Light of different speeds would consequently have different refraction angles, and starlight would thus have different degrees of aberration when viewed through air or dense media.

Arago devised a clever and simple technique to test this. He glued an achromatic prism to cover one half of the objective lens of a telescope and examined the deviation in light rays after passing through the prism. The prism for his early experiments was a piece of crown-glass and a piece of flint glass fixed together, with a total angle of roughly 24 degrees. In this manner he could precisely measure the angle of refraction and deduce the speed of light from it.

The result of Arago’s experiment surprised him—he found no significant variation of the speed of light from star to star. According to Newtonian relativity, the speed should at least have been subject to seasonal variations as the Earth moved towards and away from observed stars. Though Arago did see fluctuations comparable to the seasonal ones, they were completely uncorrelated with the seasons and dismissed as experimental uncertainty.

Arago came up with a desperate hypothesis to explain his negative result: Stars radiate over a broad range of speeds with uniform intensity, but the human eye can only detect the rays that lie within a narrow velocity and spectral range. This was not as completely off-the-wall as one might think. Infrared light was discovered in 1800 by William Herschel, and in 1801 Johann Ritter discovered ultraviolet light; both types of radiation are just outside of the visible spectrum. Arago used these new phenomena as evidence for his hypothesis, but the explanation remained unconvincing.

Some years later, another famous scientist would intervene to help explain Arago’s perplexing results. In 1815, Augustin-Jean Fresnel presented his first paper on diffraction theory to the Académie des Sciences. The paper so impressed Arago that the two quickly became friends. Fresnel further honed his diffraction theory, and in 1818 offered a revised memoir for the Académie’s prize problem: a physical explanation for diffraction. The prize committee was nonplussed when Fresnel proposed that diffraction was evidence for the wave nature of light. Siméon Denis Poisson observed that Fresnel’s theory led to the seemingly preposterous conclusion that a bright spot of light should appear in the geometrical shadow of an opaque disk. Arago performed the experiment, found “Poisson’s spot,” and thus produced the first dramatic evidence in favor of the wave nature of light.

Arago was really repaying a favor for Fresnel, who that same year had rescued Arago’s perplexing experiment on stellar aberration. In an 1818 letter, Fresnel suggested that Arago’s result could be elegantly explained by using the wave hypothesis. He reasoned that light, as a wave, must propagate in a material medium, the “aether,” as sound waves travel in air. Aether had been discussed for years by proponents of the wave theory, but its behavior was treated as independent of the motion of matter. Fresnel demonstrated theoretically that Arago’s negative result could be explained if the aether is partially dragged along in the presence of moving matter, by a degree related to the refractive index.

Fresnel’s explanation, and his other diffraction results, led Arago and others to wholeheartedly accept the wave nature of light. The idea of aether drag became an accepted aspect of the wave theory, and would seemingly be further vindicated in the 1850s in experiments by Fizeau. The aether would be rendered unnecessary when Einstein’s special theory of relativity offered a more elegant explanation: The speed of light is constant for every observer moving in an inertial frame of reference.

Arago’s work is a case study of ironic science: It was a failed experiment (no variations in the speed of light were detected), based on incorrect theories of light propagation (Newton’s corpuscular theory) and interpreted incorrectly by Fresnel (as aether drag), but this incorrect interpretation helped lead to the (correct) view that light has wavelike properties. It demonstrates that the path to understanding complicated physical phenomena is often a convoluted one.

Greg Gbur is an associate professor of physics who specializes in optical science at the University of North Carolina, Charlotte, N.C., U.S.A.

References and Resources

>> A. Fresnel. “Lettre d’Augustin Fresnel à François Arago sur l’influence du mouvement terrestre dans quelques phénomènes d’optique,” Annales de Chimie et de Physique 9, 57 (1818).
>> F. Arago. Biographies of Distinguished Scientific Men, Longman, Brown, Green, Longmans & Roberts, London, U.K., 1857.
>> F. Arago. “Vitesse de la lumière,” Œuvres Complètes 7, 548 (1858).
>> Skulls in the Stars blog. François Arago: the most interesting physicist in the world! 16 January 2012.

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