The first step on the road to Einstein’s relativity was taken a hundred years earlier by an ironic rebel of physics—Augustin Fresnel.  His radical (at the time) wave theory of light was so successful, especially the proof that it must be composed of transverse waves, that he was single-handedly responsible for creating the irksome luminiferous aether that would haunt physicists for the next century.  It was only when Einstein combined the work of Fresnel with that of Hippolyte Fizeau that the aether was ultimately banished.

Augustin Fresnel: Ironic Rebel of Physics

Augustin Fresnel was an odd genius who struggled to find his place in the technical hierarchies of France.  After graduating from the Ecole Polytechnique, Fresnel was assigned a mindless job overseeing the building of roads and bridges in the boondocks of France—work he hated.  To keep himself from going mad, he toyed with physics in his spare time, and he stumbled on inconsistencies in Newton’s particulate theory of light that Laplace, a leader of the French scientific community, embraced as if it were revealed truth . 

The final irony is that Einstein used Fresnel’s theoretical coefficient and Fizeau’s measurements—that had introduced aether drag in the first place—to show that there was no aether. 

Fresnel rebelled, realizing that effects of diffraction could be explained if light were made of waves.  He wrote up an initial outline of his new wave theory of light, but he could get no one to listen, until Francois Arago heard of it.  Arago was having his own doubts about the particle theory of light based on his experiments on stellar aberration.

Stellar Aberration and the Fresnel Drag Coefficient

Stellar aberration had been explained by James Bradley in 1729 as the effect of the motion of the Earth relative to the motion of light “particles” coming from a star.  The Earth’s motion made it look like the star was tilted at a very small angle (see my previous blog).  That explanation had worked fine for nearly a hundred years, but then around 1810 Francois Arago at the Paris Observatory made extremely precise measurements of stellar aberration while placing finely ground glass prisms in front of his telescope.  According to Snell’s law of refraction, which depended on the velocity of the light particles, the refraction angle should have been different at different times of the year when the Earth was moving one way or another relative to the speed of the light particles.  But to high precision the effect was absent.  Arago began to question the particle theory of light.  When he heard about Fresnel’s work on the wave theory, he arranged a meeting, encouraging Fresnel to continue his work. 

But at just this moment, in March of 1815, Napoleon returned from exile in Elba and began his march on Paris with a swelling army of soldiers who flocked to him.  Fresnel rebelled again, joining a royalist militia to oppose Napoleon’s return.  Napoleon won, but so did Fresnel, who was ironically placed under house arrest, which was like heaven to him.  It freed him from building roads and bridges, giving him free time to do optics experiments in his mother’s house to support his growing theoretical work on the wave nature of light. 

Arago convinced the authorities to allow Fresnel to come to Paris, where the two began experiments on diffraction and interference.  By using polarizers to control the polarization of the interfering light paths, they concluded that light must be composed of transverse waves. 

This brilliant insight was then followed by one of the great tragedies of science—waves needed a medium within which to propagate, so Fresnel conceived of the luminiferous aether to support it.  Worse, the transverse properties of light required the aether to have a form of crystalline stiffness.

How could moving objects, like the Earth orbiting the sun, travel through such an aether without resistance?  This was a serious problem for physics.  One solution was that the aether was entrained by matter, so that as matter moved, the aether was dragged along with it.  That solved the resistance problem, but it raised others, because it couldn’t explain Arago’s refraction measurements of aberration. 

Fresnel realized that Arago’s null results could be explained if aether was only partially dragged along by matter.  For instance, in the glass prisms used by Arago, the fraction of the aether being dragged along by the moving glass versus at rest would depend on the refractive index n of the glass.  The speed of light in moving glass would then be

where c is the speed of light through stationary aether, v_g is the speed of the glass prism through the stationary aether, and V is the speed of light in the moving glass.  The first term in the expression is the ordinary definition of the speed of light in stationary matter with the refractive index.  The second term is called the Fresnel drag coefficient which he communicated to Arago in a letter in 1818.  Even at the high speed of the Earth moving around the sun, this second term is a correction of only about one part in ten thousand.  It explained Arago’s null results for stellar aberration, but it was not possible to measure it directly in the laboratory at that time.

Fizeau’s Moving Water Experiment

Hippolyte Fizeau has the distinction of being the first to measure the speed of light directly in an Earth-bound experiment.  All previous measurements had been astronomical.  The story of his ingenious use of a chopper wheel and long-distance reflecting mirrors placed across the city of Paris in 1849 can be found in Chapter 3 of Interference.  However, two years later he completed an experiment that few at the time noticed but which had a much more profound impact on the history of physics.

In 1851, Fizeau modified an Arago interferometer to pass two interfering light beams along pipes of moving water.  The goal of the experiment was to measure the aether drag coefficient directly and to test Fresnel’s theory of partial aether drag.  The interferometer allowed Fizeau to measure the speed of light in moving water relative to the speed of light in stationary water.  The results of the experiment confirmed Fresnel’s drag coefficient to high accuracy, which seemed to confirm the partial drag of aether by moving matter.

This result stood for thirty years, presenting its own challenges for physicist exploring theories of the aether.  The sophistication of interferometry improved over that time, and in 1881 Albert Michelson used his newly-invented interferometer to measure the speed of the Earth through the aether.  He performed the experiment in the Potsdam Observatory outside Berlin, Germany, and found the opposite result of complete aether drag, contradicting Fizeau’s experiment.  Later, after he began collaborating with Edwin Morley at Case and Western Reserve Colleges in Cleveland, Ohio, the two repeated Fizeau’s experiment to even better precision, finding once again Fresnel’s drag coefficient, followed by their own experiment, known now as “the Michelson-Morley Experiment” in 1887, that found no effect of the Earth’s movement through the aether.

The two experiments—Fizeau’s measurement of the Fresnel drag coefficient, and Michelson’s null measurement of the Earth’s motion—were in direct contradiction with each other.  Based on the theory of the aether, they could not both be true.

But where to go from there?  For the next 15 years, there were numerous attempts to put bandages on the aether theory, from Fitzgerald’s contraction to Lorenz’ transformations, but it all seemed like kludges built on top of kludges.  None of it was elegant—until Einstein had his crucial insight.

Einstein’s Insight

While all the other top physicists at the time were trying to save the aether, taking its real existence as a fact of Nature to be reconciled with experiment, Einstein took the opposite approach—he assumed that the aether did not exist and began looking for what the experimental consequences would be. 

From the days of Galileo, it was known that measured speeds depended on the frame of reference.  This is why a knife dropped by a sailor climbing the mast of a moving ship strikes at the base of the mast, falling in a straight line in the sailor’s frame of reference, but an observer on the shore sees the knife making an arc—velocities of relative motion must add.  But physicists had over-generalized this result and tried to apply it to light—Arago, Fresnel, Fizeau, Michelson, Lorenz—they were all locked in a mindset.

Einstein stepped outside that mindset and asked what would happen if all relatively moving observers measured the same value for the speed of light, regardless of their relative motion.  It was just a little algebra to find that the way to add the speed of light c to the speed of a moving reference frame v_ref was

where the numerator was the usual Galilean relativity velocity addition, and the denominator was required to enforce the constancy of observed light speeds.  Therefore, adding the speed of light to the speed of a moving reference frame gives back simply the speed of light.

Generalizing this equation for general velocity addition between moving frames gives

where u is now the speed of some moving object being added the the speed of a reference frame, and v_obs is the “net” speed observed by some “external” observer .  This is Einstein’s famous equation for relativistic velocity addition (see pg. 12 of the English translation). It ensures that all observers with differently moving frames all measure the same speed of light, while also predicting that no velocities for objects can ever exceed the speed of light. 

This last fact is a consequence, not an assumption, as can be seen by letting the reference speed v_ref increase towards the speed of light so that v_ref ≈ c, then

so that the speed of an object launched in the forward direction from a reference frame moving near the speed of light is still observed to be no faster than the speed of light

All of this, so far, is theoretical.  Einstein then looked to find some experimental verification of his new theory of relativistic velocity addition, and he thought of the Fizeau experimental measurement of the speed of light in moving water.  Applying his new velocity addition formula to the Fizeau experiment, he set v_ref = v_water and u = c/n and found

The second term in the denominator is much smaller that unity and is expanded in a Taylor’s expansion

The last line is exactly the Fresnel drag coefficient!

Therefore, Fizeau, half a century before, in 1851, had already provided experimental verification of Einstein’s new theory for relativistic velocity addition!  It wasn’t aether drag at all—it was relativistic velocity addition.

From this point onward, Einstein followed consequence after inexorable consequence, constructing what is now called his theory of Special Relativity, complete with relativistic transformations of time and space and energy and matter—all following from a simple postulate of the constancy of the speed of light and the prescription for the addition of velocities.

The final irony is that Einstein used Fresnel’s theoretical coefficient and Fizeau’s measurements, that had established aether drag in the first place, as the proof he needed to show that there was no aether.  It was all just how you looked at it.

Further Reading

• For the full story behind Fresnel, Arago and Fizeau and the earliest interferometers, see David D. Nolte, Interference: The History of Optical Interferometry and the Scientists who Tamed Light (Oxford University Press, 2023)

• The history behind Einstein’s use of relativistic velocity addition is given in: A. Pais, Subtle is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, 2005).

• Arago’s amazing back story and the invention of the first interferometers is described in Chapter 2, “The Fresnel Connection: Particles versus Waves” of my recent book Interference. An excerpt of the chapter was published at Optics and Photonics News: David D. Nolte, “François Arago and the Birth of Interferometry,” Optics & Photonics News 34(3), 48-54 (2023)

• Einsteins original paper of 1905: A. Einstein, Zur Elektrodynamik bewegter Körper, Ann. Phys., 322: 891-921 (1905). https://doi.org/10.1002/andp.19053221004

… and the English translation: