# The speed of light controversy

Since the dawn of civilization light has always got mankind’s attention associated to its particular nature. Even though the properties of light such as color, fluorescence or absorption have found applications that date since ancient times, the measurement of its speed has undergone various changes throughout history.

In this post we will briefly explain the historical evolution in determining the speed of light (c) and the different scientists that played a role in it, from when it was considered that the speed of light was infinite to when its value was accurately calculated and standardized.

Before the seventieth century, it was widely believed that light propagated instantaneously. Galileo was the first who proposed an experiment to try to measure the speed of light, which he thought was finite. The experiment required two people, A and B, to go to the top of hills several miles apart from each other. First, person A would uncover his lantern and as soon as person B saw the light from A’s lantern, he would uncover his own lantern. The speed of light would be two times the distance (D) between person A and B divided by the time (t) passed between person A uncovered his lantern and person A saw person B’s light, that is, c = 2·D/t. The Accademia del Cimento of Florence tried to put into practice Galileo’s idea and obviously, they failed, as the speed of light if much faster than human reaction times [1].

The first measurement of the speed of light was done by Danish astronomer Olaus Roemer. He was making observations of the eclipses of Io, which is the innermost of Jupiter’s moons. Roemer realized that when the Earth moved away from Jupiter, Io appeared to stay behind the planet longer than when the Earth was moving towards Jupiter [2]. These observations would only make sense if the speed of light was finite and it took more time for the light to travel from Jupiter to the Earth when they were further apart from each other. Roemer estimated c = 2.14 · 108, an error of around 30%, which is understandable as planetary distances were not precisely known at that time. Roemer’s merit resides in demonstrating that the speed of light was finite.

In 1728, James Bradley made another estimation by employing stellar aberration, which is the difference between the observed position of a star and its real position, due to the combination of the observer’s speed and the speed of light. Bradley made his calculations by knowing the speed of the Earth around the Sun and the stelar aberration angle. He determined a value for the speed of light of 3.01·108 m/s [3].

The first estimation of c that was not based on astronomical measurements was carried out by Armand Fizeau in 1849 in which is known as the cogwheel experiment, see Figure 1. He employed a slit to produce a narrow beam that was reflected from a mirror located 8 km away. The speed of the cogwheel was progressively increased until its rotation was such that the light passed through one of the spaces between the teeth of the cogwheel and returned through the next space. With this method, Fizeau obtained a value for c of 3.15·108 m/s [3].

Leon Foucault measured the speed of light in 1850 by employing rotating mirrors [3], see Figure 2. His setup consisted in a beam that passed through a slit S and was reflected off a rotating mirror R with constant speed w, creating an image of the slit on the distant stationary and curved mirror M. The rotating mirror R moves an angle q during the time it takes the light to travel from R to M and back, so the light will be deflected from the original source. This setup provided a more precise value for c of 2.98·108 m/s by employing equation 1. In 1879, Albert Michelson redesigned Foucault’s setup and obtained a more accurate value of 299,910 km/s.

Once Maxwell published his well-known equations in 1865, the speed of light could be calculated indirectly by measuring the magnetic permeability (µ0) and the electric permittivity (e0) of free space, as he had predicted that the electromagnetic waves travelled at the speed of light, which could be defined in terms of  µ0 and e0, see equation 2. In 1907, Rosa and Dorsey employed this method to provide a value of 299,788 km/s [3].

In the second half of the twentieth century, the accuracy of the measurement of the speed of light was still improved. It is worth mentioning Froome’s measurement in 1958 [3], obtaining a value of 299,792.5 km/s by employing a microwave interferometer and a Kerr cell shutter; as well as Evenson et al. method [5], consisting in calculating c from direct frequency and wavelength measurements of a methane-stabilized laser, leading to a value of  299,792.4574 km/s.

By 1970, the speed of light was known with an uncertainty of less than 1 m/s, so it became more practical to define the meter as a function of the speed of light instead of the other way round. In 1983 it was decided by international agreement to change the definition of the meter to “the distance travelled by light in vacuum during a time interval of 1/299,792,458 of a second”, therefore making the speed of light exactly equal to 299,792.458 km/s [3].

Written by J.J. Imas

[1]      J. Deaton and T. Patrick, “History of the Speed of Light ( c ),” 1996.

[2]      “Measuring the Speed of Light.” https://physics.uwb.edu.pl/main/ptf/fizyka2000/waves_particles/lightspeed_evidence.html (accessed Mar. 21, 2021).

[3]      “How is the speed of light measured?” https://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html (accessed Mar. 21, 2021).

[4]      “Fizeau–Foucault apparatus – Wikipedia.” https://en.wikipedia.org/wiki/Fizeau–Foucault_apparatus (accessed Mar. 28, 2021).

[5]      K. M. Evenson et al., “Speed of light from direct frequency and wavelength measurements of the methane-stabilized laser,” Phys. Rev. Lett., vol. 29, no. 19, pp. 1346–1349, Nov. 1972, doi: 10.1103/PhysRevLett.29.1346.