Measuring the speed of light

Saya Kimura: https://www.pexels.com/photo/bright-clear-close-up-dark-401107/

3 x 10⁸ ms^-1. This is a value ingrained into the minds of all physicists: the speed of light (to one significant figure). Special relativity reveals that this is the ultimate speed limit of the universe. However, in the past, many believed that light propagates instantaneously. Danish astronomer, Ole Rømer, made the first quantitative measurement of the speed of light in 1676, demonstrating that light travels at a finite speed.

The Earth, the Sun and Jupiter

Rømer noticed that the distance between the Earth and Jupiter affected the time at which Io, the gas giant’s innermost moon, seemed to emerge. ^[1] When the Earth is closest to Jupiter in its orbit around the Sun, Io appeared from behind Jupiter earlier than expected. Meanwhile, when Earth was at its farthest point from Jupiter, Io emerged later than expected. ^[1] Light took longer to travel from Io to the Earth when the distance between the two was greater. Therefore, this revealed that light did not travel with infinite speed. Rømer’s value for the speed of light, obtained by measuring this time difference, was 2.14 x 10⁸ ms^-1. ^[2] This value is only an approximation because in the 17^th century, ‘planetary distances were not accurately known.’ ^[2]

Lasers

The exact value of the speed of light is now known to be 299,792,458 ms^-1. However, this is actually an adopted value. The most accurate experimental value for the speed of light was determined in 1972 by Evenson and collaborators. Using lasers, the team recorded a value of 299,792,456.2 ± 1.1 ms^-1. ^[3] They used a similar method to Michelson-Morley experiment (which disproved the existence of the aether): ‘split the beam of a laser, bounce it around two different path lengths and then recombine them to see how they interfere together.’ ^[4] By altering the path difference until you get consistent constructive interference, you can determine the wavelength of the light from the laser: the split waves are in phase and so their path difference must equal a multiple of the wavelength (ΔX = nλ – n is an integer). Although very accurate, you can see from their value that there is still a 1.1 ms^-1 uncertainty. It turns out the largest source of error in this uncertainty is the definition of the metre which is not set by the universe. Instead, it is set by humans. Historically, in 1791, it was defined as 1/10,000,000 of the ‘Earth’s circumference running from the North Pole through Paris to the equator.’ ^[5] In 1983, the General Conference on Weights and Measures decided that, since measurements for the speed of light had reached such high accuracy, the accepted value for this constant would be 299,792,458 ms^-1. As a result, the definition of the metre was now changed to 1/299,792,458 of the distance travelled by light in a vacuum per second. ^[5]

Sources:

1. Wonders of the Universe with Brian Cox: https://www.youtube.com/watch?v=DMKE5YGLnmc

2. Philip Gibbs: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html

3. Evenson et al: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.29.1346

4. Rebecca Smethurst: https://www.youtube.com/watch?v=V7PU1WN9jWY

5. Britannica: https://www.britannica.com/science/metre-measurement