# The Speed of Light

Attempts to measure the speed of light have played an important part in the development of the theory of special relativity, and, indeed, the speed of light is central to the theory.

The idea of measuring the speed of light was first proposed in 1629 by Isaac Beeckman. He proposed an experiment when he observed the flash of a cannon about one mile away and heard the bang sometime later. Some years later, In 1638, Galileo Galilei devised an experiment to measure the speed of light by observing the delay between uncovering a lantern and its perception a distance away. While he was unable to distinguish whether light travel was instantaneous or not, he did conclude that it must be extraordinarily rapid.

The first quantitative estimate of the speed of light was made in 1676 by Romer. He did this from observations that the periods of Jupiter's innermost moon, Io, appeared to be shorter when the Earth was approaching Jupiter than when receding from it. He concluded that light must travel at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of the speed of light of 220,000 km/s, a value 26% lower than the modern measured value.

Throughout the 19th century, several other experiments were devised to refine this value until in 1862, Léon Foucault improving the on the works of Hippolyte Fizeau, came to a value of 298,000 km/s. The resulting Fizeau-Foucault apparatus involves a rotating mirror which reflects light onto a distant mirror. This distant mirror, in turn, reflects light back toward the viewer. If mirror the mirror is stationary, the slit image will reform at the viewer regardless of the mirror's angle. As the mirror rotates, the angle will have moved slightly in the time it takes for the light to bounce from the slit to the mirror and back, so the light will be deflected away from the original source by a small angle. The speed of light could be calculated based on the timing of the mirror and the angle the light is reflected.

In Foucault's experiment, lens L forms an image of slit S at spherical mirror M. If mirror R is stationary, the reflected image of the slit reforms at the original position of slit S regardless of how R is tilted, as shown in the lower annotated figure. However, if R rotates rapidly, the time delay due to the finite speed of light travelling from R to M and back to R results in the reflected image of the slit at S becoming displaced.

Since then, the speed of light has been accurately measured at a fixed value of 299,792,458 metres per second in a vacuum.

## Upper Limit on Speeds

The Special theory of relativity has many counterintuitive, yet experimentally verified implications including placing an upper limit on velocity. You see, the energy of an object with rest mass *m* and speed *v* is given by γmc2, where γ is the Lorentz factor. The Lorentz factor is the factor by which time, length, and relativistic mass change for an object while that object is moving.

When *v* is zero, γ is equal to one, giving rise to the famous E = mc^{2} formula for mass–energy equivalence.

The γ factor approaches infinity as *v* approaches *c*, and it would take an infinite amount of energy to accelerate an object with mass to the speed of light, thus the speed of light is the upper limit for the speeds of objects with positive rest mass.

Last updated on: Thursday 24th August 2017

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