How Can We Find the Probabilities of the Speed of Light?

Physics students are well known about C or the speed of light. It moves around 3 x 10^8 meters per second.

More curious students will know that this is an approximation, and the figure of 299,792,458 meters per second makes up the officially accepted figure. 

That comes from the resonance of the cesium atom giving one value for the other.

But for those who are genuinely curious about measuring the speed of light, the question remains. 

How did we reach that figure and for how long have we been measuring it?

The answer includes some surprises, and some extraordinarily clever scientific ideas and experiments over the centuries.

The nature of light and whether it's speed has puzzled philosophers and scientists since ancient times, but the first experiments to measure it that you won't be surprised to hear were by Galileo in the early 17th century.

His experiment involved the observation of his assistants lighting the lamp at a known distance, and his observations failed to reach a conclusion.

Later that century, in 1676, the first numerical estimate of the speed of light was made by Danish astronomer Ole Römer, who observed a marked variation in the period of one of Jupiter's moons, depending on how close the Earth was to it.  

From this he was able to estimate the time taken for light to cross the Earth's orbit, and from there mathematician Christiaan Huygens was able to work out the figure of 220,000,000 meters per second.

The experiments we'll probably be most familiar with are the so-called time of flight measurements, which look at Galileo's idea that light travels a distance as it travels, and brings it ever higher precision.

This was first done in the mid-19th century by French physicist Hippolyte Fizzou, who reflected a beam of light from a mirror over several miles, and used a toothed wheel to cut it into like pulses.

The pulses can be increased in frequency by rapidly rotating the wheel until the time taken for the light to travel the distance from the wheel to the mirror and back to match the separation between the teeth and the back pulse can be observed.

His calculation of 313,300,000 meters per second was progressively improved through the work of a succession of others including Léon Foucault, culminating in the 1920s by American physicist Albert A. Michelson in a series of experiments.

Michelson's final figure was 299,774,000 meters per second, measured via a multi-path traversal of a one-mile-long empty tube in the California desert.

In the latter part of the century the technique shifted to laser interferometry, and in the quest to define SI units as constants, eventually according to the definition outlined in the first paragraph.

Perhaps the most fascinating part of the story encapsulates the essence of scientific discovery, namely that when it takes several scientists to build on each other's work to arrive at something, it can often be presented in a form that is Understandably, a student who hasn't had to go through all that effort.

We can replicate Fizou and Michelson's experiments with a pulse generator, laser diode, and oscilloscope, which, almost a century after Michelson's evacuated tube, have little scientific value, yet still very good.


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