Thursday, November 3, 2011

Seeing the light

Galileo was one of the first people to attempt to measure the speed of light. He failed.

Looking back with hindsight it is easy to regard his attempt as a little naive: It consisted of people stood on hill tops, flashing lanterns at each other and measuring how long it took for the flashes of light to travel around the circuit formed by these people. Clearly the reaction times of each of these individuals was a big factor in the reliability of the results and consequently Galileo was left to conclude that the time taken by the light was swamped by the uncertainties due to reaction times.

But was Galileo naive for even trying it? Many people certainly think so. But suppose we replaced the lanterns with air horns and, instead of measuring the speed of light, used a similar method to measure the speed of sound? Would that be naive? To most people the speed of sound is also pretty fast - afterall, when talking to each other we don't notice a time lapse between lips moving and hearing sounds - the speed of sound, to all intents and purposes, appears to be infinite! And yet, the Galilean method is capable of yielding pretty good results.

I like discussing Galileo's experiment with my students for several reasons, but mainly so that they can appreciate the differences between uncertainties and systematic errors and how data can be analysed in the light of such factors. Human reaction time actually has both a systematic component and an uncertainty: T systematic error (of about 0.2 seconds) is due to the physical time it takes for someone to react, whilst the random uncertainty is due to the fact that sometimes people reaction slightly faster and at other times they react slightly slower. The uncertainty can be estimated quite easily by repeating the experiment many times and looking at the spread of results. By repeating an experiment many times and taking an average the affect of the random uncertainty can also be reduced, just leaving the systematic error.

Suppose you were now to carry out the experiment using a different set of hills, so as to vary the distance that the light pulses travel. By doing so you could soon plot a graph of distance against time. The y-intercept of this line would give you the systematic error, whilst the gradient should yield your speed.

Clearly, when carried out for light, the gradient of the resulting line would be very great and have a huge uncertainty, but carried out using sound it should yield a reasonable estimate whilst teaching some very important scientific principles.

Why don't you try it out? I'm certainly planning to do so.

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