Speed of Light

Io passing in front of Jupiter

The current value of the speed of light is around 300,000 km per second. This is a staggeringly large number, which means that the speed of light is staggeringly fast.

Think about that for a minute, 300,000 km in a single second By the time you have finished thinking for one minute, light has travelled 18 million kilometers! Moon and back just under 50 times! Light would travel round the earth 7 times in 1 second. Intellectually we know how big the earth is, it's circumferance is around 25,000 miles, but this does not give us a real sense of how big it is. Even if you have run a marathon, about 26 miles, this is about a thousandth of the distance. Can you imagine what 1000 marathons would look like end to end.

Try to imagine a train journey, that covers say, 200 miles, 300 kilometers, on a high speed train this will take around 1 hour, but Light would make the same journey in 1 milli-second. The problem here though is that 1 millisecond is too fast for us to appreciate. There are few things that happen at a thousandth of a second that we are aware of. Anything faster than 20 ms will pass undetected by the human eye.

For me the above examples are the problem I have when trying to image the speed of light. Things happen too fast or involve distances so large as to be beyond my imagination. There is actually nothing in every day experience that can really give you any sense of what the speed of light really means. You can try, but I don't think it is possible.

It is so fast that for many years it was thought that light may be instantaneous. 

Galileo had tried a couple of experiments to try and determine the speed of light but had failed. The credit for the first measurement goes to Ole Rømer, a Dutch man, way back in 1676. Sadly, most of his work was lost during a fire in 1728. How did he do it? and what number did he come up with?

At the time Rømer was observing the heavens, trying to figure out longitude in navigation was still a big problem. One potential solution was to use the times of the eclipses of the moons of Jupiter! Seriously, how clever is that? They used the Jovian system as a giant clock. This was impractical on ships but could be used on land.

Jupiter has a moon Io, and in can be eclipsed by Jupiter, and it can travel across the front of Jupiter. This can be seen using a telescope. It takes 42.5 hours to do an orbit. Jupiter is large and can get in the way of observing the point were Io enters the eclipse and  leaves an eclipse. So it is only possible to do the observation for just over half of the year.

The earth itself is moving around the sun and what this means is that for some of the observations we are actually moving towards Jupiter and for some we are moving away from Jupiter. How Ole Rømer used this knowledge, is for me, a stroke of brilliance. Here is comes.

1) He works out the length of an orbit, 42 hours 28 minutes 31¼ seconds.
2) He then works out when it should be occuring in the future.
3) He measures again 7 weeks later to discover that his calculation is out by a total of 15 minutes
4) He realises that if the orbit is constant, then the difference must be because of the change in distance between the Earth and Jupiter over the 7 weeks.
5) It was common place in those days to work out the positions of Earth and Jupiter in their orbits and with a bit of (what is now) school boy trig he could work out the change in distance over this period.
6) He then argued that the difference between calculation (step 2 above) and the observation (step 3), 15 minutes was due to the time it took light to travel the extra distance between Jupiter and Earth.

It is step 6 that matters. By having confidence in his initial results he was able to propose that the difference is due to light taking time to travel the extra distance between the Earth and Jupiter. Suffice to say that this result was controversial and many thought that her was wrong. Rømer's boss Cassini, was one of these! It may have been this objection by Cassini that lead Rømer not to formally publishing his results. It actually took until 1727, more than 50 years later, that the result was formally accepted when it was backed up by other measurements. By which time Ole Rømer was well dead.

The value he came up with was around 200,000km/s, far short of the real value of around 300,000km/s. The the error is probably due to some of the assumptions he made. While this is a considerable error, it is still a remarkable result.  It did show two things, firstly that light was not instantaneous, secondly, it did move tremendously quick.

Beyond the fact that it was fast, and it was shown by Maxwell to be electro-magnetic radiation, it was not until Michelson-Morley experiment in 1887 that light showed its most peculiar property of all, and one that lead to Einstein's Special Theory of relativity. This is covered in the next post.