exist. Alternatively, if light travels infinitely fast then the light would reach our eyes instantaneously, and we would see the lightning strike as it is happening. Deciding which scenario was correct seemed to be beyond the wit of the ancients.
The same question could be asked about sound, but this time the answer was more obvious. Thunder and lightning are generated simultaneously, but we hear the thunder after we see the lightning. For the ancient philosophers, it was reasonable to assume that sound has a finite speed and certainly travels much slower than light. They thus established a theory of light and sound based on the following incomplete chain of reasoning:
1. A lightning strike creates light and sound.
2. Light travels either very fast or infinitely fast towards us.
3. We see lightning very soon after the event, or instantaneously.
4. Sound travels at a slower speed (roughly 1,000 km/h).
5. Therefore we hear the thunder some time later, depending on the distance to the lightning strike.
But still the fundamental question relating to the speed of light – whether it was finite or infinite – continued to exercise the world’s greatest minds for centuries. In the fourth century BC, Aristotle argued that light travelled with infinite speed, so the event and the observation of the event would be simultaneous. In the eleventh century AD, the Islamic scientists Ibn Sina and al-Haytham both took the opposite view, believing that the speed of light, though exceedingly high, was finite, so any event could be observed only some time after it had happened.
There was clearly a difference of opinion, but either way the debate remained merely philosophical until 1638, when Galileo proposed a method for measuring the speed of light. Two observers with lamps and shutters would stand some distance apart. The first observer would flash a signal to the second, who would then immediately flash a signal back. The first observer could then estimate the speed of light by measuring the time between sending and receiving signals. Unfortunately Galileo was already blind and under house arrest when he came up with this idea, so he was never able to conduct his experiment.
In 1667, twenty-five years after Galileo’s death, Florence’s illustrious Accademia del Cimento decided to put Galileo’s idea to the test. Initially, two observers stood relatively close together. One flashed a lantern at the other, and the other would see the signal and flash back. The first man estimated the time between sending the original flash and seeing the response flash, and the result was an interval of a fraction of a second. This, however, could be attributed to their reaction times. The experiment was repeated over and over again, with the two men moving farther apart, measuring the time of the return flash over increasing distances. Had the return time increased with distance, it would have indicated a relatively low and finite speed of light, but in fact the return time remained constant. This implied that the speed of light was either infinite, or so fast that the time taken by the light to travel between the two observers was insignificant compared with their reaction times. The experimenters could draw only the limited conclusion that the speed of light was somewhere between 10,000 km/h and infinity. Had it been any slower, they would have detected a steadily increasing delay as the men moved apart.
Whether the speed of light was finite or infinite remained an open question until a Danish astronomer named Ole Römer addressed the issue a few years later. As a young man, he had worked at Tycho Brahe’s former observatory at Uraniborg, measuring the observatory’s exact location so that Tycho’s observations could be correlated with others made elsewhere in Europe. In 1672, having earned a reputation as an excellent surveyor of the heavens, he was offered a post at the prestigious Academy of Sciences in Paris, which had been set up so that scientists could pursue independent research, free from having to pander to the whims of kings, queens or popes. It was in Paris that fellow Academician Giovanni Domenico Cassini encouraged Römer to study a strange anomaly associated with Jupiter’s moons, in particular Io. Each moon should orbit Jupiter in a perfectly regular manner, just as our Moon orbits the Earth regularly, so astronomers were shocked to discover that Io’s timings were slightly irregular. Sometimes Io appeared from behind Jupiter ahead of schedule by a few minutes, while at other times it was a few minutes late. A moon should not behave in this way, and everybody was baffled by Io’s lackadaisical attitude.
In order to investigate the mystery, Römer studied in minute detail a table of Io’s positions and timings that had been logged by Cassini. Nothing made sense, until it gradually dawned on Römer that he could explain everything if light had a finite speed, as shown in Figure 19. Sometimes the Earth and Jupiter were on the same side of the Sun, whereas at other times they were on opposite sides of the Sun and farther apart. When the Earth and Jupiter were farthest apart, then the light from Io had to travel 300,000,000 km farther before reaching the Earth compared with when the two planets were closest together. If light had a finite speed, then it would take longer for the light to cover this extra distance and it would seem as if Io was running behind schedule. In short, Römer argued that Io was perfectly regular, and its apparent irregularity was an illusion caused by the different times required for the light from Io to cover different distances to the Earth.
To help understand what is going on, imagine that you are near a cannon that is fired exactly on the hour. You hear the cannon, start your stopwatch and then start driving away in a straight line at l00 km/h, so that you are 100 km away by the time the cannon is fired again. You stop the car and hear a very faint cannon blast. Given that sound travels at roughly 1,000 km/h, you will perceive that it was 66 minutes, not 60 minutes, between the first and second cannon blasts. The 66 minutes consists of 60 minutes for the actual interval between firings and 6 minutes for the time taken for the sound of the second blast to cover the 100 km and reach you. The cannon is perfectly regular in its firings, but you will experience a delay of 6 minutes because of the finite speed of sound and your new position.
Figure 19 Ole Römer measured the speed of light by studying the movements of Jupiter’s moon Io. These diagrams represent a slight variation on his actual method. In diagram (a), Io is about to disappear behind Jupiter; in diagram (b) Io has completed half a revolution so that it is in front of Jupiter. Meanwhile, Jupiter has hardly moved and the Earth has moved significantly, because the Earth orbits the Sun twelve times more quickly than Jupiter. An astronomer on the Earth measures the time that has elapsed between (a) and (b), namely the time taken for Io to complete half a revolution.
In diagram (c), Io has completed another half-revolution back to where it started, while the Earth has moved on to a position that is farther from Jupiter. The astronomer measures the time between (b) and (c), which should be the same as the time between (a) and (b), but in fact it turns out to be significantly longer. The reason for the extra time is that it takes the light from Io a little longer to cover the extra distance to the Earth in diagram (c), because the Earth is now farther away from Jupiter. The time delay and the distance between Earth and Jupiter can be used to estimate the speed of light. (The distances moved by the Earth in these diagrams are exaggerated, because Io orbits Jupiter in less than two days. Also, Jupiter’s position would change and complicate matters.)
Having spent three years analysing the observed timings of Io and the relative positions of the Earth and Jupiter, Römer was able to estimate the speed of light to be 190,000 km/s. In fact, the true value is almost 300,000 km/s, but the important point was that Römer had shown that light had a finite speed and derived a value that was not wildly inaccurate. The age-old debate had been resolved at last.
However, Cassini was distraught when Römer announced his result, because he received no acknowledgement from Römer, even though the calculation was based largely on his observational data. Cassini became a harsh critic of Römer and a vocal spokesman for the majority who still favoured the theory that the speed of light was infinite. Römer did not relent, and used his finite light speed to predict that an eclipse of Io on 9 November 1676 would occur 10 minutes later than predicted by his opponents. In a classic case of ‘I told you so’, Io’s eclipse was indeed several minutes behind schedule. Römer was proved right, and he published another paper confirming his measurement of the speed of light.