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E is the vast domain of energies, and m is the material stuff of the universe. But c is simply the speed of light. (Celeritas is Latin for "swiftness.") How can this particular speed—what might seem an arbitrary number—control the link between all the mass and all the energy in the universe?

Before Einstein could have possibly thought of using c, someone had to confirm that light travels at a finite speed. Galileo was the first person to clearly conceive of measuring the speed of light. It took a brash young Danish astronomer named Ole Roemer, however, to accomplish the feat. He did it through one of the tensest scientific showdowns of the 17th century.

Ole Roemer's great challenge

In 1671, when Roemer was just 21 years old, he was recruited from Denmark to work at the new Paris Observatory headed by Jean-Dominique Cassini. Others might have been humbled to meet the great Cassini, a world authority on the planet Jupiter and especially on the orbits of its satellites. But Roemer was cockily proud, enough to challenge Cassini and try making his own name.

Cassini had a problem with the innermost moon of Jupiter, the one called Io. It was supposed to orbit its planet every 42 and a half hours. But it never stuck honestly to schedule. Everyone—even Cassini—assumed that the problem was in how Io traveled. Possibly it was ungainly and wobbled during its orbit. Young Roemer, though, reversed the problem. The question wasn't how Io was moving. It was how Earth was moving in relationship to Jupiter.

Cassini and almost everyone of the day assumed that light traveled as an instantaneous flash, but Roemer supposed that light took some time to travel the great distance from Jupiter. In the summer, if Earth was closer to Jupiter, the light's journey would be shorter, and Io's image would arrive sooner. In the winter, though, if Earth had swung around to the other side of the solar system, it would take a lot longer for Io's signal to reach us.

The day of reckoning

By the late summer of 1676, Roemer had an exact figure for how many extra minutes light took to fly that extra distance when Earth was far from Jupiter. At the public forum of a journal all serious astronomers read, he proclaimed a challenge: Io would appear from behind Jupiter the following November 9 not at 5:27 p.m., as Cassini calculated, but ten minutes later, at 5:37.

On November 9, observatories in France and across Europe had their telescopes ready. 5:27 p.m. arrived. No Io. 5:30 arrrived. Still no Io. 5:35 p.m. And then it appeared, at 5:37 and 49 seconds exactly. And yet Cassini declared he had not been proven wrong! It was so far away, so hard to see exactly, that perhaps those clouds from Jupiter's upper atmosphere were producing a distorting haze.

Roemer had performed an impeccable experiment, with a clear prediction, yet Europe's astronomers still did not accept that light traveled at a finite speed. Cassini's supporters won: the official line remained that the speed of light was just a mystical, unmeasureable figure.

Roemer gave up and went back to Denmark. Only 50 years later did further experiments convince astronomers that he had been right. The value Roemer had estimated for light's speed was close to the actual speed of light, which is about 670,000,000 mph.

It's fast, but what is it?

While the speed of light was pinpointed in the 1600s, the exact nature of light was poorly understood until centuries later. The story picks up in the late 1850s, when an elderly Michael Faraday began to correspond with James Clerk Maxwell, a slender Scot still in his 20s.

Back in his 1821 breakthrough, and then in much research after, Faraday had shown ways in which electricity can be turned into magnetism, and vice versa. Maxwell, who probably had the finest mathematical mind of any 19th-century theoretical physicist, extended the idea.

What was happening inside a light beam, Maxwell began to see, was just another variation of this back-and-forth movement. When a light beam starts going forward, one can think of a little bit of electricity being produced, and then as the electricity moves forward it powers up a little bit of magnetism, and as that magnetism moves on, it powers up yet another surge of electricity, and so on like a braided whip snapping forward.

Faraday's much maligned hunch that light was an electromagnetic phenomenon had been correct after all.