The unconventional Scottish physicist James Clerk Maxwell did understand mathematics. He read Faraday’s papers on electricity and magnetism and then, by pulling together all that was known about them, wrote four new equations in a paper published in 1861. For the first time, they described electromagnetism.
This was a far more difficult task than simply translating Faraday’s words into math. Maxwell had to work out that not only does an electric current produce a magnetic field but so does an electric charge that is only displaced, not flowing continuously. Contained within this idea was the math to prove that space is filled with electromagnetic waves independent of any electric currents. Electricity, therefore, was a manifestation, even a subset, of the electromagnetic force. This was something the electricians of the previous century could never have imagined. When Maxwell read his equations carefully, they also told him that electricity, magnetism, and light were aspects of each other. They all behaved as waves traveling at the speed of light across space, a speed he had calculated a few years later. This was the collection of invisible lines of force that Faraday had dreamt of and partly glimpsed. Now it was enshrined in mathematics, available for all physicists to play with.
Maxwell’s equations predicted that electromagnetic waves can be literally any length. As the physicist Neil Turok explains, the waves are just “stretched-out or shrunken-down versions of one another.” Most are invisible to humans, just as most frequencies of sound waves are inaudible, including the high frequencies of ultrasound. The electromagnetic waves we can see are far smaller than a millionth of a meter in length and they give us color. The very longest we can see are red; the shortest, violet. But there are even smaller electromagnetic waves, such as the dangerous gamma rays produced in the Large Hadron Collider, whose activities were lighting up the façade of the Niels Bohr Institute in Copenhagen when I was there, and X-rays. Extremely long waves, known as ultra-low-frequency waves, can penetrate the Earth and are used to communicate in mines. Other types include microwaves, which work in the appliance of that name but also make radar function. There is also the big group longer than microwaves called radio waves, which are put to work in cell phones, radios, and televisions. But as different as they may seem, all these waves can be described mathematically in exactly the same terms. That finding laid the groundwork for the electrical infrastructure that supports virtually all the energy and information we use in our modern world.
Ultimately, Maxwell’s equations led to the elegant math describing the standard model of physics developed in the early 1970s. Today, if the standard model equation proves that something can be true, then it is, no matter how counterintuitive it might seem. That’s how an electron can be a particle and a vibration in a field at the same time, or how the Higgs boson was imagined before it was found. The revolution in scientific thinking this represents is vast. At the beginning of electromagnetic research, the Bible was the only truth. Natural philosophers, like Galileo, had to flout authority to make observations about nature that went against what the Bible said. Data points and logical conclusions were dangerous. Later, observational results were all that mattered; the highest scientific endeavor was to explain the world through the evidence of your own eyes. Today, the standard model equation is king, with its alarming precision and its preposterous abstractions. Observation, while not passé, is not everything.
Here’s an example: Maxwell’s equations theoretically connected space and time, a profoundly improbable fact. That led directly to Albert Einstein’s special theory of relativity, which states that time and space are not fixed. Time does not march on, unheeding, as the poets might say. Neither are time and space separate from each other. Instead, they are a continuum, capable of adjusting themselves in order to make sure the speed of light—that is, Faraday’s tiny electromagnetic wave—is fixed.
Einstein published his special theory of relativity in 1905 in the journal Annalen der Physik while working in a patent office in Bern, Switzerland. It was one of four remarkable papers he published that same year, known as his annus mirabilis, or miraculous year. His work that year changed the way physicists saw time, space, mass, and energy. That same year, a few hundred kilometers to the southwest, Bernard Brunhes made his trek by horse to Pont Farin in the Cantal of France to the brand-new roadcut, where he hacked away at the seam of ancient terracotta that showed that the Earth’s poles had once been on opposite sides of the planet.
I had made a special request that James show me the entry in Faraday’s journal from the fateful day in 1831 when he wrote up his experiment with the induction ring. James pressed a code pad that allowed him into the locked archives, home not only to Faraday’s notes but also to those of Davy and other scientists who have worked at the Royal Institution over its centuries. Other researchers were ensconced there, along with the keeper of the collection. We were in the basement, just a few meters from where Faraday had worked in his magnetic laboratory.
Box after box of scientific treasure sat on the metal shelves, tidily labeled. It was the emotional and perhaps spiritual core of the institution. Faraday’s notebooks were in sturdy, flattish brown cardboard boxes with removable lids. James, with an ease born of long practice, consulted the shelves for a few moments and then took one down and removed its lid. Inside was an elegant oblong brown leather notebook inscribed with gold lettering, evidence of Faraday’s early passion for bookbinding. James opened the volume to August 29, 1831, and held it out with a slight flourish.
There, in sepia ink, in a sedate and beautiful hand, was Faraday’s description of the experiment that set him on the road to discovering that a magnet plus movement could make electricity, opening up the largely invisible world of electromagnetic fields snaking through the universe. Lines of script evenly spaced on a single page, written with scarcely a correction, a tidy diagram of the induction ring midway down the right-hand side.
It seemed to me that I could see Faraday writing the lines, sitting upright and proper in his laboratory. I could imagine him puzzling over the mysteries that were slightly out of sight. And from him I could trace a path to Maxwell working out his four famous equations at his Scottish estate south of Glasgow, and from there, to Einstein in that patent office in Bern reimagining the nature of space and time, and then over to Brunhes in his slender Renaissance tower in Clermont-Ferrand, realizing that the Earth’s magnetic field was far more mercurial than anyone had imagined.
About a hundred years later, their work, plus that of hundreds of other scientists, would unveil an electromagnetic reality that was breathtakingly more inconstant. Despite all that we now know thanks to advances in quantum physics, particle physics, geophysics, mathematics, computers, and satellite technology, we cannot predict how the Earth’s magnetic field will behave. That ability remains resolutely out of reach. But we have a few pieces of evidence. We know that the field is decaying more rapidly than many scientists had predicted. It is more unstable in the south. And if the poles are again preparing to switch places, the infrastructure that carries electrical current to our doorsteps is in danger of being damaged beyond repair.