The nature of light had been a mystery since antiquity. There were acrimonious learned debates on whether it was a particle or a wave. Popular definitions ran to the style, ‘Light is darkness – lit up’. Maxwell’s greatest contribution was his discovery that electricity and magnetism, of all things, join together to become light. The now conventional understanding of the electromagnetic spectrum – running in wavelength from gamma rays to X-rays to ultraviolet light to visible light to infrared light to radio waves – is due to Maxwell. So is radio, television and radar.
But Maxwell wasn’t after any of this. He was interested in how electricity makes magnetism and vice versa. I want to describe what Maxwell did, but his historic accomplishment is highly mathematical. In a few pages, I can at best give you only a flavour. If you do not fully understand what I’m about to say, please bear with me. There’s no way we can get a feeling for what Maxwell did without looking at a little mathematics.
Mesmer, the inventor of ‘mesmerism’, believed he had discovered a magnetic fluid, ‘almost the same thing as the electric fluid’, that permeated all things. On this matter as well, he was mistaken. We now know that there is no special magnetic fluid, and that all magnetism – including the power that resides in a bar or horseshoe magnet – is due to moving electricity. The Danish physicist Hans Christian Oersted had performed a little experiment in which electricity was made to flow down a wire and induce a nearby compass needle to waver and tremble. The wire and the compass were not in physical contact. The great English physicist Michael Faraday had done the complementary experiment: he made a magnetic force turn on and off and thereby generated a current of electricity in a nearby wire. Time-varying electricity had somehow reached out and generated magnetism, and time-varying magnetism had somehow reached out and generated electricity. This was called ‘induction’ and was deeply mysterious, close to magic.
Faraday proposed that the magnet had an invisible ‘field’ of force that extended into surrounding space, stronger close to the magnet, weaker farther away. You could track the form of the field by placing tiny iron filings on a piece of paper and waving a magnet underneath. Likewise, your hair after a good combing on a low-humidity day generates an electric field which invisibly extends out from your head, and which can even make small pieces of paper move by themselves.
The electricity in a wire, we now know, is caused by submicroscopic electrical particles, called electrons, which respond to an electric field and move. The wires are made of materials like copper which have lots of free electrons -electrons not bound within atoms, but able to move. Unlike copper, though, most materials, say, wood, are not good conductors; they are instead insulators or ‘dielectrics’. In them, comparatively few electrons are available to move in response to the impressed electric or magnetic field. Not much of a current is produced. Of course there’s some movement or ‘displacement’ of electrons, and the bigger the electric field, the more displacement occurs.
Maxwell devised a way of writing what was known about electricity and magnetism in his time, a method of summarizing precisely all those experiments with wires and currents and magnets. Here they are, the four Maxwell equations for the behaviour of electricity and magnetism in matter:
• E = á/Õ0
• B = 0
x E = -Ò
x B = Ü0j + Ü0Õ0Ì
It takes a few years of university-level physics to understand these equations. They are written using a branch of mathematics called vector calculus. A vector, written in bold-face type, is any quantity with both a magnitude and a direction. Sixty miles an hour isn’t a vector, but sixty miles an hour due north on Highway 1 is. E and B represent the electric and magnetic fields. The triangle, called a nabla (because of its resemblance to a certain ancient Middle Eastern harp), expresses how the electric or magnetic fields vary in three-dimensional space. The ‘dot product’ and the ‘cross product’ after the nablas are statements of two different kinds of spatial variation.
Ì and Ò represent the time variation, the rate of change of the electric and magnetic fields, J stands for the electrical current. The lower-case Greek letter á (rho) represents the density of electrical charges, while Õ0 (pronounced ‘epsilon zero’) and Ü0 (pronounced ‘mu zero’) are not variables, but properties of the substance E and B are measured in, and determined by experiment. In a vacuum, Õ0 and Ü0 are constants of nature.
Considering how many different quantities are being brought together in these equations, it’s striking how simple they are. They could have gone on for pages, but they don’t.
The first of the four Maxwell equations tells how an electric field due to electrical charges (electrons, for example) varies with distance (it gets weaker the farther away we go). But the greater the charge density (the more electrons, say, in a given space), the stronger the field.
The second equation tells us that there’s no comparable statement in magnetism, because Mesmer’s magnetic ‘charges’ (or magnetic ‘monopoles’) do not exist: saw a magnet in half and you won’t be holding an isolated ‘north’ pole and an isolated ‘south’ pole; each piece now has its own ‘north’ and ‘south’ pole.
The third equation tells us how a changing magnetic field induces an electric field.
The fourth describes the converse – how a changing electric field (or an electrical current) induces a magnetic field.
The four equations are essentially distillations of generations of laboratory experiments, mainly by French and British scientists. What I’ve described here vaguely and qualitatively, the equations describe exactly and quantitatively.
Maxwell then asked himself a strange question: what would these equations look like in empty space, in a vacuum, in a place where there were no electrical charges and no electrical currents? We might very well anticipate no electric and no magnetic fields in a vacuum. Instead, he suggested that the right form of the Maxwell equations for the behaviour of electricity and magnetism in empty space is this:
x E = 0
• B = 0
x E = -Ò
x B = Ü0Õ0Ì
He set á equal to zero, indicating that there are no electrical charges. He also set j equal to zero, indicating that there are no electrical currents. But he didn’t discard the last term in the fourth equation, Ü0Õ0Ì feeble displacement current in insulators.
Why not? As you can see from the equations, Maxwell’s intuition preserved the symmetry between the magnetic and electric fields. Even in a vacuum, in the total absence of electricity, or even matter, a changing magnetic field, he proposed, elicits an electric field and vice versa. The equations were to represent Nature, and Nature is, Maxwell believed, beautiful and elegant. (There was also another, more technical reason for preserving the displacement current in a vacuum, which we pass over here.) This essentially aesthetic judgement by a nerdish physicist, entirely unknown except to a few other academic scientists, has done more to shape our civilization than any ten recent presidents and prime ministers.
Briefly, the four Maxwell equations for a vacuum say (1) there are no electrical charges in a vacuum; (2) there are no magnetic monopoles in a vacuum; (3) a changing magnetic field generates an electrical field; and (4) vice versa.
When the equations were written down like this, Maxwell was readily able to show that E and B propagated through empty space as if they were waves. What’s more, he could calculate the speed of the wave. It was just 1 divided by the square root of Õ0 times Ü0. But Õ0 and Ü0 had been measured in the laboratory. When you plugged in the numbers you found that the electric and magnetic fields in a vacuum ought to propagate, astonishingly, at the same speed as had already been measured for light. The agreement was too close to be accidental. Suddenly, disconcertingly, electricity and magnetism were deeply implicated in the nature of light.
Since light now appeared to behave as waves and to derive from electric and magnetic fields, Maxwell called it electromagnetic. Those obscure experiments with batteries and wires had something to do with the brightness of the Sun, with how we see, with what light is. Ruminating on Maxwell’s discovery many years later, Albert Einstein wrote, To few men in the world has such an experience been vouchsafed.’
Maxwell himself was baffled by the results. The vacuum seemed to act like a dielectric. He said that it can be ‘electrically polarized’. Living in a mechanical age, Maxwell felt obliged to offer some kind of mechanical model for the propagation of an electromagnetic wave through a perfect vacuum. So he imagined space filled with a mysterious substance he called the aether, which supported and contained the time-varying electric and magnetic fields – something like a throbbing but invisible Jell-O permeating the Universe. The quivering of the aether was the reason that light travelled through it – just as water waves propagate through water and sound waves through air.