Note: This item comes from friend Mike Cheponis. DLH]
Maxwell’s equations: 150 years of light
A century and a half ago, James Clerk Maxwell submitted a long paper to the Royal Society containing his famous equations. Inspired by Michael Faraday’s experiments and insights, the equations unified electricity, magnetism and optics. Their far-reaching consequences for our civilisation, and our universe, are still being explored
By Jon Butterworth
Nov 22 2015
The chances are that you are reading this article on some kind of electronic technology. You are definitely seeing it via visible light, unless you have a braille or audio converter. And it probably got to you via wifi or a mobile phone signal. All of those things are understood in terms of the relationships between electric charges and electric and magnetic fields summarised in Maxwell’s equations, published by the Royal Society in 1865, 150 years ago.
Verbally, the equations can be summarised as something like:
Electric and magnetic fields make electric charges move. Electric charges cause electric fields, but there are no magnetic charges. Changes in magnetic fields cause electric fields, and vice versa.
The equations specify precisely how it all happens, but that is the gist of it.
Last week I was at a meeting celebrating the anniversary at the Royal Society in London, and was privileged to see the original manuscript, which is not generally on public view.
It was submitted in 1864 but, in a situation familiar to scientists everywhere, was held up in peer review. There’s a letter, dated March 1865, from William Thomson (later Lord Kelvin) saying he was sorry for being slow, that he’d read most of it and it seemed pretty good (“decidely suitable for publication”).
The equations seem to have been very much a bottom-up affair, in that Maxwell collected together a number of known laws which were used to describe various experimental results, and (with a little extra ingredient of his own) fitted them into a unified framework. What is amazing is how much that framework then reveals, both in terms of deep physical principles, and rich physical phenomena.
Fields and Waves
The equations show that electric and magnetic fields can exist even in the absence of electric charges. A changing electric field causes a changing magnetic field, which will cause more changes in the electric field, and so on. Mathematically this is expressed in the fact that the equations can be rearranged and combined to get a new kind of equation, that describes a travelling wave. So not only do the fields become real physical objects – something that Faraday was the first to propose – but they can carry travelling waves. Those waves are electromagnetic radiation. That is, visible light, radio, wifi, X-rays and the rest, depending on the wavelength.
The equations work in three dimensions, and relate fields pointing in different directions to each other. So the electric field in north-south direction depends upon what the magnetic field in the east-west direction is doing, for example. Maxwell wrote it all out component-by-component, direction-by-direction, in twenty seperate equations. These days we use vectors (objects with a length and an orientation, like an arrow) to condense the equations down to four. This makes a symmetry of the equations apparent. Like a sphere, they are the same from any angle. If I rotate the directions so that north becomes east, or southwest, or whatever, so long as I rotate all the axes together, nothing changes and the same equations still work.
Even more than this rotational symmetry, the equations stay the same if I boost my speed. And in particular, the speed of those waves described above stays the same. That is, the speed of light is the same for me, you and everyone, even if we are moving at different speeds relative to each other. This violates Newtonian mechanics, and it required Einstein and his relativity (for which the universality of the speed of light in a vacuum is a founding principle) to sort it out.