It’s the 150th anniversary for a series of equations electric charges and electric and magnetic fields that are still being explored. Jon Butterworth in a Nov. 22, 2015 posting on the Guardian science blog network explains (Note: A link has been removed),

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 [James Clerk Maxwell] 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.

Butterworth got a rare opportunity to see the original manuscript,

I love this description from Butterworth,

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”).

Then, there’s this,

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.

I’m not excerpting any part of Butterworth’s description of how Maxwell fit these equations together for his unification theory as I think it should be read in its totality.

The section on quantum mechanics is surprising,

Now, one thing Maxwell’s equations don’t contain is quantum mechanics [emphasis mine]. They are classical equations. But if you take the quantum mechnical description of an electron, and you enforce the same charge conservation law/voltage symmetry that was contained in the classical Maxwell’s equations, something marvellous happens [emphasis mine]. The symmetry is denoted “U(1)”, and if you enforce it locally – that it, you say that you have to be allowed make different U(1) type changes to electrons at different points in space, you actually generate the quantum mechanical version of Maxwell’s equations out of nowhere [emphasis mine]. You produce the equations that describe the photon, and the whole of quantum electrodynamics.

I encourage you to read Butterworth’s Nov. 22, 2015 posting where he also mention two related art/science projects and has embedded a video animation of the principles discussed in his posting.

For anyone unfamiliar with Butterworth, there’s this description at the Guardian,

Jon Butterworth is a physics professor at University College London. He is a member of the UCL High Energy Physics group and works on the Atlas experiment at Cern’s Large Hadron Collider. His book Smashing Physics: The Inside Story of the Hunt for the Higgs was published in May 2014