Professor Maxwell's Duplicitous Demon

by Brian Clegg

  8 – The assertion that Maxwell only took on the rings of Saturn as an exercise in puzzle-solving is from Andrew Whitaker’s contribution to Raymond Flood, Mark McCartney and Andrew Whitaker (eds.), James Clerk Maxwell: Perspectives on his Life and Work (Oxford: Oxford University Press, 2014), p. 116.

  9 – Maxwell’s letter describing his move from solid to liquid rings for Saturn is taken from Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), p. 538.

  10 – Maxwell’s final statement on the nature of Saturn’s rings is from James Clerk Maxwell, On the Stability of the Motion of Saturn’s Rings (Cambridge: Macmillan and Company, 1859), p. 67.

  11 – Maxwell’s ‘Song of the Atlantic Telegraph Company’ is in a letter to Lewis Campbell from Ardhollow, Dunoon, dated 4 September 1857, quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 279.

  12 – Faraday’s letter to Maxwell on his papers is from Albemarle Street, London (location of the Royal Institution), dated 7 November 1857. It is quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 288.

  13 – Rudolf Peierls’ remark about waking a physicist in the middle of the night is from Peierls’ contribution, ‘Field Theory Since Maxwell’, to Cyril Dombe (ed.), Clerk Maxwell and Modern Science (London: The Athlone Press, 1963), p. 26.

  14 – Maxwell’s citing of George Stokes’ results on gas particles is from ‘On the Dynamical Theory of Gases’, presented at the 29th meeting of the British Association for the Advancement of Science, held at Aberdeen in September 1859, reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), pp. 615–16.

  15 – Faraday’s remark that Maxwell should be able to find his way through a crowd is noted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 319.

  16 – Kirchhoff’s remark that Maxwell’s calculations needed checking is frequently quoted, though I could not find an original source. It is quoted in this form in Robyn Arianrhod, Einstein’s Heroes: Imagining the World through the Language of Mathematics (Oxford: Oxford University Press, 2006) p. 94.

  17 – The Marischal College reaction to the appointment of Daniel Dewar is noted in P.J. Anderson, Fasti Academiae Marsicallanae Aberdonensis, Vol. II (Aberdeen: New Spalding Club, 1898), p. 30.

  18 – The suggestion that the book Gaelic Astronomy brought Maxwell and Principal Dewar of Marischal College together is made by John Read in his chapter ‘Maxwell at Aberdeen’ for Raymond Flood, Mark McCartney and Andrew Whitaker (eds.), James Clerk Maxwell: Perspectives on his Life and Work (Oxford: Oxford University Press, 2014), p. 236.

  19 – Maxwell’s letter to Miss Cay from 129 Union Street, Aberdeen, dated 18 February 1858, is quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 303.

  20 – The article reflecting on Tait getting the job at Edinburgh over Maxwell is from David Forfar and Chris Pritchard, The Remarkable Story of Maxwell and Tait, accessed on the Clerk Maxwell Foundation website available at: www.clerkmaxwellfoundation.org/Maxwell_and_TaitSMC24_1_2002.pdf

  * Admittedly all cities were smaller back in 1856, but compared with the largest city in the UK, London, at around 2.6 million, Aberdeen was still a minnow. It was only around half the size of the Lancashire mill town of Bolton at a similar date.

  † This could be seen as a nasty put-down, but from Tait was clearly an affectionate assessment of his friend’s original thinking combined with his difficulty of communicating ideas on the fly.

  ‡ David Gill was the only one of Maxwell’s Aberdeen students known to have become a scientist – he was later Queen’s Astronomer at the Cape of Good Hope and became President of the Royal Astronomical Society.

  § Some would say that this situation applies to certain aspects of modern physics, where theory often runs wild, unrestrained by experiment or observation.

  ¶ Nice little pun there from Maxwell.

  || This is sometimes reproduced as ‘infinite number’, but leaving aside the quibble that infinity isn’t a number, Maxwell clearly was not thinking of there being an infinite set of particles.

  ** The equivalent of 40p, which would be around £36 now in monetary terms, or about £285 based on equivalent wages.

  †† Physicist Rudolf Peierls once said that ‘If you wake up a physicist in the middle of the night and say “Maxwell”, he will be sure to say “electromagnetic field”.’

  ‡‡ Statistics in the modern sense was first practised by a button maker called John Graunt in London in the 1660s, and was developed in the coffee houses to become the foundation of the insurance business.

  §§ This is arguably why pollsters have had so much trouble with predicting the outcome of political events in the 21st century. Where once voters tended to behave as large, predictable blocks, they now tend to operate more individualistically, or in more complex groupings.

  ¶¶ Bumper cars, if you prefer.

  |||| Bizarrely, the fact that probability was first devised to explain the best approach to betting and games of chance meant that in its early days it was considered a dark and dirty art. As far as a demon is concerned, that just made it all the more attractive.

  *** In effect, viscosity can be thought of as a measure of a fluid’s gloppiness.

  ††† Not to be confused with one of Maxwell’s contemporaries, another Scottish physicist who was associated with gases and temperature, James Dewar, who worked on low-temperature gases and invented the vacuum flask or ‘Thermos’ to keep them cool. You will find a statue to James Dewar outside the Buchanan Galleries shopping centre in Glasgow.

  ‡‡‡ Nothing to do with the Disney movie. The Tron church (now the Tron Theatre) is located in Trongate, a street named after an old word for weighing scales.

  §§§ Entertainingly, the Musical Hall Company continued to attempt to send dividends from its proceeds to Maxwell at the (long defunct) Marischal College right through to the early 1900s, long after his death. The lawyers responsible for dealing with the payments eventually put an advertisement in the local paper asking for Mr James Clerk Maxwell to come forward, entirely unaware of either his fame or his death.

  ¶¶¶ At the time Chancellor of the Exchequer and eight years later Prime Minister.

  Demonic Interlude IV

  In which the demon’s challenge is posed

  When you look back at my creator in his early years, it can be hard not to consider him a touch of an oddball. It’s not that he was unsociable – which has proved a problem for many a scientist, in my experience. In fact, both at home in Glenlair and in Cambridge, JCM had enjoyed socialising and was known for his playful sense of humour. This often comes through in his letters, where he could be so mischievous it is sometimes difficult to make out what he meant. A highly technical letter to a fellow scientist could suddenly break out into a moment of whimsy, as when he remarked to his friend Peter Tait in something near text-speak: ‘O T′! R. U. AT ’OME?’*

  Yet, back then, JCM was almost always to some degree an outsider. At Glenlair he had been the posh kid playing with the country yokels. He was himself a bumpkin when compared with his more sophisticated Edinburgh peers. He had been labelled as the uncouth student, accepted by Cambridge despite his personal characteristics. Did this outsider status help him develop his unique viewpoints? How should I know? I am a demon. But it’s hard to imagine that being an outsider wasn’t part of what made old JCM the way he was.

  The other things that were already starting to have an influence on his path were the unexpected direction changes in his life. Just as he was really getting somewhere on electromagnetism, the lure of the new job in Aberdeen came along. And yet before he could make a start on that he also became laird of Glenlair. Many of his contemporaries put in a similar
position would have packed in the university work and taken on the estate as their life. It’s not as if he needed the money. Science could have become a fulfilling hobby. It’s almost as if someone was trying to tempt him away from his true path. And it wouldn’t be the last time.

  The tyranny of the second law

  But enough about him – it’s me you’re interested in. It’s my name on the front of the book. I’m going to be a trifle anachronistic here in the story of my maker’s life. He would not conjure me up until eleven years after he had graduated from Cambridge. And when he did, he didn’t have the decency to name me properly. He simply called me a ‘finite being’, I suppose meaning that I wasn’t a god as I had limitations. As a name, it’s a bit on the vague side, a term that could take in anything from an earthworm to a genius. As I’ve mentioned, it was his pal, that other dashing young Scottish natural philosophy professor of the high Victorian age, William Thomson, who realised my demonic nature.

  Thomson, incidentally, got me all wrong. He claimed with a typical puritanical disdain for the interesting side of life that in calling me a demon he didn’t intend me to be anything evil and inclined to temptation. No horns or pointy tail for his demon – he had in mind more of an intermediary, a spirit that was a kind of interface between the human and the divine. These days, he’d probably have spelt the word ‘daemon’ to emphasise the distinction. Sadly for humanity, old Thomson was wrong, though. Malevolence has proved to be very much my strong suit – I have always enjoyed getting human minds in a twist.

  What is particularly satisfying is that I achieve this mental obfuscation with very little effort on my part. The role I was created for involves little more than opening and closing a door. But in doing so, I have a strangely satisfying role in the intriguing matter of disorder.

  If you recall, we are dealing with the second law of thermodynamics, which could be summarised as ‘Chaos is on the rise’ (such a pleasant statement). Long-term, this has dire consequences for the universe as you know and love it. As JCM’s frequent correspondent Thomson once put it: ‘the end of this world as a habitation for man, or for any living creature or plant, at present existing in it is mechanically inevitable …’ All thanks to my favourite law.

  The second law says, then, that the level of disorder in a system stays the same or increases. And the system in question that I was introduced to control was ridiculously simple. Let’s start by seeing the second law in action, unhampered. Imagine you’ve got a box of gas – air would do, but we’ll make it pure nitrogen to keep things simple. The box is divided into two halves by a partition – on one side the gas is hot and on the other side the gas is cold.† There is a door in the partition between the two sides which you leave open. What happens after a little time?

  Molecules of gas from each side will randomly ping through the doorway. Some – the hot ones – will be travelling particularly fast. As we have seen, temperature is just a measure of the energy of the particles. The faster they travel, the more energy they have – the higher the temperature. Other molecules, the cold ones, will be relatively slow. So, we leave the door open for a good stretch of time. To begin with, most of the molecules leaving the hot side will be hot ones – and vice versa. So, the hot side will cool down and the cool side will heat up. Eventually the box will get to a state of equilibrium – each side will be around the same temperature. And the two halves should stay that way. We wouldn’t expect to go back to a state where one side was hot and the other side was cold.

  Notice, by the way, something that physicists forget at their peril. This whole business is purely statistical. It’s entirely possible that for a fraction of a second all the molecules going one way might happen to be hot and all the molecules going the other way might be cold and the two halves of the box would reach different temperatures again. But it’s very, very unlikely that this would happen for any significant period of time. We’re talking about vast numbers of molecules. If my box was a metre cubed and the gas was at room temperature and pressure, there would be over 10 trillion trillion molecules in there. The chances of most of them acting in this way is very small – that’s the statistical driver for the second law of thermodynamics.

  As a little aside, the second law was originally conceived as a mechanical, unbreakable law that heat always moves from the hotter to the colder body, and it took some of our man Maxwell’s contemporaries quite a while to come round to the statistical way of looking at things. JCM had his own rather nice way of describing what was involved: ‘The 2nd law of thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful out.’ He was highlighting the fact that there is no absolute mechanical mechanism preventing the law being broken, it’s just very, very unlikely.

  What has all this got to do with the level of disorder? It’s a bit of an odd term, but you can think of the difference between the two setups this way. When the hot and cold gases have mixed together, a molecule could be anywhere. But when they were separate, the hot molecules were on one side and the cold on the other. Then, we knew where to find the two different kind of molecules. There was more order in the system. It’s a bit like the difference between a page of this book as it now stands and the same page with all the letters scrambled up in any old order. The randomised page is not just useless as reading matter – it has more disorder. The second law is why it’s a lot easier to break an egg or a glass than it is to unbreak it.

  The demon is summoned

  So, we’ve got an idea of how the second law applies to a partitioned box. If the hot and cold gases did separate themselves spontaneously, that would break the second law. (Or to be precise, because the law is statistical, that would be very, very, very unlikely to happen according to the second law.) My role is to make that separation happen time and again with predictable ease.

  What my creator did was to place me in charge of the door separating the two halves of the box. We start with the hot and cold molecules all mixed up. And then I simply open and close the door, depending on the kind of molecule that’s approaching it. If the molecule is fast, I only let it through if it’s travelling from left to right. If it’s slow, I only let it through going right to left. So, gradually, the hot and cold molecules separate. Order is produced from chaos and I break the second law. Neat, eh?

  I seem to have first been mentioned in a letter written in 1867 to my creator’s friend Peter Tait, who was putting together a book on thermodynamics. JCM first described the box setup (calling the wall separating the halves of the box a ‘diaphragm’), then introduced me:

  Now conceive a finite being who knows the paths and velocities of all the molecules by simple inspection, but who can do no work‡ except open and close a hole in the diaphragm by means of a slide without mass.

  Let him first observe the molecules in A [the hot side] and when he sees one coming the square of whose velocity is less than the mean square velocity of the molecules in B [the cold side] let him open the hole and let it go into B. Next, let him watch for a molecule of B, the square of whose velocity is greater than the mean square velocity in A, and when it comes to the hole, let him draw the slide and let it go into A, keeping the slide shut for all other molecules.

  Then the number of molecules in A and B are the same as at first, but the energy in A is increased and that of B is diminished, that is, the hot system has got hotter and the cold colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being§ has been employed.

  Or, in short, if heat is the motion of finite portions of matter and if we can apply tools to such portions of matter so as to deal with them separately, then we can take advantage of the different motions of different proportions to restore a uniformly hot system to unequal temperatures or to motions of large masses.

  Only we can’t, not being clever enough.

  In a letter to John Strutt (Lord Rayleigh) written three years later, JCM gave
more detail about me, calling me ‘a doorkeeper, very intelligent and exceedingly quick, with microscopic eyes but still an essentially finite being’.

  In a later work, Theory of Heat, JCM made it clear that my role was to illustrate a wider range of possibilities, where ‘delicate observations and experiments’ would make it possible to take a look at the actions of a relatively small number of molecules, and in which case the familiar behaviour of vast numbers of molecules in a body would not be applicable.

  It was four years after my first mention that William Thomson wrote a paper describing my efforts and cementing my fame, using the ‘demon’ word for the first time. He also set up a bizarre mental picture of a whole array of us demons bashing molecules with cricket bats, but this is far too undignified to give it any consideration.

  Doing it without energy

  Now, you may have spotted a slight flaw in the whole ‘deployment of demons’ business if you bothered to read one of the footnotes a way back. I pointed out that this experiment was a bit like an icebox in a warm room. Let’s make it more specific. Let’s make one half of the box a refrigerator and the other side the room it’s in. We switch the fridge on and wait. After a while, the fridge side of the box is cold, while the other side is warm.¶ A refrigerator in a room has achieved the same as I did, with no demons required.|| But there’s a major difference between this picture and my effort.

  The second law is restricted to closed systems, sealed off from the rest of the universe. The law only works if someone isn’t pumping energy into the system. It’s perfectly possible to produce more order from chaos if you work at doing so. Think of the Earth. You may consider nature to be fairly chaotic, but we see all kinds of structures that have formed over time – natural ones (including your body) and artificial ones. That wouldn’t be possible without a vast amount of energy coming into the Earth to power it – and thankfully for you, the Sun provides as much energy as is needed and far more.