Professor Maxwell's Duplicitous Demon

by Brian Clegg

  ¶¶ Induction is how, for instance, mobile phones and electric toothbrushes can be charged contactlessly. A changing current in the base produces a changing magnetic field which induces a changing current in the device to charge the battery.

  |||| Maxwell called the tiny spheres ‘idle wheels’ and the hexagonal cells ‘rotating vortices’, a term based on his earlier fluid model. He would come to think of the cells as actual vortices in the ether.

  *** To really be true Victorian in look and feel, the model should have been constructed of brass and mahogany.

  ††† Many see this as ironic, as he would later make a discovery that made the ether unnecessary but refused to accept this implication.

  ‡‡‡ Some current physicists suggest that modern equivalents of the ether might be dark matter or the inflationary concept in the Big Bang theory, which have become engrained in our way of thinking but have limited evidence to support their existence.

  §§§ Philosophical Magazine may sound like a lightweight periodical, a Popular Science of its day, but this venerable scientific publication began in 1798 and would carry papers from many of the Victorian big-hitters including Davy, Faraday, Maxwell and Joule. It is still in print. By comparison, the journal Nature, which would eventually eclipse it, first appeared in 1869. Philosophical Magazine began as a general journal of natural philosophy, but soon came to specialise in physics.

  Demonic Interlude V

  In which the demon becomes a star

  With his model representing the inner working of electromagnetism established, my master was well down the road to featuring in the scientists’ hall of fame. He wasn’t quite there yet – no one could entirely love a model based on hexagonal vortices and ball bearings, not even a demon, but he had laid the foundation for his later glory.

  It might seem that I’m biased and am singing my creator’s praises more than is justified – especially as he’s not exactly remembered by the public like a Darwin or an Einstein – but to quote Richard Feynman, generally accepted to be one of the twentieth century’s greatest physicists:

  From a long view of the history of mankind – seen from, say, ten thousand years from now – there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics.

  Feynman was a fan.

  Victorian computer dating

  It can be difficult to get a feel for the personality of a Victorian gentleman; so much that was written about individuals back then was stiff and lacked personal insights. It’s not necessarily easy for you to imagine JCM as a real person (certainly compared with someone who knew him, like me). So, it’s lucky that he filled in a questionnaire about himself – the sort of thing you might use when applying for a computer dating site these days – for fellow scientist Francis Galton.

  Galton has had a bad press of late as an advocate of eugenics, but he did wide-ranging, useful work and was fascinated by the statistical analysis of people and their heredity, particularly when considering the nature of genius. In 1874, Galton published a book called English Men of Science,* based on around 200 questionnaires, which he had persuaded Fellows of the Royal Society to fill in. It was Galton’s book that gave us the first sighting of the idea of ‘nature versus nurture’ (using those terms) and his research is seen as the starting point of the use of questionnaires in psychology.

  We, however, can ignore the rest and pick out JCM’s replies to get a little more insight into Maxwell, the man. We are told that he was 5 feet 8 inches (1.73 metres) tall, and was ‘often laid up’† before he was nineteen, but never since – what’s more, he had never had a headache. When asked about his ‘mental peculiarities’, Maxwell wrote:

  Fond of mathematical instruments and delighted with the forms of regular figures and curves of all sorts.

  Strong mechanical power. Extremely small practical business. [He also noted that his father was a ‘Very great mechanical talent’.]

  Strongly affected by music as a child, could not tell whether it was pleasant or painful, but rather the latter; never forgot melodies or the words belonging to them and these run through the mind at all times and not merely when the tunes are in fashion; can play on no instrument and never received instruction in music.

  Great continuity and steadiness; gratitude and resentment weak; στορχη‡ pretty strong; not gregarious; thoughts occupied more with things than with persons, social affections limited in range; given to theological ideas and not reticent about them; constructiveness of imagination; foresight.

  Another fascinating little insight into JCM’s mind is from his answer to the question ‘Origin of Taste for Science’:

  I always regarded mathematics as the method of obtaining the best shapes and dimensions of things; and this meant not only the most useful and economical, but chiefly the most harmonious and the most beautiful.

  I was taken to see William Nicol [see page 24] and so, with the help of Brewster’s Optics and a glazier’s diamond, I worked at polarisation of light, cutting crystals, tempering glass, etc.

  I should naturally have become an advocate by profession, with scientific proclivities, but the existence of exclusively scientific men, and in particular of Professor Forbes, convinced my father and myself that a profession was not necessary to a useful life.

  The demon’s catechism

  As my master was becoming more famous, I too was getting better established and being recognised by many physicists as an entertaining diversion – you might say I was becoming a star. So much so, that JCM felt obliged to write up a little biography of me in the form of a religious catechism§ for his friend Peter Tait. Rather irritatingly, he used the plural ‘demons’, where anyone with any sense knows that I am a singular entity:

  Concerning demons

  Who gave them this name? Thomson.

  What were they by nature? Very small but lively beings (capable of obeying orders but) incapable of doing work¶ but also able to open and shut valves which move without friction or inertia.

  What was their chief end?|| To show that the 2nd Law of Thermodynamics has only a statistical certainty.

  Is the production of an equality of temperature their only occupation? No, for less intelligent demons** can produce a difference in pressure as well as temperature by merely allowing all particles going in one direction while stopping all those going the other way. This reduces the demon to a valve. As such value him. Call him no more a demon but a valve like that of the hydraulic ram,†† suppose.

  The apparent belittling here runs counter to the appreciation of William Thomson, who later remarked of me that I was an intelligent being who was different ‘from real living animals only in extreme smallness and agility’. Some have suggested that Thomson’s enthusiasm to portray me as non-mechanical was a conscious attempt to oppose the theory of the ‘X Club’, whose members, including the Irish physicist John Tyndall and English biologist Thomas Huxley, were strong supporters of the idea that living things were mechanical automata with no concept of a soul required.

  Whether or not Thomson’s motivation was partly religious, as it happens, JCM was wrong in this instance – turning his simplified demon into a valve for the temperature and pressure experiment would not work (he didn’t need to get in extra staff, incidentally – this is something I would happily have helped him with).

  Richard Feynman, a physicist with his own demons, described in his acclaimed ‘red book’ lectures on physics that any basic mechanical replacement for a demon would heat up as a result of its efforts – so much so that it would eventually be jittering around far too much to do its job. As well as preventing us demons from being put out of a job, Feynman was pointing towards something that is special about my role – it’s not possible to do the job without being able to deal with information. You’ll never find a non-intelligent, mechanical demon.

  It ought to be stressed, though, that JCM was not setting out to wreck the second law of thermod
ynamics. He was entirely happy with its validity. But his development of the statistical approach to the kinetic theory of gases meant that he was aware that at its heart, the second theory was about probabilities, not certainty. As the English physicist James Jeans would later point out in a textbook:‡‡

  Maxwell’s sorting demon§§ could effect in a very short time what would probably take a very long time to come about if left to the play of chance. There would, however, be nothing contrary to natural laws in one case any more than the other.

  A demon like my humble self was perfectly capable of taking things in a direction that was extremely unlikely but not impossible in normal circumstances.

  So, let’s get back to JCM as he takes a break from the city after getting together his latest thoughts on electromagnetism.

  Notes

  1 – Richard Feynman’s citing the development of Maxwell’s electromagnetic theory as the most significant event of the nineteenth century is from Richard Feynman, The Feynman Lectures on Physics, Vol. II – the new millennium edition (New York: Hachette, 2015), section 1–11.*

  2 – Maxwell’s answers to Francis Galton’s psychological questionnaire were accessed on the Clerk Maxwell Foundation website, available at: www.clerkmaxwellfoundation.org/FrancisGaltonQuestionnaire2007_10_26.pdf

  3 – Maxwell’s mini-biography for the demon sent to Peter Tait is from Cargill Gilston Knott, Life and Work of Peter Guthrie Tait (Cambridge: Cambridge University Press, 1911), pp. 214–15.

  4 William Thomson’s remark that the demon was, in effect, living is from William Thomson, ‘The Kinetic Theory of the Dissipation of Energy’, Nature, 9 (1874): 441–3.

  5 – Richard Feynman’s demonstration that a mechanical valve could not do the work of a demon is in Richard Feynman, The Feynman Lectures on Physics, Vol. II – the new millennium edition (New York: Hachette, 2015) sections 46.1 to 46.9.

  6 – The comment by James Jeans that the demon merely achieved what could happen over a longer timescale anyway is from James Jeans, The Dynamical Theory of Gases (Cambridge: Cambridge University Press, 1921), p. 183.

  * The Feynman lectures don’t have page numbers.

  * The word ‘scientist’ was probably still not widely accepted enough at this point for Galton to be comfortable with using it in his title. Women, of course, given Victorian sensibilities, did not come into it. It might seem odd that the entirely Scottish JCM should be listed as an ‘English’ man of science. Galton’s main selection mechanism was those who lived or worked relatively near London, and at the time Maxwell was in Cambridge. It’s also true that the word ‘English’ was often loosely used as an alternative to ‘British’ at the time.

  † That’s to say unwell. JCM was what was known as a sickly child.

  ‡ Greek for affection or love.

  § A catechism is a summary of doctrine, often phrased as questions and answers. Maxwell attended Dean Ramsay’s catechism classes in Edinburgh as a teenager, thanks to his Aunt Jane.

  ¶ There he goes again with the personal comments.

  || It is not just the question and answer format that shows that this was based on a catechism – a well-known example, The Westminster Shorter Catechism of 1647, has for one of its questions: ‘What is the chief end of man?’

  ** Clearly this part does not refer to me as an individual. Some of my colleagues, certainly.

  †† This is a device that employs water pressure to raise part of a head of water higher than it originally was, using the greater pressure of the large body to move the smaller amount. It makes use of two one-way valves.

  ‡‡ The author would like me to point out that he still finds it remarkable, bearing in mind that the textbook quoted above was written in 1904, that while at university, he had tea with James Jeans’ widow, the organist Lady Susi Jeans. She was, admittedly, significantly younger than her husband.

  §§ This makes me sound worryingly like a Royal Mail employee.

  Chapter 5

  Seeing the light

  With his new model written up, Maxwell used the long summer vacation* of 1861 to head back to Glenlair with Katherine. Academics often take this time away to refresh themselves by either totally ignoring academic work or dealing with a pet project that had been sidelined, and it seems that it was Maxwell’s intention to concentrate on the Glenlair estate, but he could not get his electromagnetic model out of his mind. There was something not quite right in his mechanical analogy, impressive though it was at predicting most electromagnetic effects. This might simply have been because he was stretching the analogy too far, but discovering whether or not this was the case was nagging at him like the throbbing of an aching tooth.

  The power of flexible cells

  In his model, the hexagonal cells and the small spheres transferred rotating motion to adjacent components, so the movement spread up the diagrams shown on previous pages. But in a real mechanical system this would usually result in a loss of energy. This might seem to be something to do with electrical resistance, but the picture didn’t fit – and the resistance took place in the wire, not throughout the ether, which his model represented. However, there was a way to fix this if the rotating cells were no longer rigid, but he allowed them to give way under pressure, a property known in physics as being elastic.

  It was probably easier to think constructively in the familiar and relaxed surroundings of Glenlair, away from the bustle of London, with Katherine proving an effective sounding board. Maxwell envisaged a circuit consisting of an insulator between metal plates. The pair of plates would be connected to a battery, so an electric field extended through the insulator. In his model, in an insulator the tiny spheres could not flow, as they were attached to the hexagonal cells. But if the cells were flexible, each cell could twist around a little on its axis. So, in effect, a small amount of current would flow from the plate on one side to the plate on the other due to the displacement of the cells, before the torsion in the elastic material became strong enough to resist any further motion.

  At this point, one plate would be relatively positively charged, and one would be relatively negative. This meant that there would be an attraction between the plates. And, magically, the elastic mechanism he had suggested produced an attraction out of nowhere, because the twisting of the cells would make the ether contract. Each cell would shrink, just as a spring gets smaller as it is wound up, which would pull the plates towards each other. This pull provided the missing factor in his model, electrostatic attraction.

  If the battery were now removed from the circuit, that tension in the cells would remain. The attractive force would still be there. But if the two plates were then connected by a wire, the current would briefly flow between them, releasing the twists from the flexible cells – there would be a discharge of electricity and the attraction would disappear. He was describing the action of an electrical component that used to be called a condenser and is now known as a capacitor.

  Just as Maxwell had allowed the density of the cells in his model of the ether to be modified by materials it passed through to account for different magnetic properties, he was able to do the same for substances with different electrical properties. If the gap between the metal plates was filled with different materials – air or wood or mica, for example – the result would be a change in the elasticity of the ether’s cells. A substance like mica (a naturally occurring silicate crystal that forms sheets and was often used as an insulator in early electrical experiments) is more susceptible to electrical charges than, say, air. Such a material, known as a dielectric, would, in his model, make the cells twist more easily, so that a bigger charge was held and more current would flow when the plates were connected.

  By making those hexagonal cells elastic, able to twist and tighten, he had brought electrical attraction into his model. As an idea it worked, and by using the relatively new techniques that applied differential calculus – the mathematics of change – to vectors,† he was able to use his model to provide a mathemat
ical description of electrical and magnetic fields.

  Maxwell’s new version of his model portrayed the ether as a kind of invisible energy store. Static electrical energy was potential energy, stored away in the ether like the energy in a spring, while magnetic energy was kinetic energy, like that of a rotating flywheel. And his model showed that the two types of energy were unfailingly linked. Making a change in the level of one influenced the other.

  This was a remarkable achievement. But, of itself, building a model that matches reality does not necessarily make it useful. For many centuries, pre-Renaissance astronomers used a model of the structure of the universe based on epicycles, where a complex combination of circular movements allowed everything to rotate around the Earth, while explaining the oddities, for example, of the observed orbit of Mars, which reverses its direction in the sky. We now know that this is because the planets are orbiting the Sun, not the Earth. The epicycle model matched well to what was observed, but it did not give astronomers anything new to test it with – it was designed to match observation and the stubborn belief that the Earth was at the centre of the universe, and it did nothing more. But Maxwell’s model went further. It predicted something that had not previously been observed.

  Waves in the ether

  If the ether were truly like Maxwell’s model,‡ there was an extra component to be added to his mathematics. Even empty space was filled with the ether, and this meant that you should always get that little twitch of movement in the tiny spheres from the twisted elastic cells. This extra ‘displacement current’ on top of the usual conduction current added a component to his equations that made them mathematically complete. In terms of the accuracy of his model in reflecting what was actually observed, this was the turning point. Yet the introduction of elasticity into the cells had another, just as important, implication.