Professor Maxwell's Duplicitous Demon

by Brian Clegg

  The Treatise was not just Maxwell’s masterpiece, it was his last significant work. He published a short piece in Nature, improving Ludwig Boltzmann’s treatment of the kinetic theory of gases (itself derived from Maxwell’s work, but taking it sufficiently further that Boltzmann and Maxwell are fairly considered joint initiators of the theory). And he continued to work on many of his lesser pet projects, from colour vision to the theory of optical instruments, where he expanded the tools available for the theoretical description of multi-lensed instruments – a practical study, though not as distinctively original as his main topics of work.

  Most of his effort over the next couple of years, however, was dedicated to building up and running the Cavendish Laboratory. What spare time he had was given to a job that many have since thought was a matter of shouldering an obligation – but in reality, he could well have been following a topic of great personal interest.

  The Cavendish papers

  As we have seen, Henry Cavendish, the ancestor of the Duke of Devonshire who funded the Cavendish Laboratory, was an important scientist in his own right. From about 1873 onwards, Maxwell dedicated a considerable amount of his time to editing the papers of Cavendish. This could, indeed, have been a way of thanking the present Duke for the funding – but the money for the laboratory was already in place and it seems more likely that Maxwell had a genuine interest in untangling the details of Henry Cavendish’s work. Arguably, this could have come from the same kind of drive that inspires people to look into their ancestry – this was, in effect, establishing the ancestry of his laboratory – and also because Henry Cavendish had done a considerable amount of original work that was not widely known, and that Maxwell felt should be available to other physicists.

  Cavendish is probably best remembered for measuring the density of the Earth,* an experiment that would enable the first calculation of Newton’s gravitational constant G, and for discovering hydrogen. But from Maxwell’s viewpoint, Cavendish’s most interesting work was in electricity, a field that Cavendish studied for ten years from 1771. Most notably, Cavendish demonstrated the inverse square law of electrical repulsion well before the French physicist Charles-Augustin de Coulomb did. Yet it was Coulomb who was acknowledged as the discoverer of the law, as Cavendish never published this part of his work.

  It is not uncommon to see suggestions that Maxwell wasted much of the little time he had left to him on the Cavendish papers. However, leaving aside the benefits of hindsight – he had no idea that he hadn’t long to live – there is no evidence that Maxwell was pressured into doing the work, either by the university or by the Duke of Devonshire. Quite the reverse: Maxwell appears to have first shown an interest in getting hold of Cavendish’s papers two years before his involvement at Cambridge. Not only did he edit Cavendish’s output, pulled together from reluctant owners with the help of the Duke, he also recreated some of Cavendish’s experiments, using period instruments which had come into his possession from the collection of William Hyde Wollaston.

  Some of Cavendish’s results added extra information to work on electromagnetism. Maxwell commented: ‘if these experiments had been published in the author’s life time the science of electrical measurement would have been developed much earlier.’ Other parts of Cavendish’s papers simply seemed to appeal to Maxwell’s personality and sense of humour.† He was delighted with the way that Cavendish had used the pain reaction of his own body as a ‘meter’ to test the strength of electrostatic energy. Maxwell recreated this approach, using anyone he could persuade to volunteer to try out the technique.

  Arthur Schuster remembered:

  … a young American astronomer expressing in severe terms his disappointment that, after travelling on purpose to Cambridge to make Maxwell’s acquaintance and to get some hints on astronomical subjects, the latter would only talk about Cavendish, and almost compelled him to take his coat off, plunge his hands into basins of water and submit himself to the sensation of a series of electrical shocks.

  Maxwell’s edition of Cavendish’s papers was published in October 1879, shortly before his death.

  Passing fancies

  Typically, though Maxwell spent the majority of his time on his better-known fields of interest, he could not help being drawn briefly into any passing curiosity that took his fancy. For example, in 1874 he wrote to his old friend Lewis Campbell about what would now be called genetics, considerably before the concept of the gene was widely known.‡ Admittedly, Maxwell did so to dismiss the concept – but based on what he thought was the case, his argument made sense. He wrote:

  If atoms are finite in number, each of them being of a certain weight, then it becomes impossible that the germ from which a man is developed [i.e. the cell] should contain … gemmules§ of everything which the man is to inherit, and by which he is differentiated from other animals and men, – his father’s temper, his mother’s memory, his grandfather’s way of blowing his nose, his arboreal ancestor’s arrangement of hairs on his arms … if we are sure that there are not more than a few million molecules in [the cell], each molecule being composed of component molecules, identical with those of carbon, oxygen, nitrogen, hydrogen etc., there is no room left for the sort of structure which is required for pangenesis on purely physical principles.

  Maxwell proved to be wrong, by attributing too much to genetics, underestimating the number of molecules available, and in the scale of information that can be stored in a germ cell – but the fact that he was discussing this concept long before the significance of DNA and its genes was realised shows the range of his interests and thoughts.

  One of the most entertaining of Maxwell’s diversions was the Crookes radiometer, a puzzling device that was introduced to the world in 1874. William Crookes was an English scientist a year younger than Maxwell, who would go on to do important work on electrical effects in vacuum tubes, the precursors of thermionic valves, which were the first electronic devices.

  Crookes’ radiometer looked a little like a light bulb. It was a sealed glass chamber with the air mostly pumped out, but rather than having a filament inside, it had four paddles suspended from a central spindle so that they could freely rotate. Each paddle was white or silver on one side and black on the other – and when exposed to light, the paddles would rotate at high speed.¶ At first sight this might have seemed to be a vindication of Maxwell’s idea of radiation pressure – but the radiometer spins in the wrong direction for this (and anyway, Maxwell was aware that the amount of pressure on the paddles from radiation would not be sufficient to turn them).

  If the spinning paddles had been pushed by radiation pressure you would expect that the white/silver sides would move away from the light, as they would be reflecting far more of the light than would the black sides. In fact, however, it’s the black sides that move away from the light, which caused confusion and delight in equal measures among the scientific intelligentsia.

  Maxwell would come to the rescue, aided by some practical information from his friend Peter Tait. With his colleague James Dewar, the inventor of the vacuum flask and an expert on low-pressure work, Tait had discovered that the working of the radiometer was dependent on the amount of air that was left in the bulb. No experimental vacuum was perfect – there would always be some gas molecules present. With too much air or with too little, the radiometer would not work.

  Realising that the mechanism must depend on one of his other favourite topics, the kinetic theory of gases, Maxwell seems to have put himself in the frame of mind of one of his demons, able to see the gas molecules in action near to the paddles. When the light was shone onto the paddles, the black sides would absorb more of the light and would heat up. This, he thought, would speed up gas molecules that came into contact with the paddles, producing convection currents around the sides of the paddles, which would effectively suck the paddles round.

  With many of his theories, Maxwell wasn’t quite there in his first attempt – this turned out to be the case with the radiometer,
where his calculations let him down a little. The actual solution turned out, if anything, to be simpler. Gas molecules coming into contact with a warmer black paddle surface would gain a little more energy than those that hit a cooler white side. This meant that, on average, the black sides were being bombarded with more momentum than the white and started to move away from the pressure.

  Although Maxwell’s convection currents turned out not to be the driving force behind the radiometer, his effort was by no means wasted. In writing up his work for the Royal Society he generalised his mathematics to provide an equation for the behaviour of gases in such rarefied conditions which would prove to be valuable in studies of the upper atmosphere.

  A sudden end

  The paper inspired by the radiometer would be Maxwell’s last contribution to science. In early 1877, he began to have problems with his digestive system. Maxwell suffered frequent heartburn and found swallowing an increasing problem. The discomfort got worse over two years before he consulted his doctor, who took him off meat and replaced it with a milk-based diet.

  In the summer of 1879, James Clerk Maxwell was diagnosed with abdominal cancer. He died in Cambridge on 5 November 1879, just 48 years old – the same age as his mother at her death.

  Maxwell’s funeral was effectively split in two. The first part of the burial service took place in the Trinity College chapel in Cambridge, attended by many of his academic colleagues and friends. His coffin was then taken home to Glenlair, with the closing part of the funeral service held at Parton church, before his burial in the churchyard there.

  Notes

  1 – Arthur Schuster’s quote from Maxwell on never dissuading a man from trying an experiment is from Arthur Schuster, A History of the Cavendish Laboratory (London: Longmans, Green and Co., 1910), p. 39.

  2 – The review from The Ironmonger on Maxwell’s Theory of Heat is reproduced in Isobel Falconer’s chapter on ‘Cambridge and the Building of the Cavendish Laboratory’ in Raymond Flood, Mark McCartney and Andrew Whitaker (eds.), James Clerk Maxwell: Perspectives on his Life and Work (Oxford: Oxford University Press, 2014), p. 76.

  3 – Maxwell’s comment that if Cavendish’s papers had been published earlier, electrical measurement would have been developed much earlier is in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1890), p. 539.

  4 (footnote) – Maxwell’s description of himself as dp/dt comes from the equation dp/dt = JCM which shows the change of pressure as temperature changes, with J being Joule’s equivalent, C Carnot’s function and M the rate at which heat must be supplied per unit increase of volume, the temperature being constant.

  5 – Arthur Schuster’s recollection about an American complaining of being subject to electrical shocks by Maxwell is from Arthur Schuster, A History of the Cavendish Laboratory (London: Longmans, Green and Co., 1910), p. 33.

  6 – Maxwell’s comments on units of inheritance are quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 390.

  * He is also remembered for being extremely eccentric. Cavendish was so shy that he did not like to speak to more than one person at a time and would only communicate with female servants by notes. Complex arrangements ensured his meals could be served with minimal contact with staff.

  † It’s easy to think of Maxwell, from his dour photographic portraits, as a typical miserable Victorian, but all his life he displayed an impish (appropriately enough) sense of humour. This often came through, as we have seen, in his letters, which could be distinctly whimsical. For example, he tended to refer to himself as dp/dt – since an equation in his friend Peter Tait’s book read dp/dt=JCM, Maxwell’s initials. (See notes for detail of the equation.)

  ‡ The word ‘gene’ was not introduced until 1905. The concept behind the gene was in Gregor Mendel’s work suggesting that a unit of inheritance did exist, which was published in 1866, but it was not widely known until after Maxwell’s death.

  § Darwin’s term for a unit of inheritance.

  ¶ You can see a Crookes radiometer in action at the Universe Inside You website page: http://www.universeinsideyou.com/experiment4.html

  Demonic Interlude VIII

  In which the demon lives on to fight another day

  With the sad news of James Clerk Maxwell’s demise, it would be easy to consider us both finished. You may recall that many thought I could no longer do my job as a result of the suggestion that it would take energy to erase information, and so, in the overall system including me, entropy would not be reduced. There was one attempt, with a complex argument, to provide a way in which it would be possible to make the erasure process reversible, though many argued that this was cheating, since it required dumping information into an external store – which surely itself was also finite.

  The reality of loopholes

  Even so, I was thought to be doomed. However, there is a loophole which remains to this day. Although it’s true that eventually I would have to wipe some memory, it is also true that in any particular experiment I could still perform my task. There may be many billions of molecules in an experiment, but I can also have an equivalent amount of storage and perform my task without any erasure. Admittedly I wouldn’t have enough memory space to run the experiment for ever, but I would be able to reduce entropy to a considerable degree before I ran out of storage – there is no need for me to deal with every single molecule available over all time.

  Those who wish me disposed of suggest that this is not an acceptable argument because of the way thermodynamics is practised. Generally, this involves cyclic processes where the components are returned to their initial state, and the argument is that I should be left in the same state after working on a molecule as I was before it – which wouldn’t allow me a memory. But that’s something of a silly argument, as without any memory I couldn’t do my job in the first place – and the whole process is clearly not cyclical when molecules are being irreversibly moved from one side of the box to the other. It seems an argument more from dogma than from physics.

  More to the point, other physicists have come up with a concept they call blending which achieves the irreversibility of erasure without any influence over the entropy of the system. To quote one such example from Meir Hemmo and Orly Shenker:

  In particular, the principles of mechanics entail no specific relation between the pre-erasure and post-erasure entropy of the universe. In any case, our analysis of erasure demonstrates that, contrary to the conventional wisdom, classical mechanics does not entail that an erasure is necessarily dissipative [i.e. increasing entropy].

  That being the case, I hope you are clear that the challenge JCM set so long ago is, to a degree, still there. I am still a thorn in the side of the second law – almost inevitably, given its statistical nature. Despite the theoretical objections to my existence (rather demonist, if you ask me), a number of recent experiments have shown that demonic action is possible as long as you work on a small enough scale.

  In 2016 for example, at the University of Oxford, a team made use of two pulses of light instead of the two sides of my original box. Rather than employ a true demon (apparently, despite the suggestions of Philip Pullman, we are of limited availability in Oxford labs), they made a measurement on two pulses of light and depending on which was stronger, took one pulse in one direction and the other in another. The difference between the voltage produced by photodiodes receiving the two pulses charged up a capacitor. Because the more energetic pulses always go the same way, the result is to be able to produce work from a demon-style interaction.

  Closer to the original because it has a thermodynamic element, also in 2016 a Brazilian physicist and his team performed an experiment that seemed to contain its own tiny demon. They managed to produce a situation where the second law was more clearly spontaneously broken, if on a small scale. This was something that must have struck joy into the heart of those who peddle ‘free
energy’ devices. Physicists dismiss perpetual motion machines and free energy devices out of hand. Some consider this a lack of open-mindedness, but in reality, it’s just that the physicists understand the second law of thermodynamics.

  In the Brazilian experiment, heat moves from a colder to a hotter place. As we’ve seen, there’s nothing odd about heat moving from a colder to a hotter body: it’s what a fridge does, after all. But this can only be the case if energy is supplied to make it happen – this is what the ‘closed system’ bit of the definition of the second law precludes. What is interesting in the described experiment is that heat was transferred spontaneously from ‘colder’ to ‘hotter’ (I’ll come back to those inverted commas soon), which is what you need for perpetual motion and free energy.

  Physicist Roberto Serra of the Federal University of ABC in Santo André, Brazil and the University of York, and his colleagues, got molecules of chloroform – a simple organic compound where a carbon atom has one hydrogen and three chlorine atoms attached – into a special state. The hydrogen atom and the carbon atom in a molecule had one of their properties – spin* – correlated, giving them a kind of linkage. The hydrogen atom was in a higher energy state than the carbon, making the hydrogen technically hotter than the carbon (hence the inverted commas above). And without outside help, as the correlation decayed, heat was transferred from the carbon to the hydrogen. From the colder to the hotter atom.