Professor Maxwell's Duplicitous Demon

by Brian Clegg

  Maxwell had no direct equivalent of the IAS – but he had the advantage of independent wealth. When he had had enough of the pressures of his teaching work at King’s, despite the assistant to reduce his lecture commitment, he was able to make the decision to quit his post and return to year-round living at Glenlair with Katherine to work independently. After all, this had proved a great boost to his thinking over the summer breaks and no doubt it could again.

  From the view of a modern scientist, Maxwell’s action seems a retrograde step. Although science was yet to involve much teamwork, even then there was a great deal of sharing of information, and today’s physicists would feel naked without their academic institutions and conferences. Maxwell was moving away from the scientific hubs of the Royal Society and the Royal Institution to the back of beyond in scientific terms. However, he had always relied more on written sources than on face-to-face networking. He was not, in the terms of the time, a particularly clubbable man. As far as we can tell, he took limited advantage of the cultural opportunity of being in London, with no record of him attending a play or a concert or any social event beyond the philosophical gatherings at the Royal Society, the Royal Institution and the BA. The younger Maxwell may have appreciated a wider social sphere, but now Maxwell and Katherine seemed happy with their own company.

  There’s no doubt that, like Albert Einstein, who moved away from teaching as soon as he could, Maxwell had the potential to benefit from leaving his teaching duties and being able to concentrate solely on his original work. However, unlike Einstein, Maxwell seems to have enjoyed the rewards of bringing the details of physics to others. It could be that his disillusionment with London also arose from the relatively limited scope of his students there. As we saw earlier, many of them only stayed for a little over four terms and saw their education at King’s College primarily as a way to bolster careers in engineering and similar fields. There were very few who regarded physics as a serious career option – and it was only the opportunity to work somewhere that took the concept of advancement in physics seriously that would lure Maxwell back to a university some years later.

  And so in early 1865, after five fruitful years at King’s College, the Maxwells left London to return home to Glenlair. Maxwell could not even wait until the end of the academic year, leaving his assistant and successor, the ‘Lecturer in Natural Philosophy’ William Grylls Adams,**** to take over his chair, a position Adams would hold for a further 40 years. Admittedly, Maxwell’s retreat from London took some time. To keep up with his commitments outside of King’s, giving lectures to working men, Maxwell would spend a few months in his Palace Gardens Terrace home at the end of 1865 and the end of 1866, as well as the early months of 1868, before he gave up the lease. Nonetheless, as far as he was concerned, Maxwell had left academia for ever.

  Notes

  1 – Maxwell’s letter including his speculation on comets and the mechanism of gravity to John Phillips Bond from Glenlair and dated 25 August 1863 is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), pp. 104–9.

  2 – The details of Maxwell’s viscosity experiment are from James Clerk Maxwell, ‘The Bakerian Lecture: On the Viscosity or Internal Friction of Air and other Gases’, Proceedings of the Royal Society of London, Vol. 15 (1866–67), pp. 14–17.

  3 – The efforts the Maxwells went to in order to increase and decrease the temperature of the attic for the viscosity experiments are noted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 318.

  4 – Maxwell’s letter to Lewis Campbell describing seeing Wheatstone’s Stereoscope, written from Edinburgh in October 1849, is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), p. 119.

  5 – Maxwell’s notes on an electromagnetic explanation of reflection and refraction based on Jamin’s theory are reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), p. 182.

  6 – Maxwell’s admission that he did not attempt to deal with reflection is quoted in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 3 (Cambridge: Cambridge University Press, 2002), p. 752.

  7 – Maxwell’s belfry analogy for the use of ‘black box’ mathematical models is in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1890), pp. 783–4.

  8 – Michael Faraday’s request that mathematical physicists also give a lay summary of their work is in a letter from Albemarle Street, London, dated 13 November 1857 and quoted in Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 290.

  9 – Details of Michael Pupin’s attempt to understand Maxwell’s mathematical explanation of electromagnetism are from Freeman Dyson, ‘Why is Maxwell’s Theory so hard to understand?’, James Clerk Maxwell Commemorative Booklet (Edinburgh: James Clerk Maxwell Foundation, 1999), pp. 6–11.

  10 – Maxwell’s humorous comment about Nabla and Nablody is in a letter to Lewis Campbell written on 19 October 1872, found in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1890), p. 760.

  11 – Maxwell’s suggestion of using ‘space-variation’ as a name for Nabla is in a letter to Peter Tait written on 1 December 1873, found in William Davidson Niven (ed.), The Scientific Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1890), p. 945.

  * This was probably a sneaky dig on the part of Newton. ‘Fingo’ is not a particularly complimentary way of describing coming up with an idea. His assertion could probably be loosely translated as: ‘I’m not going to just make a hypothesis up.’

  † Literally.

  ‡ The same Charles Wheatstone that Faraday filled in for in 1846.

  § Calotype was the name given to W.H. Fox Talbot’s negative-based photography (as opposed to the older daguerreotype process which produced a direct positive image).

  ¶ Probably, given this odd structure of the word, this was named for consistency with the farad, the unit of electrical capacitance, named after Michael Faraday. The ‘ohm’ part is from the German physicist Georg Ohm, who discovered the relationship between electrical voltage and current.

  || Which is where ‘ohmad’ came from in the first place. A few years later, the ohm was given the symbol Ω to reflect the convenient assonance between the name ohm and the start of the Greek letter omega.

  ** Maxwell would have had sympathy with the builders of the LIGO gravitational wave observatories in the twenty-first century, which are so sensitive that they can detect the gravitational influence of a passing truck.

  †† To be fair to Maxwell, this is just as well, as the interaction of light and matter could not have been properly understood without quantum theory.

  ‡‡ The other contenders were Archimedes and Galileo – Galileo won the debate.

  §§ In other words, as Kant might say, stick to phenomena and forget noumena.

  ¶¶ Strictly, a hole in the ceiling, from the point of view of the ringers.

  |||| What Maxwell means in this rather clumsy wording is that by defining the velocity of this particular rope as 1, they can establish a standard to measure the relative velocities of the other ropes.

  *** In physics, ‘degrees of freedom’ means the number of different parameters defining the state of a system – if you know all of these, you can say exactly how it will behave, but if you only know some of them, you will be limited in your ability to predict its response.

  ††† Maxwell’s great fan Albert Einstein suffered a similar problem initially when he suggested that light consisted of quantum packets of energy or photons, rather than such quanta merely being a way to make the mathematics work. When the leading Ge
rman physicist Max Planck (whose theory was the starting point for Einstein’s thinking) proposed Einstein for the Prussian Academy of Sciences in 1913, he asked them to overlook the way Einstein ‘missed the target’ with speculation like that over light quanta. This speculation would eventually win Einstein the Nobel Prize when the approach became widely accepted.

  ‡‡‡ Heaviside is probably best known for the Heaviside layer, familiar to fans of the musical Cats, a layer of ionised gas in the upper atmosphere that reflects radio waves, and so allows radio transmission to be sent beyond the horizon (bearing in mind electromagnetic waves travel in straight lines). Heaviside was, to put it mildly, a character, often described as cantankerous and a maverick.

  §§§ Remember that Maxwell’s mechanical model involved both linear flows of little spheres and rotation of cells.

  ¶¶¶ Electrical field is usually represented by an E, but here D is used to represent the ‘displacement’ field that Maxwell referred to in the displacement of the spheres during the ‘twitches’ where his cells twisted elastically.

  |||||| Arguably too late, as by the time Einstein moved to Princeton, all his great work was behind him.

  **** Adams was later one of the co-discoverers of the earliest form of photoelectric cell.

  Demonic Interlude VI

  In which the demon suffers a setback

  It’s entertaining that my creator’s new mathematical approach baffled many of his contemporaries, since it represented a step-change in the methods of physicists. Einstein famously had James Clerk Maxwell as one of the few portraits on his study wall, and said of JCM:

  Since Maxwell’s time, Physical Reality has been thought of as represented by continuous fields … and not capable of mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton.

  The cost of measurement

  As far as my progress went, we need to take a leap forward in time to long after Maxwell’s death (this is no problem for a demon like me), reaching the 1920s and the work of a young Hungarian physicist, Leo Szilard, whose greatest claim to fame would later be his realisation of how a nuclear chain reaction could work. Remarkably, Szilard would show that JCM’s humble demon was in fact a precursor to information theory. To understand Szilard’s take on me, you first need to see the other side of the second law of thermodynamics in a little more detail.

  As you’ll recall, my master and his friends were largely concerned with the second law in terms of heat and the movement of molecules – the whole business of thermodynamics was devised, after all, as a way of getting a better understanding of how steam engines worked. JCM may have made things deliciously probabilistic with his statistical approach – but he was still thinking of the second law being primarily about the way heat never flows from a colder to a hotter body, unless it’s given a helping hand. By Szilard’s time, though, the dominant aspect of the second law was the way it dealt with entropy.

  As I’ve already mentioned, entropy is a measure of the level of disorder in a system – but it’s not as vague a thing as it sounds: it has a clear numerical value. The entropy of a system is based on the number of unique ways you can arrange the components that make up that system.* At first glance it’s not totally obvious why this is a measure of disorder, but a good example would be the letters of the alphabet. If we put them in the familiar alphabetic order: A, B, C, D … there is just one way to arrange them. But scramble them up and there are many ways to arrange them:

  A C B D …

  G Q C E …

  L A Q V …

  … and so on. This means that in alphabetic order, the letters of the alphabet have much lower entropy than they do when they are scrambled up and more disordered, where there are more ways to arrange them.

  Szilard believed that for a demon like me to do the job, it would have to be an intelligent being,† and that the process of measurement the demon would have to undertake to decide whether or not to let a molecule through would itself result in an increase in entropy which would precisely cancel out the decrease caused by the demon’s excellent contribution. The reason that Szilard assumed this to be the case is that the demon has to measure the speed or kinetic energy of the molecule. He then has to store that information in his brain in order to make the decision whether or not to open the door. The business of taking the measurement, Szilard argued, would result in the use of energy and an overall increase in entropy of the system as a whole, as the demon would have to be considered part of the system and his increase in entropy from using energy would be greater than the decrease in entropy in the gas.

  It has been suggested that it’s not surprising that Szilard came up with a take on my activities that involved me as an intelligent observer, where scientists of Maxwell’s day would not have made the distinction. For JCM and friends, the scientist was a totally detached being, an objective observer, entirely separate from the experiment. But by the time Szilard got his hands on me, quantum theory had begun to be developed.‡

  One essential of quantum physics is that the act of measurement – just looking at something, even – has the potential to have an effect on it. For example, if the demon were to take a measurement of a particle’s position using light, that would involve light photons bouncing off the molecule, potentially changing its path and momentum. More significantly still, quantum theory said that until a measurement was made, a quantum particle such as a molecule didn’t have a position. It could even tunnel its way through my door and appear on the other side.

  In Maxwell’s approach to statistical mechanics, the probabilities are in the model. All the molecules have a definite position at all times, but we don’t know what those positions are, and so we use probability to take a statistical overview of how the collection of molecules is likely to behave. But quantum reality tells us that the positions of the molecules are literally and actually just probabilities until an observation is made. This was the aspect of quantum physics that so worried Einstein, resulting in his famous remarks about God not playing dice. God may not do so – but as for demons …

  Taking a quantum physics viewpoint, you can never entirely separate the observer and the experiment. Szilard’s big contribution was to make the demon’s role part of the overall system of the experiment. My measurements, he suggested, must influence the system in a way that forces the entropy back up just enough to counter any benefits that I had produced.

  Although it’s not of importance to me, it’s interesting to note that Szilard’s work on my problem directly led to the American engineer Claude Shannon developing information theory, which introduced the concept of entropy to information, such as the information transmitted from place to place by Maxwell’s electromagnetic waves.

  As it happens, with true demonic slipperiness, I managed to escape from Szilard’s apparent solution to continue to threaten the second law – but that can wait. We need to see how JCM was coping after his move away from the academic world.

  Notes

  1 – Einstein’s assertion that Maxwell made the most profound change in the perception of reality since Newton is taken from Albert Einstein, ‘Maxwell’s influence on the development of the conception of physical reality’, in James Clerk Maxwell: A Commemorative Volume 1831–1931 (Cambridge: Cambridge University Press, 1931), pp. 66–73.

  2 – Leo Szilard’s analysis of the demon’s measurement and memory storage process is in his paper ‘On the Decrease in Entropy in a Thermodynamic System by the Intervention of Intelligent Beings’, in Bernard Feld and Gertrud Weiss (eds.), The Collected Works of Leo Szilard: Scientific Papers (Cambridge, MA: MIT Press, 1972), pp. 103–29.

  3 – The suggestion that Szilard’s consideration of the demon as part of the experiment was influenced by quantum theory comes 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 Univ
ersity Press, 2014), p. 183.

  4 – Bragg’s remark about God running electromagnetics by the wave theory and the devil by quantum mechanics is quoted in Daniel Kevles, The Physicists (Harvard: Harvard University Press, 1977), p. 159.

  * If you want to get technical, entropy = k ln W, where k is Boltzmann’s constant, and ln W is the natural logarithm of the number of ways the components can be arranged.

  † I would have thought by now that this went without saying.

  ‡ It’s not for nothing that the British physicist William Bragg wrote: ‘God runs electromagnetics on Monday, Wednesday and Friday by the wave theory, and the devil runs it by quantum theory on Tuesday, Thursday and Saturday.’ Nice to see a physicist acknowledging the importance of the demonic contribution to physics, though one does wonder what happened to electromagnetics on Sunday.

  Chapter 7

  On the estate

  One advantage to having control of his own time at Glenlair was the opportunity for Maxwell to focus on writing as well as spending time on his experiments and development of theory. With his old friend Peter Tait, who had stayed as Professor of Natural Philosophy at Edinburgh, Maxwell was assembling a book that was extremely wide in coverage – called A Treatise on Natural Philosophy, it was in effect a textbook for the entire physics syllabus at university level. There would arguably not be another physics book that combined such an impressive breadth with being held in such high regard until Richard Feynman’s famous ‘red books’ based on his undergraduate lecture series from the 1960s.

  Today, working on a jointly authored book is relatively simple. Not only can chapters and comments fly backwards and forwards by email, collaborators can work on a shared version hosted in the cloud.* For Maxwell and Tait it was a matter of writing letters by hand and waiting for a response in the mail – there was a steady flow of letters back and forth between Glenlair and Edinburgh as the volume came together. In fact, such was the volume of post that Maxwell generated with his wide-reaching scientific correspondence that a post box was installed into the wall of the road by Glenlair for Maxwell’s personal use.