by Brian Clegg
If a material is elastic – if the substance that makes it up has some flexibility – it is possible to send a wave through it. Waves involve a repetitive displacement of the parts of the material the wave is passing through, and that can only happen if the material is not completely rigid. Imagine Maxwell’s cells and spheres stretching through the void of space. If there were a twitch of movement in a row of spheres, caused by electrical energy, that would cause a brief torsion in the adjacent cells – representing a short movement of magnetic energy. That in turn would twitch the next row of spheres – generating a new electrical surge.
This succession of twitches would pass through the apparently empty space occupied by the ether. It would not progress instantaneously, as the cells would have some inertia, so each would take a little time to get moving. What Maxwell’s model was predicting is that it should be possible to send out a wave of alternating electrical and magnetic displacement through an insulator – even through the vacuum of space – because the ether was always present. And as the displacement in the spheres and cells was happening at right angles to the direction this disruption was travelling, what was observed would be a transverse wave, like ripples on water, where the material is displaced at 90 degrees to the direction of travel of the wave.
The concept of the displacement current introduced a role for the theoretical physicist that seems to have been Maxwell’s own invention. At the time, theoretical physicists did most of their work producing theories to match observations. But Maxwell saw a role for the theoretician in looking for the holes that were left in experimental evidence and making predictions that could later be tested. The displacement current was not the result of any observation – it was purely a prediction from his model. This apparently small contribution, often overlooked in popular descriptions of Maxwell’s work, was revolutionary. There was considerable resistance to this approach from some of his colleagues, but Maxwell’s daring step became a central role of theoreticians, to the extent that in some fields this kind of deduction from models came to dominate.
FIG. 5. The features of a transverse wave.
The introduction of the displacement current was a remarkable achievement for Maxwell’s method – other contemporary attempts to explain electromagnetism relied still on action at a distance. Dismissing Faraday’s electrical and magnetic fields, they used instead the idea of point charges producing a force at a distance and did not come up with this extra component which would allow for electromagnetic waves. Einstein considered this move to be crucial. Writing in his book Autobiographical Notes, he said:
The most fascinating subject at the time I was a student was Maxwell’s theory. What made this theory appear revolutionary was the transition from action at a distance to fields as the fundamental variables … it was like a revelation …
As it happens, there already was a transverse wave known to science that travelled through insulators and even empty space – light. What’s more, as we have seen, Maxwell’s hero Faraday had speculated that light somehow involved electricity and magnetism.
Remember that in 1846, when Maxwell was fifteen, Faraday had filled in for Charles Wheatstone at a lecture and had told his audience:
The views which I am so bold as to put forth consider, there-fore, radiation as a high species of vibration in the lines of force which are known to connect particles, and also masses of matter, together. It endeavours to dismiss the aether, but not the vibrations.
In his inspired vision, Faraday was prepared to go a step further than Maxwell. Where Maxwell believed that his model of cells and spheres represented the ether, Faraday believed that the fields of electricity and magnetism extended through empty space without the need for an ether. Either way, both had realised that light was a vibration in those fields, Faraday in visionary concept and Maxwell with the mathematical backing of his mechanical model.
Seeing the light
We don’t know the exact process by which Maxwell realised that the waves his model predicted seemed remarkably similar to light, but it’s hard to imagine that he was unaware of Faraday’s ‘Thoughts on Ray-vibrations’ talk. Whatever the means of reaching this idea, Maxwell’s model gave him a way to test out whether this relationship between light and electromagnetism was valid. It was known that the speed of waves through a medium could be calculated from a combination of the elasticity of the medium and its density. In his model, elasticity corresponded to the electrostatic force and density to the magnetic equivalent.
Although not all the values required were perfectly pinned down for his model, if Maxwell took the minimum values for the elasticity of a vacuum, the speed of the predicted wave would match the velocity produced by dividing the unit of magnetic charge by the unit of electrical charge, which was unlikely to be a coincidence. Maxwell was able to calculate that his model predicted that in a vacuum, such electromagnetic waves should travel at 193,088 miles per second (310,700 kilometres per second).
All Maxwell had to do was to compare his prediction with the speed of light, a value that had first been made calculable in 1676 by the observations of Danish astronomer Ole Rømer of variations in the timings of the moons of Jupiter as the distance between the giant planet and Earth varied. More recently it had been measured by French physicist Armand Fizeau using a mechanical device which sent flashes of light from a fast-rotating toothed wheel down a 9-kilometre track, before returning the light through the wheel, using the speed of rotation of the wheel to measure the elapsed time.
Unfortunately, Maxwell did not have any documentation on Fizeau’s work with him at Glenlair,§ and though his speed for electromagnetic waves was certainly relatively close to what had been measured, he couldn’t remember the value sufficiently well to be sure how effective his prediction was. He had to wait until his return to London in October to compare his theoretical wave’s speed with that of light. Back at King’s College he discovered that the latest figure from Fizeau gave light speed as 195,647 miles (314,850 kilometres) per second, with other estimates in the 192,000 to 193,118 miles per second (308,990 to 310,790 kilometres per second) range. This was less than 1.5 per cent different from his calculated speed.
Such a similarity seemed highly unlikely to be a coincidence. Maxwell wrote:
The velocity … agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists … [of] undulations of the same medium which is the cause of electric and magnetic phenomena.¶
His ‘mechanical analogy’, which had aroused in Poincaré that ‘feeling of discomfort and even of mistrust’, had revealed the truth behind a mystery that had puzzled humanity for millennia – what was light?
Although Maxwell had considered On Physical Lines of Force to be complete with the first two parts, he now decided to extend it to add a third section in 1862 which included the displacement current and electromagnetic waves. This was soon followed by a part four, as he realised that his electromagnetic waves would account for another previously unexplained phenomenon.
We have already seen on page 25 how Maxwell as an undergraduate had made use of polarised light in his home laboratory. Faraday had also studied polarised light and had discovered that passing such light through a magnetic field would rotate its direction of polarisation. Now that Maxwell had identified light as a combination of electrical and magnetic waves at right angles to each other, and assuming that polarisation represented the direction of these waves, it was natural that a magnetic field would have an influence on the changing fields in the wave and cause them to rotate, just as it caused a wire carrying a changing current to rotate in an electric motor.
Too heavy for one person to discharge
Maxwell had a little more time available for his own work after his return to London in October 1861 with the appointment of George Robarts Smalley as a physics lecturer to assist him. Maxwell had complained to the college that his teaching requirements were ‘too heavy f
or one person to discharge’. This appointment did not represent any financial generosity on the part of King’s College. Smalley’s pay of 7 shillings per student per term was deducted from Maxwell’s salary.
Smalley continued in the post until July 1863, when he was appointed Astronomer Royal for New South Wales. Maxwell wrote a reference for Smalley to the British Astronomer Royal, George Biddell Airy, noting that:
I believe Mr Smalley to possess the scientific knowledge and the habits of accuracy which would fit him for work at the Observatory … I consider that he would be steady, accurate and skilful in Observatory work.
William Grylls Adams replaced Smalley (and later took over Maxwell’s own position). Smalley and Adams took some of the weight from Maxwell’s shoulders.
Despite this reduction in work pressure while in London, Maxwell remained at his happiest when back at Glenlair. Here he could both think in peace about his physics and enjoy the rural life. In a letter written from Glenlair just after Christmas 1861 to Henry Droop, who had become a friend while they were both fellows at Trinity College, Cambridge, Maxwell noted:
I have nothing to do in King’s College till Jany. 20, so we came here to rusticate. We have clear hard frost without snow, and all the people are having curling matches on the ice, so that all day you hear the curling-stones on the lochs in every direction for miles, for the large expanse of ice vibrating in a regular manner makes a noise which, though not particularly loud on the spot, is very little diminished by distance.
It shouldn’t be deduced, though, from his pleasure at having free time, that Maxwell was the kind of scientist whose only concerns were his own research and who had little interest in his students (as was the case with, say, Newton or Einstein). As we have seen, he stood up for his students in the use of the library and he lectured to working men. A good example of his attention to detail in this respect was a letter he wrote to J.W. Cunningham, the secretary of King’s College London, in December 1862.
Dear Sir
I am very anxious that the examination papers in Mechanics should be printed from type instead of from stone.
I find that the lithographic papers are printed so that even if everything is plain in perfect copies, uncertainties exist in other copies which are very apt to make the examination not quite a fair one.
Mr Smalley has the M.S. and expects to give it in at the office today.
Lithography, literally stone writing, is a printing technique where the dark parts of an image (the letters in a text) are marked out on the surface of a flat piece of stone – typically limestone – (or later metal) with a resistant substance such as wax or fat. Then the surface is treated with acid, which etches into the surface where there is no resistant material. The surface is cleaned then moistened, with water being retained in the etched sections between the letters or raised imagery. Finally, an ink that is immiscible with water is applied – the ink stays on the nonetched parts, and so reproduces the image or text.
Related, but more sophisticated techniques known as offset lithography and photolithography are still in use today, for printing and for producing printed circuits respectively (though, despite the names, no stone is involved). However, in Maxwell’s time the process, though relatively cheap, was not as consistent in its results as using moveable type – metal letters fixed into a frame. Maxwell, as always a champion of the students, was ensuring his examination papers were legible despite additional cost to the college.
The Great London Exposition
Maxwell also continued with his interest in communication of science to the wider public that had come through in both his work with the British Association and in lecturing at the Royal Institution. An opportunity arose in 1862, when it was decided to follow up on the huge success of the 1851 Great Exhibition. Although France had put on a pair of national events earlier, the Great Exhibition was effectively the first World’s Fair, a chance to show off and revel in the wonders of Victorian technology.
Such was the success of the first event that its profits funded the construction of the Science Museum, Natural History Museum and Victoria and Albert Museum. Before they were built, however, the land that would be the site of the Natural History Museum was used to house the Great London Exposition of 1862, also known as the International Exhibition.
As a money-making event, this proved a relative failure compared with its predecessor, doing little more than break even thanks to the far more lavish building constructed for the purpose, but still around 6 million people filed through the vast halls. Maxwell was responsible for producing the guide to a section of philosophical (scientific) instruments connected with light. His might have been a small contribution to a massive venture, but he went far beyond a simple catalogue, taking the opportunity to throw in some history of science and descriptions of the physical mechanisms involved, showing his expertise with leading-edge experimental optics.
Meanwhile, once Smalley was in place at King’s, there was soon an opportunity for Maxwell to make use of that freed-up time. It wouldn’t be understating things to say that Maxwell’s model of electromagnetism and its prediction of electromagnetic waves was a huge breakthrough – not only in this specific case, but also for the way that physics itself would be undertaken, in which Maxwell’s approach of producing a model and testing its predictions has become a central part of the scientific method.|| Even so, and despite a largely positive reaction when he wrote it up, Maxwell was not entirely happy. Perhaps Poincaré’s mistrust stung him – but he felt it ought to be possible to take away the framework of analogy, removing his mechanical model and keeping only the pure, untrammelled mathematics.
Notes
1 – Albert Einstein’s observation that the most fascinating subject as a student was Maxwell’s theory is quoted in Albert Einstein, Autobiographical Notes (Illinois: Open Court, 1996), pp. 31–3.
2 – Maxwell’s words on the inference that light was an electromagnetic wave are from his paper ‘On Physical Lines of Force’ in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), pp. 499–500.
3 – Maxwell’s comment about his teaching duties being too heavy is from King’s College London Archives, King’s College Council, Vol. I, minute 42, 11 October 1861.
4 – Maxwell’s reference for Smalley’s application as Astronomer Royal for New South Wales is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), p. 87.
5 – Maxwell’s letter mentioning the noise of curling to Henry Droop, written from Glenlair on 28 December 1861, is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 1 (Cambridge: Cambridge University Press, 1990), p. 703.
6 – Maxwell’s letter to J.W. Cunningham on printing the examination papers in mechanics is reproduced in Peter Harman (ed.), The Scientific Letters and Papers of James Clerk Maxwell, Vol. 2 (Cambridge: Cambridge University Press, 1995), p. 61.
* Long by most people’s standards. After the six-month summer vacation at Aberdeen, the mere four months allowed by King’s College may have seemed quite short to Maxwell.
† A vector is a quantity with both size and direction, where a scalar quantity only has size. Speed is a scalar – 50 kilometres per hour, for example. Velocity is a vector – 50 kilometres per hour heading north, for example.
‡ Always bear in mind that the ether does not exist. This was Maxwell’s thinking at a time when it was still assumed that there was such a thing.
§ Ironic, given that Maxwell’s work would provide an essential foundation for the internet that enables anyone to look up this value pretty much instantly.
¶ Maxwell’s italics.
|| In fact there was a third reason this breakthrough was so important, though Maxwell would not live to witness it. Maxwell’s model required light to always travel at a particular speed in a vacuum, a fact that Einstein wo
uld use to develop his special theory of relativity.
Chapter 6
Science by numbers
Like many Victorian scientists, Maxwell did not suffer from the modern tendency to remain constrained by a tight focus – he clearly appreciated the chance to roam free across the topics covered by physics. This is apparent in some of his letters, where he happily discussed a wide range of physical subjects with fellow scientists.
A good example would be a letter that Maxwell wrote in August 1863 to George Phillips Bond, an American astronomer based at Harvard University. Bond had met Maxwell in London that May and subsequently had written to him both about the rings of Saturn and about comets. At the time, the behaviour of comets’ tails was a puzzle. Back in 1619, the German astronomer Johannes Kepler had pointed out that the tails of comets always pointed away from the Sun. When the comet is heading into the solar system, towards the Sun, its tail flows out behind it, but when the comet is moving in the opposite direction away from the Sun, the tail lies confusingly in front of it.
This behaviour suggested to Kepler that, rather than being left behind like a stream of smoke from a moving flame, the comet’s tail was being pushed by something emanating from the Sun. Somehow, the Sun’s rays were forcing the comet’s tail away. Late in his career, Maxwell would come up with a better explanation for this (see Chapter 9), but in responding to Bond, he speculated about the nature of the ether that he still believed was the medium for light waves.