Professor Maxwell's Duplicitous Demon
Page 25
To understand why this happened requires the alternative definition of the second law, the one involving entropy. As we’ve seen, entropy is measured by the number of different ways the components of a system can be organised. The more ways, the higher the entropy. In the case of the chloroform experiment, entropy decreases because there are more ways to arrange the quantum states† when they are correlated than when the correlation goes away – it’s a bit like there being more different ways to throw a six with two dice together than there are with either of two dice individually.‡ However, free energy enthusiasts don’t need to get too excited. Although there does appear to have been a spontaneous reduction in entropy, getting the molecules into the right state to start with would have taken far more energy than could be extracted. This is never going to be a free source of energy.
Dr Serra’s chloroform molecules have none of the sophistication of a true demon at work – but they are an actual physical manifestation of that most enduring of laws being, at the very least, cheekily tweaked. Whether or not my challenge remains, one thing is certain. Our man, James Clerk Maxwell, has an impressive legacy and I’m proud to be associated with it.
Notes
1 – The assertion that the erasure of information need not result in the increase of entropy comes from Meir Hemmo and Orly Shenker, Maxwell’s Demon (Oxford: Oxford Handbooks Online, 2016), accessed at: http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199935314.001.0001/oxfordhb-9780199935314-e-63
2 – The Oxford University paper describing a photonic demon is Mihai Vidrighin, et al., ‘Photonic Maxwell’s Demon’, Physical Review Letters, 116 (2016), p. 050401.
3 – The chloroform-based quantum demon is described in Patrice Camati, et al., ‘Experimental rectification of entropy production by Maxwell’s demon in a quantum system’, Physical Review Letters, V. 117 (2016), p. 240502.
* Quantum spin is one of the standard properties of a quantum particle. It was called spin as it loosely corresponds to the familiar rotation of an object, but it does not involve actual spinning around: quantum spin has values of multiples of a half, and can only be either up or down in the direction of measurement.
† The quantum state of a particle (or system) is the collection of the values of its properties such as charge, spin, etc.
‡ With two dice individually, you can only get a six if six comes up on one of the dice. But with two dice together you can get a six with 1+5, 2+4 and 3+3.
Chapter 10
The legacy
If you were to ask a scientist around the end of the nineteenth century who – of that century’s big names – scientists in the future would regard as the leading British physicist of the era, he would undoubtedly have said Lord Kelvin. Maxwell’s old friend William Thomson was feted in his day – a reality that was reflected in his elevation to the House of Lords, the first scientist ever to have received this honour.* Certainly, there is no doubt that Kelvin did essential work in thermodynamics, as well as working on many practical applications of science – his name appears on over 70 patents of the period, and as we have seen, he was a leading figure in the laying of the transatlantic cable.
It was Kelvin, not Maxwell, who ended up alongside Isaac Newton in Westminster Abbey, and Kelvin who has a scientific unit named after him. Not long after Kelvin died in 1907, statues of him would be erected in both his birthplace of Belfast and in the city where he did the majority of his work, Glasgow. By contrast, Maxwell was buried in a little country churchyard and there would not be a statue of him put up in his native Scotland for over 100 years after his death.
By the first half of the twentieth century, though, the picture was transformed. While Kelvin’s achievements have not been belittled, they now seem a lot less significant in the grand scheme of things. By comparison, the appreciation of Maxwell’s work on electromagnetism, his contribution to statistical mechanics, and his transformation of the way that theoretical physics was undertaken have made him far more of a hero to modern physicists. It’s not for nothing that Einstein is reported as saying: ‘There would be no modern physics without Maxwell’s electromagnetic equations; I owe more to Maxwell than to anyone.’
Those who knew him best were aware from the outset that there was something special about James Clerk Maxwell. His friend since schooldays, Peter Tait, wrote of him in Nature at the end of a summary of Maxwell’s work, providing a eulogy that would stand up well today in its reference to the resistance to ‘vain-babbling’ and pseudo-science:
I cannot adequately express in words the extent of the loss which his early death has inflicted not merely on his personal friends, on the University of Cambridge, on the whole scientific world, but also, and most especially, on the cause of common sense, of true science, and of religion itself, in these days of much vain-babbling, pseudo-science, and materialism.
There was something very special about Maxwell’s breadth of contribution. Charles Coulson, who in 1947 took on the same chair that Maxwell had held at King’s College London, remarked: ‘There is scarcely a single topic that he touched upon which he did not change almost beyond recognition.’ This volume of output was matched by Maxwell’s insight – his ability to develop models and mathematics to model reality when this approach was a novelty. In a booklet put together to celebrate the centenary of Maxwell’s birth in 1931, the English physicist James Jeans gave striking testimony to this intuitive force when describing Maxwell’s distribution for the velocities of gas molecules. Jeans wrote:
Maxwell, by a train of argument which seems to bear no relation at all to molecules, or even to the dynamics of their movements, or to logic, or even to ordinary common sense, reached a formula which according to all precedents and all the rules of scientific philosophy, ought to have been hopelessly wrong. In actual fact, it was subsequently shown to be exactly right … it was this power of profound physical intuition, coupled with adequate, though not outstanding mathematical technique, that lay at the basis of Maxwell’s greatness.
It’s not uncommon when trying to give Maxwell his rightful place in the pantheon of physics to bracket him with Newton and Einstein (probably throwing in Faraday as well). And though there is no doubt that a considerable amount of Newton’s work was concerned with physics, it’s arguable that Newton was far less of a physicist than Maxwell.
It’s interesting to compare the catalogues of Newton’s and Maxwell’s libraries. Newton left behind a remarkable† 2,100 books. Of these 109 were on physics and astronomy, 138 on alchemy, 126 on maths and 477 on theology.‡ By comparison, over half Maxwell’s books were on physics. Newton was arguably an applied mathematician (when he wasn’t occupied as an alchemist, a theologian or working at the Mint). Maxwell, like Einstein, was undoubtedly a physicist.
Looking back from the twenty-first century, Maxwell comes across as unusually unstuffy for his day. Someone far from the stereotypical image of the humourless Victorian scientist. And we are now also in a position to appreciate just how much his work on electromagnetism would help launch a technological revolution.
Considering how fresh much of Maxwell’s science was, we can see in some of his later writing and talks a very modern approach to scientific matters. In 1873, he gave a speech entitled ‘Discourse on molecules’ at the British Association’s meeting in Bradford, a small part of which makes an ideal dip into Maxwell’s own words.
In the heavens we discover by their light, and by their light alone, stars so distant from each other that no material thing can have passed from one to the other;§ and yet this light, which is to us the sole evidence of the existence of these distant worlds, tells us also that each of them is built up of molecules of the same kinds as those which we find on earth. A molecule of hydrogen, for example, whether in Sirius or in Arcturus, executes its vibrations in precisely the same time.
Each molecule therefore through the universe bears impressed on it the stamp of a metric system¶ as distinctly as does the metre of the Archives at Paris, or the double ro
yal cubit in the temple of Karnak.
No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction.
None of the processes of Nature, since the time when Nature began, have produced the slightest difference in the properties of any molecule.
At this point, Maxwell deviates from modern science as he assumes that molecules have to have been made from something, given their identical nature, but that there was no process that could do so that ‘we can call natural’. We now know there are perfectly natural processes for the interchange of matter and energy which can account for the creation of matter, but when Maxwell wrote, this science was still 23 years in the future, with Einstein’s special theory of relativity. (And the special theory would not have come about without Maxwell’s work.) Even so, until that point, and allowing for some change in language, we could have just as easily have been listening to a Brian Cox or Neil deGrasse Tyson expanding on the wonders of the universe as to a Victorian. Maxwell’s vision was far removed from the semi-mystical meandering of earlier physics, a fault that stayed with it even when Newton and his followers had started to include some mathematics.
Throughout this book, a minor part of Maxwell’s output – the demon – has played a significant role. I wanted the demon to have his say because he reflects so well Maxwell’s ability to challenge the way that his colleagues thought about things, to use interesting new approaches to modelling, and to incorporate a touch of humour into what can be a very po-faced science. More than a great scientist, Maxwell seems to have been a remarkable man, someone with whom it must have been a pleasure to be a friend.
Maxwell and his demon deserve to be remembered as long as science has an impact on our lives.
Notes
1 – Einstein’s claim to owe more to Maxwell than anyone is from Esther Salaman, ‘A Talk with Einstein’, The Listener, 8 September 1955, Vol. 54, pp. 370–71.
2 – Peter Tait’s eulogy to Maxwell is from Nature, Vol. 21 (1880): 317–21.
3 – Charles Coulson’s remark about Maxwell is from C. Dombe (ed.), Clerk Maxwell and Modern Science: Six Commemorative Lectures (London: Athlone Press, 1963), pp. 43–4.
4 – James Jeans’ remarks about Maxwell’s intuitive ability are from his entry, ‘Clerk Maxwell’s Method’, in James Clerk Maxwell: A Commemorative Volume 1831–1931 (Cambridge: Cambridge University Press, 1931), pp. 97–8.
5 – The quote from Maxwell’s lecture on molecules is from Lewis Campbell and William Garnett, The Life of James Clerk Maxwell (London: Macmillan, 1882), p. 358.
* It’s often said, incidentally, that Isaac Newton was the first person to be knighted for his contribution to science. I’ve even heard this claimed on that unequalled source of knowledge, the BBC’s Pointless TV quiz programme. But in reality, Newton was knighted for doing a good job at the Royal Mint, where his enthusiasm for catching those who clipped the edges of coins to sell the metal (and for having them hanged, drawn and quartered) was legendary. A man after my own demonic heart, was Newton.
† Particularly for the period, when books were an expensive rarity.
‡ Which Newton would have considered a science.
§ Funnily, in saying this Maxwell was wrong, but for the right reason. At the time, the universe was thought to be much smaller than we now know it to be – but it was also considered so much younger that it was assumed there wasn’t time for anything to get from one extreme of the universe to the other. The current Big Bang theory fixes this with a universe that expanded so quickly during the inflation phase that right at the beginning, the extremes of the observable universe could still have been in direct physical contact.
¶ By ‘metric system’ Maxwell did not intend the modern usage of a system to base 10, but just a system of measurement.
Index
A
Aberdeen as city divided 1
evening education 1
JCM move to 1
see also Marischal College
Aberdeen School of Science and Art 1
Aberdeen, University of 1
absolute zero 1
action at a distance 1, 2, 3
Adams, John Couch 1
Adams, William Grylls 1, 2
Adams Prize 1, 2
aether see ether
Airy, George 1, 2, 3
Albert, Prince 1
amp 1, 2
analogy, power of 1
analytical engine 1
antigravity 1
antimatter 1
Apostles, the 1
Archimedes 1, 2
argon 1
Aristotle 1
atoms 1, 2
attraction electrostatic 1
modelling 1
B
B.A. standard resistor 1
B.A. unit 1
Babbage, Charles 1
Bacon, Roger 1, 2
Baden-Powell, Robert 1
balloons 1, 2
Balmoral 1
Bartholin, Erasmus 1
belfry 1
Bernoulli, Daniel 1
Bettany, George 1
Big Bang theory 1, 2
billiard balls 1
binary systems 1
Birmingham 1
Blackburn, Hugh 1
blending 1
Blore, Edward 1, 2
Boltzmann, Ludwig 1
Bond, George Phillips 1, 2
books by JCM Elementary Treatise on Electricity 1
Theory of Heat 1, 2, 3
Treatise on Electricity and Magnetism 1, 2, 3, 4
A Treatise on Natural Philosophy 1
Bragg, William 1, 2
Bragg, William Lawrence 1
Brewster, David 1
British Association for the Advancement of Science (BA) 1, 2, 3, 4
Byers, Mrs 1
C
cable car 1
calculus 1
caloric theory 1, 2, 3
Calotype 1
Cambridge, New Museums Site 1
Cambridge, University of Department of Applied Mathematics and Theoretical Physics 1 JCM inaugural lecture on return 1
leading university for physics 1
religious requirements 1
Campbell, Lewis best man 1
biography of JCM 1, 2
as friend of JCM 1, 2, 3
pen sketch of JCM 1
capacitors 1
Carnot, Sadi 1
Cassini, Giovanni 1
catechism 1
cats 1
Cavendish, Henry 1, 2, 3
Cavendish, William (Duke of Devonshire) 1, 2, 3, 4
Cavendish Laboratory building and equipping 1
early years 1
name change 1
running 1, 2
women in 1
Cavendish Professorship 1, 2, 3
Cay, Jane 1, 2, 3, 4, 5
Cay, John 1
Cay, Lizzie 1
Cayley, Arthur 1
cells, flexible 1
centrifugal forces 1, 2
centripetal forces 1
Challis, James 1
chance, games of 1
chaotic systems 1
charge density 1
unit 1
Chemical Society 1
chloroform 1
City Philosophical Society 1, 2
Clausius, Rudolf 1, 2, 3, 4, 5
Clerk, George 1
Clerk, Isabella (later Wedderburn) 1, 2, 3, 4
Clerk, John 1
Clifton, Professor 1
coffin 1
collodion 1
colour 1
colour blindness 1, 2
colour theory, Royal Institution lecture 1
colour tops 1, 2
colour triangle 1, 2
colour vision 1, 2, 3
colours, primary 1
comets 1, 2, 3
compasses 1
complex numb
ers 1
condensers 1
conductors 1
Connell, D.M. 1
conservation of energy 1, 2
continuous functions 1
control systems theory 1, 2
convergence 1
Corpus Christi College, Cambridge 1
corpuscles 1
cosmic rays 1
Coulomb, Charles-Augustin de 1
coulomb 1
Coulson, Charles 1
Crookes, William 1
Crookes radiometer 1
cross product 1
Cunningham, J.W. 1
curl 1, 2
current, unit of 1
curves 1, 2
cyan 1
cybernetics 1
D
Dalton, John 1, 2, 3
dark matter 1
Darwin, Charles 1
Davy, Humphry 1, 2, 3, 4
degrees of freedom 1
del (nabla) 1
Democritus 1
‘demon’ thought experiment described 1
demonstrations 1
density 1, 2
Descartes, René 1
Dewar, Daniel 1
Dewar, Donald 1
Dewar, James 1, 2
Dewar, Susan 1
diabolo 1
dielectrics 1
difference engine 1
differential calculus 1
disorder, level increasing 1, 2
displacement current 1, 2
displacement field 1
divergence (div) 1, 2
DNA 1, 2
dot product 1
Droop, Henry 1
dynamical theory of gases see thermodynamic theory of gases
E
Earth density 1, 2
energy coming into 1
as oblate spheroid 1