Thursday, April 11, 2013

A demon-haunted theory

Here is a piece I’ve just published in the April issue of Physics World, in pre-edited form (sort of).


James Clerk Maxwell originally devised his demon as a thought experiment to evade the second law of thermodynamics. But some of the physicist’s contemporaries actually believed it was an intelligent being that could bridge hidden worlds and provide a scientific route to immortality of the human soul.

Maxwell’s demon represents one of the great “thought experiments” of physics. Just like Einstein riding a light wave or Schrödinger’s cat facing quantum extermination, it poses a ‘what if’ question that illuminates a deep property of nature. The Scottish physicist James Clerk Maxwell proposed his little being as a way of picking a hole in the second law of thermodynamics by enabling heat to flow from cold to hot and resisting entropy’s disruptive influence. He had no idea that he was actually posing a riddle for the theory of information, which would lead ultimately to the recent demonstration that information and energy can be interconverted.

But the popularity that Maxwell’s demon has enjoyed thanks to the current burgeoning interest in the thermodynamics of information overlooks the way this little being was regarded by Maxwell and his contemporaries. Placed in its historical context, Maxwell’s demon played a rather different role – one that is surprising and in some respects shocking. For one thing, this wasn’t exactly a thought experiment at all. Some of Maxwell’s contemporaries saw in the demon a link between science and religion, a solution to the problem of free will, a bridge to hidden worlds, even a scientific route to immortality of the human soul. In some ways, Maxwell’s original demon seems more closely linked to ancient demonology than to the future of computing and information science.

Picking holes

Maxwell’s idea was a response to the gloomy prediction of a ‘cosmic heat death’ of the universe. In 1850 the German physicist Rudolph Clausius formulated the first and second laws of thermodynamics: the conservation of energy and the irreversibility of heat flow from hot to cold. A year later William Thomson (later Lord Kelvin) pointed out that the flow of heat involves ‘dissipation’ of mechanical energy: it flows into random motions of molecules and can never be recovered. This process, he said, must eventually create a universe of uniform temperature, from which no useful work can be extracted, and in which nothing really happens.

Maxwell realised that this inexorable slide into an inert state challenged human free will. If, as the second law says, there is only one way for things to happen, we would seem to be locked into rigid determinism, with human freedom just an illusion. As a devout Christian, he could not accept that God would arrange things this way. But how could free will be rescued without violating thermodynamics?

Maxwell’s seminal work on the microscopic theory of gases gave him an escape clause. He was convinced that the second law is simply statistical. Gases contain molecules with a bell-shaped statistical distribution of speeds, the faster ones being in a sense ‘hotter’. Temperature gradients get dissipated because it is far more likely that the faster molecules will mingle with the slower, rather than by chance congregating into a ‘hot’ patch. There’s nothing in the laws of mechanics to forbid the latter; it’s just very unlikely.

But what if we could arrange for that to happen? Then the second law would be undone. We can’t manage it in practice, Maxwell recognized, because we can’t possibly find out about the velocities of all the individual molecules. But what if there were, as Maxwell put it, a “finite being”, small enough to ‘see’ each molecule and able to keep track of it, who could open and shut a trapdoor in a wall dividing a gas-filled vessel? This being could let through fast-moving molecules in one direction so as to congregate the heat in one compartment, separating hot from cold and creating a temperature gradient that could be tapped to do work.

Maxwell laid out this idea in December 1867 in response to a letter from his friend, the physicist Peter Guthrie Tait, who was drafting a book on the history of thermodynamics. Maxwell told Tait that his aim was explicitly to “pick a hole” in the second law – to show that it was “only a statistical certainty”. The thought experiment offered a loophole that might rescue free will.

Exorcising the demon

It took over a century for the problem with Maxwell’s demon to be identified. In 1929 the Hungarian physicist Leo Szilárd believed he saw a flaw: to measure the speed of molecules the demon would have to expend energy, which would dissipate enough heat – produce enough entropy – to compensate for the demon’s manipulations. But in 1961 the German-American physicist Rolf Landauer, drawing on the relationship between information processing and thermodynamics developed by Claude Shannon in the 1940s, pointed out that measurements can in principle be conducted without increasing entropy.

That may be done, however, only by retaining all the information that the demon acquires. But, said Landauer, if he is a ‘finite being’ with a finite memory, this accumulation of data can’t go on forever: eventually some information will have to be erased to make room for more. And Landauer showed that while measurement can be free of an entropic cost, erasing data can’t be. Resetting a binary digit (from 1 to 0, say) must inevitably dissipate energy of at least kTln2, where k is Boltzmann’s constant. So in effect the demon generates entropy by forgetting. Charles Bennett of IBM’s research centre in Yorktown Heights later showed that this act of ‘forgetting’ is unavoidable, since it is equivalent to resetting the measuring equipment ready for the next measurement.

Landauer’s discovery has profound implications for the theory of computation. The digital circuits in today’s computers – which are inevitably reset from one calculation to the next – will always dissipate a certain minimum amount of heat during processing, although at present they still create far more heat than this lower limit because of other sources of dissipation. The existence of this unavoidable heat output in computing was proved experimentally last year by a team at the University of Augsburg in Germany, who were able to measure the amount of energy dissipated when a microscopic silica bead was moved between two optical traps to encode a binary digit. They found that as a cycle of switching and resetting the bead’s position was made ever slower, the amount of energy dissipated fell to a minimum of kTln2: for infinitely slow switching, all of this was due solely to the resetting operation [1].

In effect Landauer’s principle implies an equivalence between information and heat: information itself can be converted to heat. This too has recently been confirmed experimentally. In 2010 a team of physicists at the University of Tokyo led by Shoichi Toyabe moved a nanoscale polystyrene bead in a particular direction, doing useful work, not by using any energy as such but by taking advantage of the information gathered about the bead’s position [2]. They put the bead on a spiral staircase of sorts, on which the bead could hop up or down one step at a time using thermal energy. Left to its own devices, the ball would, on average, move down the staircase. But if a demon knew the position of the ball, it could place a barrier to prevent any downhill motion, so that the ball only moves uphill. In the experiment, the physicists took on the role of the demon: if the bead was measured to have moved uphill by one step, the barrier was moved upwards by one step too. By taking advantage of information gathered about the bead’s position, the physicists – using no energy as such – ensured the bead’s net uphill movement and thereby caused the bead to gain potential energy. This demonstrated experimentally that information can be converted into energy.

These studies reveal that Maxwell’s thought experiment is now accessible to direct experimental probing, and that such efforts are at the forefront of information science and technology. Moreover, even if Landauer’s principle currently represents the standard doctrine, some commentators feel that it may still be too early to be sure that the demon is dead, and that ultimately it will prove to have ramifications for the foundations of quantum information theory [3,4].

Little helpers

Maxwell didn’t intend his creature to be called a demon. That label was applied by Thomson in an 1874 paper in Nature, where he defined it as “an intelligent being endowed with free will, and fine enough tactile and perceptive organization to give him the faculty of observing and influencing individual molecules of matter.” Whether he meant it or not, this seemingly trivial change connected Maxwell’s being to a long genealogy of tiny or invisible spirits acting as agents and familiars with special powers, dating back to the demon that allegedly advised Socrates. Maxwell was not pleased. “Call him no more a demon but a valve”, he grumbled to Tait.

"Who gave them this name? Thomson." Maxwell grumbles to Tait in this letter.

Maxwell’s apparent victory over the second law in the nineteenth century might seem decidedly Pyrrhic, since as he admitted, we can’t possibly do what the demon does anyway. Maxwell presumably could have argued that we might one day have the technological means, but he didn’t seem to hold out much prospect of that. There is, however, another way that his thought experiment could work: the demons might be real. Maxwell seems to have entertained this idea, for he took seriously the possibility that free will depended on it.

The notion of invisible, perhaps demonic, beings that intervene in the world was widely shared among philosophers of the Middle Ages and the Renaissance. But surely such ideas were banished by Victorian times? Not at all. Maxwell himself seems never to have stated whether he regarded his ‘demon’ as a being – his references to a “valve” and a “self-acting” device suggest he may have preferred the image of a machine, as physicists do today – albeit a ‘machine’ with intelligence and autonomy, as he once put it “a doorkeeper, very intelligent and exceedingly quick.” Yet his touchiness about Thomson’s quip seems rather puritanical even for a religious man until one realises that Maxwell might have entertained a belief in evil spirits.

Demons performing useful work for humans in a sixteenth-century illustration.

Several of his contemporaries had little doubt that these ‘demons’ were to be taken literally. Thomson himself took pains to stress that the demon was plausible, calling it “a being with no preternatural qualities, [which] differs from real animals only in extreme smallness and agility.” Tait evidently believed they might exist, and he enlisted them for an extraordinary cause. In 1875 Tait and the Scottish physicist Balfour Stewart, an expert on the theory of heat, published a book called The Unseen Universe in which they attempted to show that “the presumed incompatibility of Science and Religion does not exist.” There must be, they wrote, “an invisible order of things which will remain and possess energy when the present system has passed away.” They believed that this “invisible” or “spiritual” domain must be capable of interacting energetically with the familiar physical world, perhaps bridged by the pervasive ether that was then thought to carry Maxwell’s electromagnetic waves. Thus energy might be transferred from the physical to the invisible realm to sustain our souls after death: through living, we store up immortality.

Tait and Stewart were aware of the apparent conflict between the Christian doctrine of the immortality of the soul and the second law of thermodynamics, which seemed to enforce an eventual universe of insensate stasis. “The dissipation of energy must hold true”, they admitted, “and although the process of decay may be delayed by the storing up of energy in the invisible universe, it cannot be permanently arrested.” Maxwell’s demon gave them a way out. “Clerk-Maxwell’s demons”, they wrote, “could be made to restore energy in the present universe without spending work” – and as a result, “immortality is possible.”

Today these speculations, coming from two highly respected scientists who Maxwell esteemed, look bizarre. But in the late nineteenth century such ideas were widely held. Spiritualism interested many scientists, including William Crookes, Oliver Lodge, J. J. Thomson and Pierre Curie. Even though some, like Tait and Stewart, were sceptical of the claims of mediums, they did not object to the basic concept.

Scientific spirit

Not only did these scientists believe in a spiritual world, but they felt that science was on the threshold of proving its existence. Many regarded the ether as a mediator. Cromwell Varley, a pioneer in transatlantic telegraphy, drew analogies between the use of electromagnetic signals for long-distance communication and the invisible messages that were alleged to pass from spirits to the living. The distinguished English physicist William Barrett wrote in 1917 that “it is not a very incredible thing to suppose that in the luminiferous ether life of some kind exists.” He speculated about “four-dimensional beings” and “human-like intelligences – good or bad daimonia” that might be responsible for events at séances. The Irish physicist Edmund Fournier d’Albe proposed in 1907 that there might exist “infra-men” on the scale of atoms, and drew on the discoveries of radioactivity and the electron to present a “physical theory of immortality.”

Indeed, the discoveries of new ‘invisible rays’, such as X-rays and radioactivity (“Roentgen rays”) bolstered beliefs in unseen universes. William Crookes – one of the most notorious sympathizers of the Spiritualists, mediums and Theosophists of the age – felt that vibrations beyond X-rays might account for telepathy. He too found a striking role for Maxwell’s demon, arguing that it might in effect explain the mystery of radioactive uranium’s seemingly inexhaustible supply of energy. He suggested that uranium atoms might be like demons themselves, mining energy from the surrounding atmosphere by sifting hot gas molecules from cold. “Let uranium or polonium”, he said at the annual meeting of the British Association in 1898, “have a structure that enables them to throw off the slow moving molecules of the atmosphere, while the quick moving molecules, smashing on to the surface, have their energy reduced and that of the target correspondingly increased.” It’s not clear that Crookes thought any intelligent agency was involved here, although he certainly believed in the possibility of invisible beings that have “intelligence, thought, and will, existing without form or matter” – and Maxwell had made clear that intelligence was needed to make the selection among gas molecules.

All this reveals that Maxwell’s demons had a much more ambiguous ontological status than imaginary ‘thought-creatures’. As well as reminding us that even apparently ‘modern’ historical scientists didn’t necessarily see things was we do, it shows how sometimes science doesn’t banish mystical beliefs but offers ‘rational’ justifications for them.

1. A. Bérut et al. Nature 483, 187–189 (2012).
2. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki & M. Sano, Nat. Phys. 6, 988-992 (2010).
3. J. Earman & J. D. Norton, Stud. Hist. Phil. Mod. Phys. 29, 435-471 (1998) & 30, 1-40 (1999).
4. K. Maruyama, F. Nori & V. Vedral, Rev. Mod. Phys. 81, 1-23 (2009).

Further reading
B. Stewart & P. G. Tait, The Unseen Universe. Macmillan, London, 1875.
R. H. Harman, The Natural Philosophy of James Clerk Maxwell. Cambridge University Press, 1998.
W. H. Brock, William Crookes (1832-1919) and the Commercialization of Science. Ashgate, Aldershot, 2008.
J. Canales & M Krajewski, Interdisciplinary Science Reviews 37, 314-331 (2012).


Mark Avrum Gubrud said...

"By taking advantage of information gathered about the bead’s position, the physicists – using no energy as such – ensured the bead’s net uphill movement and thereby caused the bead to gain potential energy. This demonstrated experimentally that information can be converted into energy."

I think this is rather overstating the case, with unwarranted suggestions about the ontological status of "information" as independent and separable from matter/energy/spacetime, or convertible into energy.

Clearly the potential energy gained by the bead was harvested from the thermal bath. The total energy of the system was unchanged. The free energy of the bead increased, but taking into account both the bath and the mechanism, the free energy of the total system was surely decreased, with a net production of (classical) entropy.

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