Heat Death

The Second Law of Thermodynamics has an oddly talismanic status in the public life of physics. Flanders and Swann wrote a song about it; C.P. Snow lectured on it. Whether it refers to the impossibility in a sealed system of letting heat flow from a cooler to a hotter body, or to the tendency of the universe to run down to more chaotic and disorderly states, it forms a key element in the magnificent edifice of the science of heat and energy constructed in the closing decades of the 19th century. Snow apparently thought it fairly easy to describe, and in a strange version of the humiliation game reckoned that to confess ignorance of the Second Law was like an admission that one had never read Shakespeare. His literary dinner companions’ response was suitably thermodynamic – ‘cold and negative’ – convincing him that they were all fatally and stupidly antiscientific.

This was not a new complaint. Snow’s remarks appeared in the Rede Lecture he gave at Cambridge in 1959: back in 1873, a Rede lecturer had already been warned not ‘to speak familiarly of a second law of thermodynamics, as of a thing known for some years to men of culture, who have never even heard of a first law’. For an unproblematic description of this law is neither easy nor straightforward. Ludwig Boltzmann, the greatest physicist of the Austro-Hungarian Empire, spent most of his career trying to define its meaning and clarify its basis. Now Carlo Cercignani, a mathematical physicist working in Milan, tries to explain the importance of Boltzmann’s search and to link it, somehow, to his extraordinary life. ‘The most important thing in a literary work is to give it the right title,’ Boltzmann told Viennese philosophers in 1905. Cercignani’s subtitle refers to trust, but this biography is not a story in which trust seems to play an important role. Instead, it offers a window onto the remarkable battles between self-confident scientific dogmas which raged across Europe at the end of the 19th century – and which continue today.

When professional scientists write books about past heroes, they often have a contemporary aim in view. Cercignani is no exception. He is an expert in rarefied gas dynamics, a science which describes the behaviour of vast arrays of very small particles moving and interacting relatively freely. He has shown how kinetics and heat theory can be used to understand the way in which space vehicles move, not to mention fashionable environmental concerns such as ozone holes, radioactive emissions, aerosols and carbon fibres. Any picture of such particle systems needs the tools of probability and statistics, since, as physicists of the last century began to realise, if you cannot follow the path of each and every particle, you have to judge the chances of any of a vast number of such particles possessing a given energy, or velocity, or position.

Getting Boltzmann right still matters, because the science he helped develop continues to have immense practical value, and, even more important, because there’s no easy consensus about what this science looks like. Cercignani begins by declaring that ‘a good understanding of the Second Law is related to understanding how life is possible,’ because living beings keep going by preserving their good order, struggling against the universal tendency to dissipation and chaos. It is just this struggle which the Second Law is supposed to describe. On the other hand, Cercignani’s book is also a brave attempt to understand the Law through an understanding of Boltzmann’s life of struggle; and, at the same time, it is an account of the problems which arise whenever a scientist tries to appeal to the general public for support, understanding or attention.

The story therefore starts with Boltzmann’s life, or rather his death. In September 1906, the 62-year-old Vienna professor of physics hanged himself from the sashcord in his hotel room. He’d been on holiday with his wife and daughter at Duino, the Habsburgs’ favoured seaside resort near Trieste, after neurasthenia prevented him continuing to lecture in the Austrian capital. Cercignani returns an open verdict on Boltzmann’s suicide, though he aptly refers to Rilke’s Duino Elegies on the tragic fate of the disappointed lover: ‘Boltzmann was a deceived lover who had devoted himself to atomic theory, but his love was not reciprocated because his contemporaries were not able to understand his great vision.’ High-level suicide was a Viennese preoccupation at the turn of the century – as witness the deaths of the royal lovers at Mayerling, and those of the brothers of both Mahler and Wittgenstein. Indeed, Wittgenstein himself had contemplated studying under Boltzmann, a plan frustrated by the physicist’s death. Perversely, Boltzmann’s fate made him typical of a culture in a way in which, apparently, he had never quite managed during his life.

Cercignani divides his study into four parts: a well-documented sketch of the life; a summary of the state of physics, especially the theory of moving particles, when Boltzmann started work in the 1860s; a very detailed analysis of the major contributions he made to the field; then a series of brief essays on his legacy and philosophy. Appendices back up the vaguer formulations of thermodynamic principles with precise mathematical formulae. Much of this work involves the correction and refinement of what Boltzmann originally proposed: retrospection helps make theories work. Remembering Boltzmann matters for contemporary physics, both in public and in private. As Cercignani concludes, ‘the mainstream of fundamental physics has somehow departed from Boltzmann’s views,’ notably in finding a ‘varied zoo’ of more fundamental particles precisely within those atoms which Boltzmann and his colleagues treated in their sums as so many simple bodies. Yet what this book indicates is not that he was proved wrong by what happened later in physics, but that the puzzles he confronted remain current.

The principal puzzle which Boltzmann inherited from his great forbears, the German Rudolf Clausius and the Scotsman James Clerk Maxwell, was entropy, a term designed to describe the apparently universal and irreversible tendency of heat to become less capable of doing useful work. Thus entropy measured disorder and the loss of accumulated resources, and reflected the strange but apparently obvious fact that the world was slowly running down. Clausius defined the notion of ‘entropy’; Maxwell as usual played around with it, imagining a cunning intelligence, a tiny demon who might be able to overcome its dread effects by manipulating the behaviour of microscopic particles. ‘The Second Law of Thermodynamics,’ Maxwell explained, ‘has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful out of the water again.’ This was a time when many saw the link between physics and economics: the science of mechanics was based on principles of ‘greed’ and ‘laziness’, and energy theory was integral to industry’s search for efficiency and productivity. Late Victorians even foresaw a heat death for the universe, when all things would reach thermal equilibrium, just the kind of degenerate vision which H.G. Wells coloured in the pastel shades of fashionable aesthetics at the end of his Time Machine: ‘This has ever been the fate of energy in security; it takes to art and to eroticism, and then come languor and decay.’

This kind of languorous decay was a problem for Boltzmann because he saw nature as a vast array of independent, individual particles, all absolutely governed by the laws of mechanics. ‘The movements of a body do not occur purely accidentally, going sometimes here, sometimes there, but they are completely determined by the circumstances to which the body is subject.’ At the very end of the century, Boltzmann lectured at Munich on the continuing validity of this picture: ‘I therefore present myself to you as a reactionary, one who has stayed behind and remains enthusiastic for the old classical doctrines as against the men of today.’ As Cercignani points out, it was this conservatism which made Boltzmann’s work so radical. The mechanical laws to which he adhered were obviously time-reversible. Film a collision between two billiard balls on a smooth table. Run the film backwards, and you still see a collision which obeys the principles of mechanics. But there are phenomena, precisely those where Boltzmann’s thermodynamics comes into play, where the trick doesn’t work so well: film steam coming out of a boiling kettle, or gamblers throwing dice, then reverse the movie and you’ll quickly notice something which, although mechanically explicable, strikes us as utterly implausible. Between 1868 and 1872, first in Vienna, then in the provincial university at Graz, Boltzmann worked out how to derive the measure of disorder and randomness from the basic mechanical laws; he claimed that those strange processes when disorder seemed to go into reverse were not impossible, merely very unlikely indeed. His new physics described how this probability value changed through time, and could be derived from apparently deterministic principles alone.

The fundamental intuitions of Boltzmann’s new world order were statistical, and resonated nicely with the avalanche of statistical tables which dominated the milieu of his father, a Habsburg tax official of Prussian descent. Even the smallest volume of a hot gas must contain so many colliding particles, a number cleverly computed by Boltzmann’s Viennese colleagues, and those collisions would produce orderly states so rarely, that disorder would swamp any alternative and the world would then seem destined to run down. By 1877, when Boltzmann had made himself a European reputation as the master analyst of probabilistic dynamics, he had an equation linking the entropy of a system with its probability – there it is, engraved on his tombstone in Vienna’s Zentralfriedhof. Many eminent contemporaries sought to kill off this remarkable intrusion of chance into the very basis of physics. Cercignani confessedly finds the hostility strange, since many physical phenomena so quickly fitted with Boltzmann’s principles; yet he also finds it explicable, since, as he puts it, ‘most people, even some mathematicians, think that probability is something non-rigorous, non-scientific and approximate.’ But consider the opposite: the challenges to Boltzmann were unsurprising, since this was the norm in the physics of the time; and the attacks developed not because of a lack of understanding or sympathy for probability theory, but because of a proliferation of different ways of making sense of what was going on in those unobservable collisions.

The challenges to Boltzmann’s programme all emerged directly from the predicaments of the Fin de Siècle, which just like our own impoverished millenarianism combined stunning philosophical pessimism with overweening optimism about the achievements of industry and science. Boltzmann celebrated the technologies of his time – ‘the god by whose grace kings rule is the fundamental law of mechanics.’ As a scientific tourist in California’s biology labs, he foresaw genetic engineering: ‘men will simply become superfluous, a little bottle filled with carefully mixed chemicals will replace them completely,’ and heredity would no longer be a matter of chance. He scolded fashionable forms of romantic metaphysics, offering a proof that Schopenhauer is ‘a stupid ignorant philosophaster scribbling nonsense that rots people’s brains’, and lauding Darwinism as philosophy’s only salvation. (He even gave an evolutionary, and anti-Californian, explanation of the need to drink good alcohol.) Cercignani dimly perceives links between Fin-de-Siècle philosophical preoccupations and those innate in probabilistic physics. Pious Scottish physicists argued that if Boltzmann’s kind of materialism were true, then the world might run in reverse, and ‘living creatures would grow backwards with conscious knowledge of the future but no memory of the past.’ One of Boltzmann’s own colleagues in Vienna set out to undermine the probabilism of the Second Law of Thermodynamics, ‘a principle of destruction for all living creatures in the universe’. If the predicted heat death could be avoided by some cosmic reversal, then an ‘inexhaustible supply of transformable heat’ would be on offer to modern industry.

Boltzmann dismissed these notions of reversibility, reiterating his point that the number of transitions to more disorderly, less profitable states swamped those rare cases where available work was recovered. Notions of eternal recurrence, publicised by Nietzsche in the 1880s, were high on the agenda at the century’s end: they were given a more rigorous proof in the 1890s by mathematicians in Paris and Berlin, who urged that in time any state of a universal system must recur. Cercignani points out that Nietzsche’s reverie about the inevitable circularity of time, and his associated critique of unilinear progress, was not much less rigorous than these mathematical arguments. In any case, Boltzmann abused his critics as so many ‘louts’, conceded that ‘time’ might indeed simply be defined as the direction from less to more probable states, and noted that the time needed for recurrence in any sense understood by his critics was longer than the age of the universe itself.

In the end, however, the most violent attacks on Boltzmann’s world came from the fashionably successful natural philosophers of the century’s end, the so-called energeticists, led by the German chemist Wilhelm Ostwald. They denied the existence of innately massive molecules, atoms or matter, and instead asserted that all of nature was a vast system of energy flows, an image made increasingly familiar by the new light and power systems of 1900, with energy ultimately to be identified with the favoured ghost of idealist philosophy, Spirit itself. Boltzmann found himself an increasingly lonely voice, battling repeatedly against the easy charms of energetics in the name of material atoms and what he saw as traditional physics. It has often been suggested that these last battles led to his suicide. His brilliant achievement in changing the questions of thermodynamics, asking why entropy was now so low – that is, why there is so much order in the universe – rather than asking about its reality, only later became vital elements in the equipment of theoretical physicists. Meanwhile, as Boltzmann put it, Ostwald proceeded ‘through images and general considerations’ with ‘an illusion of rigorous logic’ which seduced the young and bamboozled the public. When, in 1904, Ostwald even provided an energeticist formula for ‘happiness’ (measured, oddly, as the precise difference between the squares of the energy spent successfully and that spent with dislike), Boltzmann went on the attack, damning this ‘relapse into delight in the merely formal, which will always please the masses more than does the method of natural science’.

This theme of mass delusion and élite truth matters, both then and now, and especially when scientists are in dispute with each other. Cercignani prudently sets the fight with the energeticists at some distance from his exposition of Boltzmann’s positive physics. He damns Boltzmann’s enemies as so many ‘pontiffs, ready to excommunicate all those who opposed their axioms’. Certainly, Ostwald’s reputation has suffered somewhat in comparison with that of the great Austrian. But we must place the contest with the energeticists alongside a more current controversy among the pontiffs of thermodynamics and public science, on which Cercignani also has something to say. Two decades ago, the Belgian Nobel laureate Ilya Prigogine published an influential account of chaotic systems and the puzzles of irreversibility: ‘in the classical picture’, he wrote, ‘irreversibility was due to our ignorance.’ And indeed, many expert physicists have read and continue to read Boltzmann in that subjectivist way. The complexity physics of Prigogine and his allies has attracted enormous attention. Prigogine himself insists that Boltzmann’s work needs major correction: ‘the fact that his attempt would end in failure now seems self-evident.’ Then, in 1995, another Belgian physicist, Jean Bricmont, engaged in a fierce exchange with Prigogine in the pages of Belgium’s major physics journal. Cercignani here backs up Bricmont’s polemic: ‘Prigogine with his brilliant style writes sentences that may sound appealing to philosophers and laymen, and unfortunately to some scientists as well, but puzzle well-informed scientists.’ The analogy with Boltzmann’s view of Ostwald is clear. When Bricmont launched himself onto the more public stage, allying himself first with North American critics of all forms of Post-Modernism, relativism and populism, then with the notorious hoaxer Alan Sokal, he did so from the first as a warrior in Boltzmann’s image, fiercely opposed to ‘serious confusions that are found in the literature on irreversibility, chaos or time’. Prigogine was cast as Ostwald in a strange recurrence of the scientific dramas of a century ago. And this is one reason why it is now so important for such writers to revive Boltzmann as a pioneer and hero, who made venomous remarks about philosophers and fashionable publicists, was misunderstood and sometimes persecuted, but ultimately vindicated by the direction in which physics developed.

Cercignani’s book has already received a strongly hostile review from Prigogine himself: The Man who Trusted Atoms, it is alleged, fails to cite up-to-date work which shows the contradiction between reversible molecular dynamics and irreversible macroscopic processes. Equally intriguingly, however, this biography provides us with a chance to reflect on the manners of public debate in and around the sciences. For Snow, Bricmont, Cercignani et al, important and consequential differences in the interpretation of physical theories fought out between specialists are ingeniously transformed into the much simpler problem of popular ignorance and of the so-called ‘intellectual impostors’ who exploit that ignorance. It is as though physics is so organically harmonious that major disputes about foundational principles can be caused only by ill-informed interlopers. Not so: Boltzmann reckoned that ‘available energy is the main object at stake in the struggle for existence and the evolution of the world,’ and that getting energy physics right was thus a matter of supreme public importance. He nowhere denied the entanglement of the life of physics with that of his society.

Cercignani’s book does sterling service in bringing much of Boltzmann’s extraordinary achievement to life, and in sketching the ways in which it was indeed linked with the predicaments of his time. It therefore does his science an astonishing disservice to rebuild the walls around specialist expertise, by damning other experts as pontiffs or charlatans, so that important controversy becomes a sign of intellectual imposture rather than intellectual energy.