Science as drama
Critical Point: September 2006 – From PhysicsWeb.org
Ludwig Boltzmann, who died 100 years ago this month, played a critical role in the development of thermodynamics. However, he was just one of a colourful cast of characters in a hugely dramatic story, says Robert P Crease.
In his famous 1962 book The Two Cultures, the British physicist and novelist C P Snow recounts meeting people who think they are cultured yet are totally unembarrassed by their lack of scientific knowledge. But to Snow, asking if someone can describe the second law of thermodynamics is like asking if they have ever read a work of Shakespeare. It should be equally shameful for any cultured person to say "no" to either question.
My thoughts on this subject are even more radical. I think that the second law of thermodynamics is actually Shakespearean. Its story involves high drama and powerful characters, and it has fundamental implications for human life. This is no better illustrated than through the story of Ludwig Boltzmann, whose life ended abruptly 100 years ago this month when he committed suicide after suffering from depression (see pp34–37).
Yet the full plot is richer still. Here I offer a tentative summary of how one version of that drama might go.
Prologue: Europe, late 1700s
A new mechanics is on the horizon. The steam engine and other technologies have drawn attention to phenomena relating to heat. This "force" cannot be explained by Newtonian pushes and pulls, and it is only crudely framed by the "caloric" theory that treats heat as an invisible and weightless fluid. Several scientists – whose motives range from curiosity and professional duty to pride and ambition – decide to investigate this force. However, they are soon embroiled in a conflict about conservation and conversion, the resolution of which will be the key to the new mechanics.
Act one: Paris and Munich
Scene 1: Paris, 1803
Lazare Carnot (1753–1823), a military engineer whose particular talent is uncovering and eliminating administrative and mechanical inefficiency, publishes a treatise on water-powered machines. Follow the water, he writes: the maximum power depends on how great a distance it falls. Track down and eradicate sources of waste to make your machine work better.
But Carnot cannot pursue these insights. He is forced back to military duties; then he seduces a woman betrothed to another and ends up in jail. He is released as the French Revolution begins and joins the revolutionaries, who nickname him "Organizer of Victory" for the innovative way he mobilizes, trains and supplies troops.
Scene 2: Munich, 1797–1798
Count Rumford (1753–1814), soldier of fortune and amateur scientist, is in Munich, momentarily between courtships of wealthy widows. Keen to reveal the mysteries of heat, he puts a six-pound brass cannon in a vat of water, inserts a drill bit driven by a winch, hitches up a horse to the winch, and finds that enough heat has been generated through the drilling to boil the water in two-and-a-half hours. He concludes that the caloric theory – formulated by Antoine Lavoisier, a former husband of one of Rumford's mistresses – is wrong, because the heat is obviously a form of motion coming from the friction between the bit and the cannon.
Reporting his findings to the Royal Society, Rumford implicitly likens himself to Newton, saying that the laws of heat are as important as those of gravity. But Rumford is no Newton; his arguments are not entirely convincing and he has no overall theory. Yet his idea that one can quantitatively compare motive forces lays the ground for the looming conflict between conservation and conversion.
Act two: Paris, Manchester and Oxford
Scene 1: Paris, 1823
Sadi Carnot (1796–1832), a quiet engineer, returns from his father Lazare's deathbed. Determined to carry on his father's work, he composes Reflections on the Motive Power of Heat. Follow the heat, he writes. Caloric in a heat engine, like water in a water engine, is conserved as it flows from hot to cold, and the maximum power depends on the magnitude of the temperature drop. The most efficient machine is modelled by an ideal cycle of expansion and compression in which the engine works reversibly, the caloric being conserved in going back and forth between the two temperature endpoints with no heat loss due to friction or dissipation. This is a key insight, but Reflections is almost totally ignored. He publishes nothing more, then catches scarlet fever, brain fever and cholera, before dying, aged 36, in an asylum.
Scene 2: Manchester, 1840s
James Prescott Joule (1818–1889), who as a youth built a home lab in his parents' brewery, obtains highly accurate measurements of various conversions of heat and electrical, mechanical and chemical energy into each other, such as the temperature increase that rotating paddles produce in water by friction. Joule determines the mechanical equivalent of heat: 772 foot-pounds of work lead to a 1 °F rise in 29 cubic inches of water.
Scene 3: Oxford, 1847
The conflict between conservation and conversion comes to a head. Young William Thomson (1824–1907), later known as Lord Kelvin, travels to Paris, where this polymathic, trilingual and far-sighted son of a mathematics professor reads the only published comment on Sadi Carnot's work. He is so impressed that he tries to find a copy of the original but he fails to do so. He then attends a conference in Oxford, where he hears Joule speak. Joule is treated badly by the conference organizers, who instructed him to be brief. But Joule's words jolt Kelvin. How can heat be converted into something else when Carnot's spectacular work relies on the amount of caloric in an engine being constant? Joule's work must have "great flaws" and Kelvin resolves to find them.
Act three: 1840s-1860s
Scene 1: Kelvin gets another jolt
Kelvin reads a paper by German physicist Rudolf Clausius (1822–1888), who has also noticed the Carnot–Joule conflict. Clausius says that it arises because two principles are in play. One involves the conservation of something (not heat, soon called energy) in exchanges of heat and mechanical work. The other involves the conversion of heat into energy, and the property that heat cannot flow spontaneously from colder to warmer bodies. Kelvin, inspired, studies the new heat-mechanics and in 1854 names it "thermodynamics" after the Greek for heat and force.
Some heat in every engine, Kelvin writes, "is irrevocably lost to man, and therefore 'wasted' although not annihilated" – his version of the second of Clausius's two principles. In 1865 Clausius names the tendency of the energy-transfer process to occur spontaneously as "entropy", from the Greek for transformation. In 1867 Kelvin and his collaborator Peter Tait compose their massive Treatise on Natural Philosophy, the Principia of thermodynamics. In 1872 Clausius formulates what become known as the two laws of thermodynamics: "The energy of the world is constant; the entropy of the world strives toward a maximum."
Scene 2: Priority battles erupt
In 1847 German physician Robert Mayer (1814–1878) reads a paper by Joule on the conversion of heat into mechanical energy and says that he discovered it first. Some seven years previously, as a doctor on a Dutch ship in the East Indies, Mayer had realized that the unusual redness of the blood of the crew, meaning that it was oxygen-rich, was due to the fact that the human metabolism is slower in the tropics. This inspired him to write a paper on the interchangeability of mechanical work and heat – but it had been treated as a crackpot letter by the journal that he sent it to. After not receiving a reply, Mayer revised the paper and published it elsewhere.
Depressed when Joule disputes his priority, Mayer flings himself out a third-floor window of his house and is later committed to an asylum in a straitjacket. Meanwhile, another German physicist, Hermann von Helmholtz (1821–1894), also becomes a contender for discovering the first law, thanks to an 1847 paper on "the conservation of force". Tait and Clausius battle over who discovered various principles of thermodynamics, slinging mud at each other in journals and books.
Act four: 1870s
Scene 1: Another battle breaks out, this time over which of the two laws is more important
The first law (conservation of heat/energy) implies that processes are reversible, while the second (heat cannot be completely turned back into work) implies irreversibility, or what is later known as the "arrow of time". The problem comes to a head with Clausius's speciality – the kinetic theory of gases. For a gas is a macroscopic object, governed by irreversible processes and the second law, yet is made of microscopic atoms and molecules that obey reversible Newtonian principles.
James Clerk Maxwell (1831–1879) concludes that the second law is statistical, applying not to individual atoms or molecules but only to massive numbers of them. But it is still not clear why reversibility is not possible – why heat cannot sometimes flow from a cold to a hot body. Maxwell demonstrates this point with a thought experiment involving a tiny creature (or "demon", in Kelvin's mocking term) that opens and shuts a little door to make slightly faster atoms flow from a cold to a hot space.
Scene 2: Graz, 1870s
Ludwig Boltzmann (1844–1906) extends Maxwell's work, proving the second law in a novel way that addresses how entropy increases with time. But Kelvin and others criticize it for not having explained the relation between the second law and the first: if big systems are made of little reversible systems, why are big systems not sometimes reversible?
In 1877 Boltzmann replies that, when a big state corresponds to many equally probable little states, its probability is related to the number of little states. This all but forces big states to evolve in the direction of its more probable states. An explicitly probabilistic interpretation of entropy, it proves the centrality of irreversibility to thermodynamics. Newton's laws plus objects made of myriads of pieces plus the laws of probability equals the arrow of time. On large scales, you play dice, and statistics rule. But Boltzmann became vulnerable to depression late in life, and in 1906, on vacation near Trieste, he hangs himself while his wife and daughter are out swimming.
Act five: 1890s
Scene 1: Berlin, early 1890s
Physicist Wilhelm Wien (1864–1928), an introvert who is repeatedly thwarted in his attempts to become a farmer like his parents, extends Boltzmann's ideas about the second law of thermodynamics and produces a law mapping radiation's dependence on temperature. Wien's law says that the energy emitted increases with temperature, though the increase is not equally distributed across all wavelengths but shifts towards shorter ones.
Scene 2: Berlin, late 1890s
Max Planck (1858–1947), a reluctant revolutionary, tries his hand at reconciling the two laws of thermodynamics, revising Boltzmann's work and reformulating Wien's law – hoping to tie all of the loose ends of thermodynamics, statistical mechanics and electromagnetic theory together. But the neat package comes at a cost. In 1900, to make the law fit experimental data on black-body radiation, he is forced to introduce a new constant, now called Planck's constant.
Neither he nor anyone else realizes that, in completing the foundations of thermodynamics, they have given birth to an entirely new conception of energy and arrived at the threshold of a radically new world.
In 1900 Kelvin warns that there are two clouds shadowing the 19th-century theory of heat and light: one is the difficulty of conceiving the Earth as moving through ether; the other understanding black-body radiation. These two clouds develop into 20th-century hurricanes: relativity and quantum mechanics. But these are dramas for another time.
The critical point
Other versions may differ in detail and scope, and number and size of roles, but this drama, I claim, is Shakespearean. The cast involves powerful human beings who dedicate themselves, body and soul, to their work. The action unfolds as these individuals are troubled – sometimes deeply and tragically – by differences between what they find and their expectations, and try to make greater sense of the world by intervening in it. Has any drama ever had such finely drawn and unique characters, or more profoundly reshaped our understanding of ourselves and the world?
About the author
Robert P Crease is chairman of the Department of Philosophy, State University of New York at Stony Brook and historian at the Brookhaven National Laboratory, e-mail email@example.com