If a metal poker has been left standing for a long time with one end in the fire, never grab the other end. Obvious, right? Heat flows from hot to cold: that’s the second law of thermodynamics (a word that literally means “movement of heat”), to which there are no known exceptions. But what is it, exactly, that flows from the heated end of the metal bar to make the rest of it searing to the touch? What is it that we feel emanating from the stove, beating down from the noonday sun, or that warms our hands around a mug of chocolate on a winter’s night?

The question is at least as old as civilization. Yet less than two centuries have passed since we finally understood the true nature of heat. Not until we began to truly comprehend the nature of matter itself could we have ever hoped to resolve this—forgive me—burning question.

The mere fact that we speak of heat flowing is a relic of the longstanding view that it must be some kind of fluid substance—that the heat at the red-hot end of a poker must seep along the metal bar like moisture spreading through the fibres of a wet cloth. To the ancient Greeks, heat and cold were identified with the four fundamental elements classified by Empedocles and endorsed by Aristotle in the fourth century BCE. But this was a subtle matter. Each of the four classical elements—fire, air, earth and water—possessed two out of four fundamental qualities: fire was hot and dry, air hot and moist. Fire was thus a substance that could confer hotness.

There was also, Aristotle said, a vital heat produced by the body: generated by the heart, it was connected to the soul itself. He thought that heat was responsible for the digestion of food. His mentor Plato had proposed his own theory for this phenomenon, arguing that the four elements were composed of atom-like particles with geometric shapes. The pointy, sharp-edged tetrahedra of fire could cut up food matter to release its nourishment. It was because of the sharp, prickly edges of fire particles that a burn is so painful.

Of course, we now know they were wrong. What remains impressive, however, is how Plato and Aristotle sought to rationalize our experience of the world in terms of general principles, even if these operated beyond our perception (no one could hope to see these fire particles). But the long road from Plato’s tetrahedral atoms and Aristotle’s vitalism to our modern view of heat as motion, not matter, is more than a linear correction of old ideas. In getting to the heart of heat, we’ve found ourselves facing questions of cosmic significance—about the fate of the universe, the origin of time, and the riddle of life itself.

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The Aristotelian scheme of elements remained predominant in the Christian and Islamic worlds until the waning of the Middle Ages, by which time natural philosophers had begun to suspect that things were more complicated. One popular alternative way to think about the constitution of matter was proposed by the Swiss alchemist Paracelsus, who said in the early sixteenth century that all substances were made of three “principles”: sulfur, mercury, and salt. These weren’t quite as arbitrary as they might sound, for the eighth-century Islamic alchemist Jabir ibn Hayyan had asserted that sulfur and mercury were the ingredients of all metals. By adding salt, Paracelsus claimed to include all other materials too, including our own bodies. Besides, in inflammable sulfur we can recognize a kind of substitute for Aristotelian fire; fluid mercury was analogous to water and salt akin to earth.

The German chemist Johann Becher, an advocate of Paracelsus’s ideas, replaced this trio of principles with three kinds of “earth”: terra lapida (stony earth), terra mercurialis (mercurial earth), and terra pinguis (oily or fatty earth). Fire and hotness still feature in these elemental schemes: the last of these ‘earths’ was thought to be abundant in things that burn. In the early eighteenth century another German chemist, Georg Ernst Stahl, renamed terra pinguis “phlogiston” from the Greek word “to burn”.

Was heat, then, the same as this “fire-element” flowing from hot objects, or was it simply a property of phlogiston? Natural philosophers at that time were hazy about such distinctions. The fact was: where there was heat, there was phlogiston.

Phlogiston has a bad reputation for misleading chemists for the better part of a century. But while it doesn't feature in today's roster of chemical elements, its theory offered a valuable framework for thinking with. It helped to make sense of various observations about burning: why, say, many substances like wood lose mass as they burn (their phlogiston escapes to the air), and why a candle burning inside a sealed glass jar will eventually go out (the air has become saturated with phlogiston and will absorb no more). But in the end there were just too many problems with the idea. If, for instance, phlogiston is lost from a material when it burns, why do “burned” metals—those heated in air—gain mass?

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In 1783, the French chemist Antoine Lavoisier wrote a paper which offered an alternative idea: when things burn, they don’t release phlogiston but instead combine with a gaseous element in the air, which Lavoisier called oxygène. Covered candles stop burning when they have used up all available oxygène.

Lavoisier was right about oxygen, of course, and French chemists quickly adopted his new system of chemistry. (Those in other countries dragged their heels.) In the void of phlogiston, Lavoisier offered a new theory: there was a “subtle fluid, the accumulation of which is the cause of heat and the absence of which is the cause of coldness.” Like Aristotelian fire, this fluid could flow through the gaps between the “corpuscles of matter”, and it moved from hot bodies to cold ones. Lavoisier called this stuff “igneous fluid, the matter of heat and fire.”

Four years later, Lavoisier and his colleague Louis-Bernard Guyton de Morveau introduced a different and rather more original name for this fluid: calorique, or caloric in English, from the Latin calor, meaning heat or warmth. In his influential 1789 textbook Traité Élémentaire de Chimie, Lavoisier listed no fewer than 33 substances he considered to be elements, including oxygen and caloric. He also showed how one could measure the flow of caloric using a device he called a calorimeter.

Was cold then just a paucity of caloric? In 1790 the French experimental scientist Marc-Auguste Pictet claimed that he could collect and focus cold using mirrors, just as one could focus light. In this way, a cold object could be used to cool another one nearby. Pictet’s experiments suggested, at least to the American scientist Benjamin Thomson—who was later ennobled as an officer in the Bavarian army, and became known as Count Rumford—that cold was produced by a kind of wave-like radiation. Rumford called this radiation frigorific rays. He also embraced the idea, common among his contemporaries, that all of space was filled with an imperceptible fluid called the ether, which he believed could carry coldness just as water carries ocean waves.

But wait a minute! If cold was a wave—a vibration of the ether—then maybe heat was too? Rumford started to promote the idea that heat is indeed merely a vibration, which could be carried not only by ether but by the “corpuscles”—the atoms, we’d now say—of matter. That idea faced stiff opposition from the caloric theory of the mighty Lavoisier. But in a paper presented in 1798 to the Royal Society in London, Rumford described strong evidence in his favor—which he’d happened upon while superintending the boring of cannons for the Bavarian army.

When the hollow central channel was bored into brass cannons, Rumford noticed, the metal became intensely hot through friction. Military engineers had likely observed something similar for several centuries—but if the heat were caused by a flow of caloric from the metal of the cylinder, then repeated boring ought gradually to exhaust its supply, with the amount of heat produced decreasing over time. Yet it didn’t. No matter how many times the same cylinder was bored, a seemingly boundless amount of heat was generated. So much, in fact, that when iron was bored inside a box filled with water, the water could be raised to a boil. “It would be difficult to describe the surprise and astonishment expressed in the countenances of the by-standers,” Rumford wrote in his paper, “on seeing so large a quantity of cold water heated, and actually made to boil, without any fire.”

Thus did Rumford conclude that heat “cannot possibly be a material substance.” Instead, it must be produced by motion. But motion of what? “I shall not presume to trouble the Society with mere conjectures”, Rumford airily wrote.

More than 40 years later, an English engineer named James Joule had an idea about the matter. Joule was a student of the chemist John Dalton, who in 1808 had proposed that all substances are composed of atoms. What if heat, Joule proposed, was the motion of these atoms?

Joule was little known at that time, and his idea was dismissed at first by some of the giants of British science, such as Michael Faraday and William Thomson (later Lord Kelvin, after whom the scientific temperature scale is named). But in the late 1840s, Joule conducted experiments that changed many minds.

He made a cylindrical copper container, filled with water, that held a kind of paddle wheel, which could be turned by strings attached to an axle. Joule attached weights to the string, which passed over pulleys, and by cranking the axle he could lift the weight and set the paddle wheel spinning inside the chamber. As the wheel turned, the agitated water warmed up little by little. From the raising of the weight, Joule could calculate how much work was done in turning the crank-handle—and after taking account of all the sources of heat loss, he showed that the amount of work done in lifting was equal to the amount of heat generated in the chamber. “Wherever mechanical force is expended”, Joule wrote in 1850, “an exact equivalent of heat is always obtained.”

The German physicist Rudolf Clausius expressed this principle in a different way. “By the expenditure of an equal quantity of work an equal quantity of heat is produced”, he wrote. In terms of Joule’s experiment, this meant the amount of energy expended to turn the paddlewheel was equal to the amount of heat energy added to the water (plus the heat that leaks away into the surroundings). No energy simply vanishes: all can be accounted for. Or in the formulation intoned by school pupils today: energy can be neither created nor destroyed. And that is the first law of thermodynamics, the science of heat flow that Clausius (who also articulated the second law that we saw earlier) helped to launch.

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Joule’s work killed off caloric theory. Or almost did. Today scientists measure energy (such as heat energy) in units of joules, but the older units of calories still persist.

So there it was, as Kelvin and others soon accepted: heat is motion. Specifically, it is the motion of atoms. As bodies rub against one another, their atoms are set jiggling, and the bodies get warmer. The sun’s rays falling on a surface are absorbed by the material’s lattice of atoms, which are made to vibrate more vigorously. Chemical energy released by metabolic reactions in our bodies jangle our molecules and keep our bodies warmer than their surroundings typically are.

It's no coincidence that the science of thermodynamics arose at the peak of the Industrial Revolution. For it was then that efficiency became the watchword: how could the steam engines, the mills and blast furnaces, be operated most efficiently, which is to say, so that the maximum amount of work could be obtained from a given amount of fuel? This was all about reducing the losses of energy as useless heat, like that which radiated away into the surroundings by the hot chamber of a steam engine. The second law revealed that it was impossible to operate any machine with 100 percent efficiency: some energy was always squandered as heat. That was a sad fact of life for the factory manager—but for the physicist it meant something remarkable, even alarming. Eventually, all pockets of energy in the universe would be dissipated as heat, leaking into the environment and equilibrating until everything reached the same temperature. At that point, it would be impossible to extract any more work, because there wouldn’t be an impetus for heat to flow from hot to cold. Then there could be no further change: the entire universe would be a barren, uniform buzz of vibrating atoms. Kelvin christened that gloomy future the Heat Death of the universe. Devout Christians were dismayed: what kind of eternal life was that? Did thermodynamics undermine their faith? There was a lot more at stake in understanding heat than merely keeping a factory’s fuel bills down.

By the same token, the universe is only the vibrant, lively place it is today because it began so far away from that sterile final state of thermal equilibrium. Since the beginning of all time and space, all change has followed a preferred direction: the one dictated by the second law, whereby heat flows from hot to cold and thereby gets inexorably more equal everywhere. The second law thus seems to impose a definite direction on time itself.

There are still revelations to be made in the science of heat. The second law can now be connected to the theory of information and computation: in short, information itself can be used as a source of work, as if it is itself a kind of fuel. In 2010, researchers in Japan showed that they could convert information to energy. By nudging a microscopic particle with an electric field, they were able to increase its energy simply by gathering information about its position. The particle gained more energy than was supplied by the field alone, meaning that the excess was coming from the information itself.

By the same token, information can only be erased at the cost of dissipating some heat—which is why any computational process that lets go of some information, as both our laptops and our brains do when we delete data or forget, will inevitably release some heat into the surroundings. And because quantum physics permits information to be manipulated in ways that classical physics does not, quantum mechanics can modify the second law itself. The phenomenon called quantum entanglement allows information to be shared between quantum particles in a way that seems almost magical, so that one of an entangled pair of particles appears instantaneously to “know” what happens to the other. In some cases, this “mutual information” shared by entangled particles can even be used to compensate for a flow of heat between them, so that it can pass from cold to hot—apparently (but only apparently!) defying the second law.

What is and is not possible in managing flows of heat thus tells us something very deep about the laws of physics as a kind of computation. We’d be wise to anticipate that heat, whether experienced in the hearth’s humble poker or as a force changing our fast-warming planet, still has surprises in store for us. ♦