Explaining Energy

The search for more energy to meet humankind’s seemingly inexhaustible needs is perennial. The disastrous Fukushima Daiichi nuclear power plant meltdown in Japan earlier this year has resulted in the current controversy regarding the use of nuclear power to help meet this need. Thus, Jennifer Coopersmith’s book “Energy, The Subtle Concept: The Discovery of Feynman’s Blocks from Leibniz to Einstein” is particularly timely.

Physics and chemistry are the sciences dealing with the physical and chemical changes that affect matter. Unlike matter, which we all understand as anything that possesses mass and occupies volume, energy (from a Greek word meaning “at work”) is a “subtle concept,” Coopersmith says. She points out that energy can appear in various guises—potential, kinetic, chemical, electrical, nuclear, heat, light, rest mass, and so on. But what is it actually?

To try to answer that question, Coopersmith cites 1965 physics Nobel Laureate and universally acknowledged genius Richard Feynman’s imaginary allegory of a child, “Dennis the Menace,” playing with blocks. Feynman used this allegory in “The Feynman Lectures on Physics” to illustrate how difficult the concept of energy actually is. As Coopersmith writes, “If Feynman says the concept of energy is difficult then you know it really is difficult.”

In the Feynman allegory, Dennis’ mother discovers a law: After every play session the total number of blocks is always the same. In order to evaluate what this constant number of blocks is, the mother determines and examines the various mathematical expressions—for example, the depth of water in the bathtub displaced by one block, the weight of a locked treasure chest divided by the weight of a block—and so on. These expressions must be determined for each circumstance; they are complex and unrelated to each other.

The constant number of blocks is derived from a sum of unrelated mathematical formulas, and the constant total energy is derived from a sum of unrelated mathematical formulas. However, there is a crucial difference between these play blocks and energy. Although the first law of thermodynamics states that energy can neither be created nor destroyed but can be transformed from one form to another, it lacks the type of reality that we would associate with a building block. Feynman explains, “What is the analogy of this to the conservation of energy? The most remarkable aspect that must be abstracted from this picture is that there are no blocks.”

In other words, according to Coopersmith, when it comes to energy, all we have when examining it are mathematical expressions; there is no substance or essence of energy. Therefore, she writes, we must examine actual formulas such as ½ mv² for kinetic energy, I²R for the heat energy in an electrical circuit, ∫ F·dr for the work done by a force, Albert Einstein’s E = mc², and so on. These formulas are among the “blocks” referred to in her book’s title. And they are also among the 14 blocks on its cover, each bearing a mathematical formula related to energy that she thinks might have been used in Feynman’s allegory.

Coopersmith asks, “Something is conserved—but what? There are two other lessons to be learned from Feynman’s allegory: A system must be defined and kept isolated, and quantification and mathematization are essential. We shall attempt to understand the nature of these non-existent ‘blocks’ of energy through the history of their discovery.” Her quest to find the origin and discoverer of each formula for energy provides the narrative thread of her book.

She begins her chronology with Aristotle and continues through to today. However, the first recognizable formula for energy was proposed by German philosopher Gottfried Wilhelm Leibniz, mv² (now modified to ½ mv²), for kinetic energy, which he called vis viva, or living force, in 1656. The last formula that she discusses in detail is Albert Einstein’s celebrated E = mc². This is the reason for the subtitle of her book.

Coopersmith’s knack for explaining scientific concepts in simple, colloquial terms is manifest and so is her ability to relate to both lay readers and scientists. Her tone is casual and informal: “Simply imagine that we’re in conversation during a very long train journey or over endless cups of coffee in the common room,” she writes in the book’s introduction.

This approach to science writing, Coopersmith says, is “hugely entertaining. In fact, the history of scientific ideas—of knowledge—is the ultimate ‘human interest’ story; and it is a ceaseless wonder that our universal, objective science comes out of human—sometimes all too human—enquiry,” she writes.

Anthropocentric concepts such as work, machine, engine, and efficiency that figure prominently in her story show the practical origins of the development and evolution of the concept of energy.

There was no formula for potential energy until 1785, when French mathematician Pierre-Simon Laplace proposed an expression for gravitational potential energy, Coopersmith tells us. In 1829, French mathematician, engineer, and scientist Gaspard-Gustave Coriolis declared that “work” = ∫ F·dr, but engineers such as Guillaume Amontons, Antoine Parent, and James Watt had been using “force times distance” since the beginning of the 18th century. By the end of that century, she writes, mathematicians like Joseph-Louis Lagrange understood that summing the total potential and kinetic energy yielded the “mechanical energy” and that this mechanical energy was conserved.

Meanwhile, ideas about heat were being developed, Coopersmith continues. Robert Boyle, Isaac Newton, Robert Hooke, Daniel Bernoulli, Henry Cavendish, and others proposed that heat was kinetic in origin, whereas Hermann Boerhaave, Joseph Black, Antoine-Laurent Lavoisier, Laplace, and others thought of it as a “subtle” substance in itself. The formula for heat, the author explains, could not be determined absolutely, and it first needed to be distinguished from temperature.

Black, a chemist, quantified heat and realized that for one material and one phase, the heat change was proportional to the temperature change, whereas for a change in phase, the heat change was proportional to the mass (of ice, water, or steam) that changed phase. Coopersmith emphasizes the astounding fact that, while Black and other heat researchers were working away at their definitions, and even while James Watt’s steam engine was powering the Industrial Revolution, it was still not realized what energy is or, indeed, that heat is a form of energy.

Chemist Humphry Davy in the late-18th, early-19th centuries was among those like Count Rumford and Thomas Young who began to realize that the caloric theory of heat was untenable and to guess at links between heat, light, electricity, and chemical reactions. However, uniting all of these as “energy” and merging them with mechanical energy was a difficult step. According to Coopersmith: “That there could be a quantitative link was hard to contemplate. It was like a category error—like comparing, say, p.s.i. (pounds per square inch) and psa (pleasant Sunday afternoon).”

Chapter 12, one of the most enlightening chapters in the book, describes the extraordinary discoveries of Sadi Carnot, a young French engineer, who in 1824 examined the limiting efficiency of “heat engines” such as Watt’s steam engine, which led to the second law of thermodynamics.

In Chapter 14, Coopersmith shows how, in the mid-19th century, the final step of accepting the mechanical equivalent of heat was taken—first by Julius Robert Mayer in Germany and soon afterward by James Prescott Joule in England. They realized that heat was not conserved per se but could be converted into mechanical energy—and vice versa. Of special relevance to chemists, Coopersmith shows how Carl Friedrich Scheele discovered radiant heat and how the pioneering work of John Dalton, Joseph Louis Gay-Lussac, Pierre Louis Dulong, Alexis Thérèse Petit, and others led not only to the atomic theory but also to the theory of energy.

Since Coopersmith explains energy by using the history of its emergence, her book is primarily an explanation of physics. She breaks up her chronology by frequent asides and explanations in modern terms. Interestingly enough, the amount of biographical detail that she provides is almost inversely proportional to the fame of the given scientist, and many important scientists are omitted entirely. Thus, we learn many interesting facts about a host of less well-known figures. For example, Daniel Gabriel Fahrenheit of temperature scale fame once stole some money, and a warrant was issued for his arrest; Daniel Bernoulli believed that he had been robbed of the fruits of a decade of his work by his father, Johann; and Gay-Lussac ascended higher in a balloon than anyone ever before, a record that was not matched for another half-century.

Coopersmith categorizes many of the characters—and I use the term advisedly—who play parts in her tale as, among others, “persecuted genius” (Galileo), “one who made a loaf of bread last a week” (Faraday), “foundling” (d’Alembert), “pharmacists” (Scheele and Mayer), “spy, ladies’ man, and gregarious American” (Count Rumford), and “brewer” (Joule). Almost all the participants in her narrative are male, but she lists “two wives” (Mme. Lavoisier, later married to Rumford, and Mrs. Maxwell) and “a mistress” (Marquise du Châtelet).

Coopersmith’s gripping historical account, which consistently uses British spelling, is extremely well organized and well written. It includes frequent cross-references to related material in other parts of the book. Peppered with anecdotes and insightful opinions, it considers not only large and small advances but also twists, turns, and dead ends. It is meticulously documented but, as expected for a semipopular book, the Notes and References are relegated to a separate section near the end of the book. Although comprehensive, it nevertheless has some omissions: For example, magnetic energy and Gibbs free energy receive scant attention. I hope that these topics can be included in future editions.

I am pleased to heartily recommend Coopersmith’s readable, enjoyable, and largely nonmathematical yet profound account of the development of an important physical concept—energy. With a vein of humor running throughout, it deals with an enormous compass of important topics seldom found elsewhere at this level. It should be of great interest and utility to students, both undergraduate and graduate, historians of science, and anyone interested in the concepts of energy and their evolution through time.