Special relativity, car batteries, and the pursuit of problems

Despite subscribing to the Economist for 25 years, I’ve yet to become a regular reader of the newspaper’s Science and Technology department. Because my job entails keeping up to date with scientific developments, the science covered in the Economist is often already familiar. Other stories—a smaller number—describe long-shot ideas that would overthrow current thinking, provided they’re true.

But the lead story in the current issue was neither familiar nor about long-shot science. In “A Spark of Genius,” the Economist‘s anonymous reporter described a paper entitled “Relativity and the Lead-Acid Battery” that had recently appeared in Physical Review Letters.

I encourage you to read the story, which is a tour de force of science writing. Here’s a brief summary.

The University of Helsinki’s Pekka Pyykkö and his colleagues asked themselves a question that you’d think had been answered before: Why are lead–acid batteries—the type that have been used in cars for more than a century—so effective?

The science behind a lead–acid battery is outwardly simple. Each of the battery’s six cells consists of two electrodes dipped in a solution of 35% sulfuric acid and 65% water. The anode is made of lead(IV) oxide; the cathode is made of lead. Immersion in sulfuric acid causes the Pb cathode to shed electrons, which readily accumulate on the PbO₂ anode, creating the all-important potential difference—about 2 V per cell.

Lead belongs to the periodic table’s carbon family, as does tin, which lies just above it. Given the two elements’ similar chemistry, a tin–acid battery ought to work nearly as well as, or even slightly better than, a lead–acid battery, but it doesn’t.

Pyykkö suspected that special relativity might account for lead’s better battery performance. As one gets deeper into the periodic table, the positive charge on an atom’s nucleus becomes bigger. Consequently, the outermost electrons, the ones that participate in chemistry, feel a stronger force—so strong, in the case of lead, that the electrons whizz around the nucleus at 0.6 the speed of light, c.

According to special relativity, a particle traveling with speed v behaves like a particle that’s more massive by a factor, γ, given by

The effect of relativity on a lead–acid battery’s electrode materials is opposite but not equal. In lead, the increase in effective mass causes the outer electrons to sink closer to the nucleus. In lead oxide, it deepens the empty potentials into which free electrons can fall. Lead becomes a worse cathode, but lead oxide becomes an even better anode. For tin, γ is a nonnegligible 1.07, but for lead, γ is a chemistry-changing, battery-boosting 1.25.

That relativity influences atomic properties wasn’t new to me. The exotic superconductivity of so-called heavy fermion systems arise from partially filled d and f orbitals. Spin–orbit coupling, the interaction between an electron’s spin and orbital angular momentum, underlies the spin Hall effect and other phenomena. The coupling increases with atomic weight.

In hindsight, Pyykkö’s evocation of special relativity doesn’t seem, well, special. What is remarkable, at least to me, is his choice of problem. In high school and university, we learn how to solve problems that already have worked-out answers. Being a scientist entails identifying new problems, which is sometimes harder than solving them.