Einstein’s Mistakes

The Human Failings of Genius

Hans C. Ohanian

W.W. Norton: 394 pp., $24.95

When Donald Crowhurst’s abandoned sailboat was found adrift in the Atlantic in 1969, his captain’s log recorded the ravings of a man whose mind had snapped. On page after page, he spouted fulminations and pseudoscience, finally ripping his chronometer from its mountings and throwing it and then himself into the drink.

During the voyage, an around-the-globe sailboat race, Crowhurst had been reading Einstein’s book “Relativity: The Special and the General Theory.” A chapter called “On the Idea of Time in Physics” seems to have pushed him over the edge.

Einstein was pondering what it means to say that two lightning bolts strike the ground simultaneously. For this to be true, he suggested, someone positioned halfway between the events would have to observe the flashes occurring at the same instant. That assumes that the two signals are traveling at the same speed -- a condition, Einstein wrote, rather oddly, that “is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own free will in order to arrive at a definition of simultaneity.”

“You can’t do THAT!” Crowhurst, an electrical engineer, protested to his journal. “I thought, ‘the swindler.’ ” From there he descended into madness.

Hans C. Ohanian, who tells this strange tale at the beginning of “Einstein’s Mistakes: The Human Failings of Genius,” sympathizes with poor Crowhurst.

“The speed of light is either constant or not, and only measurement can decide what it is,” Ohanian writes. For Einstein to make a postulation rather than propose it as a hypothesis to be tested may seem like a fine distinction. (Earlier in his book, Einstein does cite an empirical basis for his assumption: the Dutch astronomer Willem de Sitter’s paper, “An Astronomical Proof for the Constancy of the Speed of Light,” which was based on observations of binary stars.) But to Ohanian, the act was as outrageous as when Indiana lawmakers tried to legislate the value for pi. And so he adds it to his roster of Einstein’s mistakes.

Ohanian, the author of physics textbooks and a former associate editor of the American Journal of Physics, sometimes seems to be overreaching in his attempt to humble the great man, but the book’s quixotic approach -- retelling Einstein’s story by homing in on his blunders -- makes for good intellectual entertainment. Having read two books about Einstein just in the last year, I wasn’t sure I could take another. But with his idiosyncratic style and cranky asides (at one point he calls the young Einstein “an incorrigible and tactless loudmouth”), Ohanian kept me eagerly turning the pages.

We have all heard that math wasn’t Einstein’s strong point, and Ohanian ruthlessly lays out the details. A 12-page marathon calculation in Einstein’s doctoral dissertation, “A New Determination of the Molecular Size,” was “a comedy of errors” based on “zany” physical assumptions, such as treating sugar molecules dissolved in water as though they were tiny spheres sitting at rest instead of spinning like tops.

“It is a total mystery why his thesis advisors overlooked this glaring mistake,” Ohanian writes. “They were quite ordinary, dull professors at what was then a dull, second-rate university, but even the dullest of dull physics professors should not have been this blind. Einstein’s dissertation should have been rejected.”

Fumbling ever forward, Einstein went on to commit more errors in the suite of famous papers he wrote in 1905, what came to be called his miracle year. The miracle, as Ohanian tells it, is that Einstein could have been wrong on so many details while coming through, in the end, with some of the greatest insights of the century.

In his paper on the photoelectric effect, for example, he claimed to prove that a phenomenon called blackbody radiation behaves like a gas made of light particles, or photons. Not so fast, Ohanian objects: Though the theory worked for high-frequency photons, Einstein glossed over the fact that it didn’t work for low-frequency ones, “like a tailor who tells the customer how beautifully the jacket fits at the shoulders, and pretends not to notice that the sleeves are much too long, ending somewhere near the knees.”

Most of the errors Ohanian describes will be just as esoteric for many readers, but his exasperated outbursts make the book fun. E=mc2? Don’t get him started. No matter what you have been told, it was not such an important equation, a trifle, really. And not even original. Nevertheless, in deriving the formula, Einstein left a hole in his argument “almost big enough for a truck to drive through.” He proved the case for slow-moving bodies and then extrapolated, without justification, to fast-moving ones.

“The mistake is the sort of thing every amateur mathematician knows to watch out for,” Ohanian scolds. Over the years, Einstein came up with more proofs; they all contained errors.

Einstein buffs have read numerous times about what he called his “biggest mistake” (introducing a fudge factor in general relativity to avoid the seeming absurdity of an expanding universe). Ohanian gives us Einstein’s “zaniest mistake.” In trying to nail down the equivalence between energy and mass, he engaged in a mathematical fraud as egregious as that “perpetrated by some sleazy Italian purveyors of olive oil, who pour a bottleful of genuine olive oil into a barrelful of vegetable oil of unknown provenance and then sell this mix as pure olive oil, extra vergine.”

Sometimes, Einstein’s friend Marcel Grossmann tried to help him with his figures but not always to good effect. When Einstein was trying to get his mind around curved space-time, one of Grossmann’s bungled equations led him astray. Einstein didn’t notice. “In a performance worthy of Elmer Fudd marching off to hunt ‘wabbits’ and failing to notice that Bugs Bunny is sitting on top of his hunting cap, Einstein failed to recognize the mistake.” In going through Einstein’s life, some of what Ohanian marks down as errors seem more like philosophical disputes. Einstein’s quest to find a unified theory and to expunge quantum craziness from physics ultimately failed. But that doesn’t mean it wasn’t a noble attempt.

Ohanian assures us that his crankiness comes not out of schadenfreude, "[b]ut, rather, because these mistakes made Einstein appear so much more human. They brought him down from the Olympian heights of his great discoveries to my own level, where I could imagine talking to him as a colleague, and maybe bluntly say, in the give-and-take of a friendly discussion among colleagues, ‘Albert, now that is really stupid!’ ”

We can imagine Einstein responding favorably. “We all must from time to time make a sacrifice at the altar of stupidity,” he once wrote to his colleague Max Born, “for the entertainment of the deity and mankind.” Most important, Ohanian notes, Einstein’s instincts were dead on. Light is made of photons. Mass is equivalent to energy. Space-time is curved. Nothing can exceed the speed of light. Einstein, Ohanian writes, had “a mystical intuitive approach to physics” that led him to the right answers -- if not always by the right path.