Physicist Richard Feynman (left) once said of the fine structure constant that “all good theoretical physicists put this number up on their wall and worry about it ... it’s one of the greatest damn mysteries of physics: a magic number ... You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed his pencil.’”
Historically, that didn’t stop people from trying to decipher it. English astronomer Arthur Eddington, who provided the first experimental proof of relativity during a solar eclipse, grew fascinated with alpha. Eddington had a penchant, and it must be said a talent, for numerology, and in the early 1900s, after the fine structure was measured to be around 1/136, Eddington began concocting “proofs” that alpha equaled exactly 1/136, partly because he found a mathematical link between numbers like ten, 136, and 666. (One colleague derisively suggested rewriting the Book of Revelation to take these “findings” into account.) Later measurements showed that alpha was closer to 1/137, but Eddington just tossed a one into his formula somewhere and continued on as if his sandcastle hadn’t crumbled—earning him the nickname of Sir Arthur “Adding-One” (Today, alpha equals 1/137.0359 ...)
About the same time as Eddington, the great physicist Paul Dirac, an obsessively shy man who helped formulate quantum mechanics, popularized the idea of inconstants. Dirac was looking at protons and electrons when he noticed some startling coincidences. On the atomic level, the electrical attraction between the proton and electron dwarfs the attraction of gravity between them. In fact, the ratio is about 10^40, an unfathomable ten-thousand trillion trillion trillion times larger. Dirac also happened to be looking at how quickly electrons zoom across atoms, and he compared that fraction of a nanosecond with the time it takes beams of light to zoom across the entire universe. Lo and behold, the ratio was 10^40.
Perhaps predictably, the more Dirac sought for it, the more that ratio popped up: the size of the universe compared to an electron’s size; the mass of the universe compared to a proton’s mass; etc. (Eddington had also once testified that there were approximately 10^40 times 10^40 protons and electrons in the universe—another manifestation.) Overall, Dirac and others became convinced that some unknown law of physics forced those ratios to be the same. The only problem was that that some ratios were based on changing numbers, like the size of the expanding universe. To keep his ratios equal, Dirac hit upon a radical idea—that gravity grew weaker with time. The only plausible way this could happen was if the fundamental gravitational constant, G, had shrunk. As a bonus, an attenuated G also explained why the universe was expanding, since less gravity bound it together.
Dirac’s ideas fell apart pretty quickly. Among other flaws that scientists pointed out, the brightness of stars depends heavily on G, and if G had been much higher in the past, the earth would have no oceans, since the overbright sun would have boiled them away. But Dirac’s inspiring search for inconstants thrived. At the height of this research, one scientist even suggested that all fundamental constants were constantly diminishing—which meant the universe wasn’t getting bigger, as commonly thought, but that Earth and human beings were shrinking! Overall, the history of varying constants resembles the history of alchemy: Even when there’s real science going on, it’s hard to sift it from the mysticism. Especially since scientists in different eras tended to summon up inconstants to explain away cosmological mysteries, like the accelerating universe.
Sam Kean is associate editor of Search.
