The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos

by Brian Greene

This line of thought establishes that the suggestion of “extra” spatial dimensions, however unfamiliar, is not absurd. That’s a good start, but it invites an essential question: Why, back in the 1920s, would someone invoke such an exotic idea? Kaluza’s motivation came from an insight he had shortly after Einstein published the general theory of relativity. He found that with a single stroke of the pen—literally—he could modify Einstein’s equations to make them apply to a universe with one additional dimension of space. And when he analyzed those modified equations, the results were so thrilling that, as his son has recounted, Kaluza discarded his normally reserved demeanor, pounded his desk with both hands, shot to his feet, and erupted into an aria from The Marriage of Figaro.10 Within the modified equations, Kaluza found the ones Einstein had already used successfully to describe gravity in the familiar three dimensions of space and one of time. But because his new formulation included an additional dimension of space, Kaluza found an additional equation. Lo and behold, when Kaluza derived this equation he recognized it as the very one Maxwell had discovered half a century earlier to describe the electromagnetic field.