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

by Brian Greene

I’d love to explain in purely nontechnical terms how this comes about, but I can’t, and I’ve never encountered anyone who can. I made an attempt in The Elegant Universe, but that treatment only describes, in general terms, how the number of dimensions affects aspects of string vibrations, and doesn’t explain where the specific number ten comes from. So, in one slightly technical line, here’s the mathematical skinny. There’s an equation in string theory that has a contribution of the form (D — 10) times (Trouble), where D represents the number of spacetime dimensions and Trouble is a mathematical expression resulting in troublesome physical phenomena, such as the violation of energy conservation mentioned above. As to why the equation takes this precise form, I can’t offer any intuitive, nontechnical explanation. But if you do the calculation, that’s where the math leads. Now, the simple but key observation is that if the number of spacetime dimensions is ten, not the four we expect, the contribution becomes 0 times Trouble. And since 0 times anything is 0, in a universe with ten spacetime dimensions the trouble gets wiped away. That’s how the math plays out. Really. And that’s why string theorists argue for a universe with more than four spacetime dimensions.