The most powerful formula in physics starts with a slender S, the symbol for a sort of sum known as an integral. Further along comes a second S, representing a quantity known as action. Together, these twin S’s form the essence of an equation that is arguably the most effective diviner of the future yet devised.
The oracular formula is known as the Feynman path integral. As far as physicists can tell, it precisely predicts the behavior of any quantum system—an electron, a light ray, or even a black hole. The path integral has racked up so many successes that many physicists believe it to be a direct window into the heart of reality.
The interference pattern is a supremely strange result because it implies that both of the particle’s possible paths through the barrier have a physical reality.
The path integral assumes this is how particles behave even when there are no barriers or slits around. First, imagine cutting a third slit in the barrier. The interference pattern on the far wall will shift to reflect the new possible route. Now keep cutting slits until the barrier is nothing but slits. Finally, fill in the rest of space with all-slit “barriers.” A particle fired into this space takes, in some sense, all routes through all slits to the far wall—even bizarre routes with looping detours. And somehow, when summed correctly, all those options add up to what you’d expect if there are no barriers: a single bright spot on the far wall.