Richard Feynman’s path integral is a powerful prediction machine and a philosophy. Physicists still struggle to figure out how to use it, and what it means.
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.
“It’s how the world really is,” said Renate Loll, a theoretical physicist at Radboud University in the Netherlands.
But the equation, although it graces the pages of thousands of physics publications, is more of a philosophy than a rigorous recipe. It suggests that our reality is a sort of blending—a sum—of all imaginable possibilities. But it does not tell researchers exactly how to carry out the sum. So physicists have spent decades developing an arsenal of approximation schemes for constructing and computing the integral for different quantum systems. The approximations work well enough that intrepid physicists like Loll are now pursuing the ultimate path integral: one that blends all conceivable shapes of space and time and produces a universe shaped like ours as the net result. But in this quest to show that reality is indeed the sum of all possible realities, they face deep confusion about which possibilities should enter the sum.
Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
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