Our reality can be a sum of all possible realities

The most powerful formula in physics begins with a slender S, the symbol for a kind of sum known as an integral. Further on comes a second S, representing a quantity called action. Together, these twin S's form the essence of an equation that is arguably the most efficient diviner of the future ever devised.

The oracular formula is known as the Feynman path integral. As far as physicists can tell, it accurately predicts the behavior of any quantum system - an electron, a light ray, or even a black hole. The path integral has accumulated so much success that many physicists believe it is a direct window into the heart of reality.

"That's how the world really is," said Renate Loll, a theoretical physicist at Radboud University in the Netherlands.

But the equation, though it graces the pages of thousands of physics publications, is more of a philosophy than a rigorous recipe. This suggests that our reality is a kind of mixture - a sum - of all imaginable possibilities. But that doesn't tell researchers exactly how to do the sum. Physicists have therefore spent decades developing an arsenal of approximation schemes to construct and calculate the integral of different quantum systems.

The approximations work well enough that intrepid physicists like Loll are now pursuing the ultimate path integral: one that blends all imaginable forms 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 as to which possibilities should go into the sum.

Quantum mechanics really took off in 1926 when Erwin Schrödinger devised an equation describing how the wave states of particles change from moment to moment. The following decade, Paul Dirac advanced an alternative view of the quantum world. His was based on the venerable notion that things take the “least action” route to get from A to B – the route that, by and large, takes the least amount of time and energy. Later, Richard Feynman came across Dirac's work and fleshed out the idea, unveiling the full path in 1948.

The heart of the philosophy is on full display in the quintessential demonstration of quantum mechanics: the double-slit experiment.

Physicists shoot particles at a barrier with two slits and observe where the particles land on a wall behind the barrier. If the particles were balls, they would form a cluster behind each slit. Instead, the particles land along the back wall in repeating bands. The experiment suggests that what travels through the slits is actually a wave representing the possible locations of the particle. The two emerging wavefronts interfere with each other, producing a series of peaks where the particle might end up being detected.

The interference pattern is an extremely strange result because it implies that the two possible paths of the particle through the barrier have physical reality.

The path integral assumes that this is how particles behave even when there are no barriers or gaps around them. First, imagine cutting a third slot in the barrier. The interference pattern on the far wall will shift to reflect the new possible route. Now continue cutting slits until the barrier is just slits. Finally, fill the rest of the space with split "barriers". A particle fired into this space takes, in a sense, all routes through all the slits to the back wall - even bizarre routes with looping detours. And somehow, when added together correctly, all of these options add up to what you'd expect if there were no barriers: a single point of light on the wall of the background.

This is a radical view of quantum behavior that many physicists take seriously. "I consider it to be completely real," said Richard MacKenzie, a physicist at the University of Montreal.

But how can an infinite number of curved paths add up to a single straight line? The Feynman scheme, roughly speaking, is to take each path, calculate its action (the time and energy it takes to travel the path), and from that get a number called amplitude, which tells you the probability that a particle travels this path. ...