This question relates to the paper commented in this 2010 article.
The paper itself is Ruling Out Multi-Order Interference in Quantum Mechanics; it is the discussion of a triple-slit interference experiment testing the validity of Born rule.
The abstract asserts that
Born’s rule predicts that quantum interference, as shown by a double slit diffraction experiment, occurs from pairs of paths.
I do not understand this statement.
The theory behind it originates from Quantum Mechanics as Quantum Measure Theory (Sorkin, 1994) where is is said
Why are probabilities squares of amplitudes; why are they expressed most naturally in terms of pairs of paths rather than individual paths?
Why indeed? If we refer to the path integral description all possible paths are taken into account, including the very weird ones, and there is an infinity of them. What is the point in decomposing the interference pattern of a three-slit diffraction in terms of pairs of paths ?
When the first article says
Born's rule is one of the key laws in quantum mechanics and it proposes that interference occurs in pairs of possibilities. Interferences of higher order are ruled out.
what does it means exactly? Is there something here that gives any real insight about Born rule, or is this way of picturing interferences just the effect of a specific mathematical treatment, while being actually equivalent to the path integral formalism?
More generally, what is the significance of this experiment?