Ruling Out Multi-Order Interference in Quantum Mechanics

Quantum Mechanics Born to Be Linear Two pillars of modern physics, quantum mechanics and gravity, have so far resisted attempts to be reconciled into one grand theory. This has prompted suggestions that theories about either or both need to be modified at a fundamental level. Sinha et al. (p. 418; see the Perspective by Franson) looked at the interference pattern resulting from a number of slits, to test the “Born rule” of quantum mechanics. They verified that Born holds true—that the interference pattern is built up by the interference from two paths, and two paths only, with no higher-order paths interfering. The result rules out any nonlinear theories of quantum mechanics; thus, any modification of theory will need to take into account that quantum mechanics is linear. A multiple-slit diffraction experiment shows that interference arises from pairs of paths. Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification. For example, Born’s rule—one of the axioms of quantum mechanics—could be violated. Born’s rule predicts that quantum interference, as shown by a double-slit diffraction experiment, occurs from pairs of paths. A generalized version of quantum mechanics might allow multipath (i.e., higher-order) interference, thus leading to a deviation from the theory. We performed a three-slit experiment with photons and bounded the magnitude of three-path interference to less than 10−2 of the expected two-path interference, thus ruling out third- and higher-order interference and providing a bound on the accuracy of Born’s rule. Our experiment is consistent with the postulate both in semiclassical and quantum regimes.

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