Superposition revisited: Proposed resolution of double-slit experiment paradox using Feynman path integral formalism

The Schrödinger's Cat thought experiment, published in 1926 by Erwin Schrödinger, may be the most widely-known metaphorical explanation of quantum superposition and collapse. (Superposition is a fundamental principle of quantum mechanics stating that a physical system – such as a photon or electron – simultaneously exists partly in all theoretically possible states; but when measured or observed gives a result corresponding to only one of the possible states.)

That being said, the earlier foundational double-slit experiment has the advantage of being, well, an actual experiment that provides a window into this often counterintuitive realm. (As a somewhat surprising aside, while the Michelson–Morley experiment, published in 1887 by Albert A. Michelson and Edward W. Morley, demonstrated temporal coherence, a much earlier device – Thomas Young's 1803 double-slit interferometer – demonstrated spatial coherence, contradicting Newtonian physics a century before quantum mechanics and special relativity by showing that light, like sound, was also a wave motion.) Despite its long legacy, however, the double-slit experiment remains the subject of research. One such focus is a curious discrepancy: The Schrödinger (yes, the same Schrödinger) equation, or wavefunction– which describes how the quantum state of a physical system changes with time – when both slits are open differs slightly from the sum of the wavefunctions with the two slits alternately open. The problem is that the three alternatives (slits A and B, slit A, slit B) correspond to separate boundary conditions – equations that specify the behavior of the solution to a system of differential equations at the boundary of that system's domain – meaning that superposition does not apply.

Recently, however, scientists at the Raman Research Institute and the Indian Institute of Science, both in Bangalore, India, theoretically resolved this paradox by quantifying nonclassical path contributions in quantum interference experiments using the Feynman path integral formalism, which involves an integration over all possible paths that can be taken by the particle through the two slits, thereby calculating a quantum amplitude by replacing the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinite number of possible trajectories. This allows them to replace the approximate wavefunction with both slits open (ψAB = ψA + ψB) with an integral that includes both the classical paths – the nearly straight paths from the source to the detector through either slit – and the nonclassical, or looped, paths that make a small but finite contribution to the total intensity at the detector screen (ψAB = ψA + ψB + ψL).