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Whirling waves in interference experiments

Rahul Sawant, Joseph Samuel, Aninda Sinha, Supurna Sinha, Urbasi Sinha

Published Aug 9, 2013• 1 citation
OpenAlex

Abstract

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption, the wave function hypothesis, which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in interference experiments which provide a measurable deviation from the wave function hypothesis. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

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In a double slit interference experiment, the wave function at the screen with both slits open is not exactly the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption, the wave function hypothesis, which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in interference experiments which provide a measurable deviation from the wave function hypothesis. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
The Feynman path integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub-leading terms in the path integral which can be described by what are popularly called non-classical paths. In this work, we report an experiment where we have a controllable parameter that can be varied in its contribution such that the effect due to these non-classical paths, which we will refer to as sub-leading paths, can be increased or diminished at will. Thus, the reality of these sub-leading paths is brought forth in a classical experiment using microwaves, thereby proving that the boundary condition effect being investigated transcends the classical-quantum divide and that the Feynman path integral formalism is an overarching framework. We report the first measurement of a deviation (as big as 6%) from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. We also show that our results can have potential applications in astronomy.
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by what are popularly called non-classical paths. In this work, we report an experiment where we have a controllable parameter that can be varied in its contribution such that the effect due to these non-classical paths can be increased or diminished at will. Thus, the reality of these non-classical paths is brought forth in a classical experiment using microwaves, thereby proving that the boundary condition effect being investigated transcends the classical-quantum divide. We report the first measurement of a deviation (as big as 6%6\%6%) from the superposition principle in the microwave domain using antennas as sources and detectors of the electromagnetic waves. We also show that our results can have potential applications in astronomy.
Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ψAB=ψA+ψB{ψ_{AB}} = {ψ_A} + {ψ_B}ψAB​=ψA​+ψB​ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-slit interferometer. The result shows that the non-classical paths effect will cause a relative deviation of 10−310^{-3}10−3 in electron's Bohmian velocity, which is observable by doing weak measurement similar to previous work.
Probability and interference According to Feynman, single-particle interference is ‘the only mystery’ of quantum theory (Feynman, Leighton and Sands 1965, ch. 1, p. 1). Feynman considered an experiment in which particles are fired, one at a time, towards a screen with two holes labelled 1 and 2. With both holes open, the distribution P 12 of particles at the backstop displays an oscillatory pattern of bright and dark fringes. If P 1 is the distribution with only hole 1 open, and P 2 is the distribution with only hole 2 open, then experimentally it is found that P 12 ≠ P 1 + P 2 . According to the argument given by Feynman (as well as by many other authors), this result is inexplicable by ‘classical’ reasoning. By his presentation of the two-slit experiment (as well as by his development of the path-integral formulation of quantum theory), Feynman popularised the idea that the usual probability calculus breaks down in the presence of quantum interference, where it is probability amplitudes (and not probabilities themselves) that are to be added. As pointed out by Koopman (1955), and by Ballentine (1986), this argument is mistaken: the probability distributions at the backstop – P 12 , P 1 and P 2 – are conditional probabilities with three distinct conditions (both slits open, one or other slit closed), and probability calculus does not imply any relationship between these. Feynman's argument notwithstanding, standard probability calculus is perfectly consistent with the two-slit experiment.
Young’s double slit experiments revived the wave theory of light. The standard interpretation is that the light behaves as waves before and after passing through the double slit. Feynman called the double slit experiment the only mystery in quantum mechanics. By placing a convex lens at different positions, we have shown: (1) Near the diaphragm, light behaves as photons and produces a non-interference pattern; near the screen, the photons produce an interference pattern; (2) The non-interference pattern evolves to the orthogonal interference pattern gradually in the same experiment; (3) The convex lens stops the further evolution. It is heuristic for study the nature of light by showing all of three different kinds of patterns on the screen simultaneously. For this purpose, in this article, we setup three paths. The light is divided into three portions, each portion propagates along one path. Then inserting three lenses to different Zones of different paths. Experiments show that two non-interference patterns and interference pattern simultaneously emerge on the same screen. The experiments: (1) challenge the wave theories of light; (2) violate Bohr’s complementarity principle; (3) provide profound phenomena for further development of optics and for study of the nature of light; (4) suggest that a complete theory should be able to simultaneously interpret the non-interference pattern, the interference pattern, and the evolution from the non-interference to the interference pattern in the same experiment.