Quantum Fluctuations and the N -Slit Interference
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Quantum Fluctuations and the N -Slit Interference Jaime Madrid1 · Jaume Gine´ 2
· Daniel Chemisana1
Received: 8 May 2020 / Accepted: 22 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The generalization of the double-slit experiment to an arbitrary number of slits is worthwhile to validate the fundamentally probabilistic nature of quantum mechanics and presents an increasing number of applications. In this work we present an explanation of this experiment from the vacuum fluctuations near the slits with two different approaches: the Heisenberg uncertainty principle and the Kubo-Martin-Schwinger relation characterizing thermalized states. Both descriptions reach analogous results when applied to the sea of virtual particles near the slits. Keywords N -slit interference · Vacuum fluctuations · Uncertainty principle · Quantum fields
1 Introduction Diffraction grating experiments are key to analyze fundamental characteristics of quantum mechanics as Heisenberg uncertainty. The well known double-slit experiment with electrons represents one of the main pillars of quantum physics, surrounded by different interpretations but demonstrating the interference behaviour of those electrons [6]. Recently, Sinha et al. [16] investigated the validity of Born’s rule - interference appearing from pairs of wave functions - in a three-slit experiment with photons. Results indicate that third and higher order interference can be dismissed, limiting the magnitude of the three-path interference to
Jaume Gin´e
[email protected] Jaime Madrid [email protected] Daniel Chemisana [email protected] 1
Applied Physics Section of Environmental Science Department, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Spain
2
Departament de Matem`atica, Universitat de Lleida, Av. Jaume II, 69, 25001 Lleida, Catalonia, Spain
International Journal of Theoretical Physics
less than 10-2 of the expected two-path one. Therefore, Born’s postulate is empirically verified. Nevertheless, De Raedt et al. [1] analyzed the multi-path interference in the three-slit experiment by numerically solving Maxwell’s equations concluding that the Sorkin parameter [17] for three-slit interference is nonzero or, otherwise, Born’s postulate is not fulfilled. The Sorkin parameter κ can be obtained by the following probabilities relation: κ = Pabc − (Pab + Pbc + Pac ) + Pa + Pb + Pc
(1)
where a, b and c subscripts indicate the first, second and third slit of the grating and P ≡ || 2 . In addition, they pointed out that the hypothesis that the three-path interference κ should be zero could be a good approximation for experiments conducted in the Fraunhofer regime. Even in this regime, they found the magnitude of the three-slit interference with respect to the two-slit interference should be several orders of magnitude smaller than the upper bound (10-2 ) stated in Sinha et al. [16]. Afterwords, Sawant et al. [15] attributed the result reported in [1] to non-clasical paths in the interference t
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