Abstract
Shahriar S. Afshar claimed that his 2007 modified version of the double-slit experiment violates complementarity (Afshar et al. in Found Phys 37:295–305, 2007). He makes two modifications to the standard double-slit experiment. First, he adds a wire grid that is placed in between the slits and the screen at locations of interference minima. The second modification is to place a converging lens just after the wire grid. The idea is that the wire grid implies the existence of interference minima (wave-like behavior), while the lens can simultaneously obtain which-way information (particle-like behavior). More recently, Cramer (The quantum handshake: entanglement, nonlocality, and transactions, Springer, Berlin, 2016) argued that the experiment bolstered the Transactional Interpretation of Quantum mechanics (TIQM). His argument scrutinizes Bohr’s complementarity in favor of TIQM. We analyze this experiment by simulation using the path integral formulation of quantum mechanics (Feynman in Rev Mod Phys 20367–20387, 1948) and find that it agrees with the wave-particle duality relation given by Englert, Greenberg and Yasin (E–G–Y) (Englert in Phys Rev Lett 77:2154, 1996; Greenberger and Yasin in Phys Lett A 128:391–394, 1988). We conclude that the use of Afshar’s experiment to provide a testbed for quantum mechanical interpretations is limited.
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Data and code are available upon request.
Notes
Note that in this example with point like sources, a simplified definition of D is used (Eq. 1). When inserting the wires, the complete form is needed and is used for our calculations: \(D = |P_{1,1}-P_{2,1}|+|P_{1,2}-P_{2,2}|\) where \(P_{i,j}\) is the probability to detect at detector i following path j [9]
The simulation code can be found at https://git.unl.edu/bgergely/simulation-of-afshar-experiment
In the simulation, the integral of Eq. (3) becomes a sum over a finite number of grid points between the slit (or wire grid) boundaries.
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Acknowledgements
We gratefully acknowledge support by the National Science Foundation (NSF) under the Award Number PHY-1912504.
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Gergely, B., Batelaan, H. Simulation of Afshar’s Double Slit Experiment. Found Phys 52, 69 (2022). https://doi.org/10.1007/s10701-022-00585-7
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DOI: https://doi.org/10.1007/s10701-022-00585-7