Probing space with the two-slit experiment

M. Bauer

Siddhant Das, Dirk-André Deckert, Leopold Kellers +2 more

M. Bauer

Unlike the usual interference experiment with two slits separated in space, a time double-slit experiment uses the equivalent of a single slit covered by a shutter that is opened and closed and then quickly opened and closed again. Such experiments have recently been performed, providing further confirmation of wave-particle duality. In either type of experiment, the wave function beyond the slit(s) initially has two peaks that then spread and interfere. This article derives the results of these experiments in a schematic, but analytic solution of the time-dependent Schrödinger equation with appropriate initial conditions. In the space double-slit case, in addition to the transverse interference pattern, the time evolution at a fixed position exhibits an oscillating transient behavior similar to that obtained in the time double-slit experiment. Finally, the schematic model also reproduces the observed progressive visibility of the interference pattern obtained as a movable mask is displaced in front of the double-slit.

C. Ellegaard, Mogens T. Levinsen

While bouncing walking silicone oil droplets (walkers) do show many quantumlike phenomena, the original, most intriguing, double-slit experiment with walkers has been shown to be an overinterpretation of data. Several experiments and numerical simulations have proven that for at least some parameter region there is no randomness. Still, true randomness was claimed to be observed in an experiment on chaotically bouncing walkers. Also, most of the available phase space has not been investigated. The main goal of this paper is therefore to look for true interference and chaos in the entire phase space. Recently, we made an extensive investigation of drops interacting with slits, but still in a limited range. However, the outcome was always deterministic and only incidentally mimicked the statistics of the corresponding quantum case. We also showed that the extra interference, already seen by others, in the double-slit case was caused by reflection of waves from the outlet of the unused slit after passage and thus was not a true double-slit effect. A new theoretical treatment of bouncing drop dynamics has since given analytic relations for the associated wave field, leading to a proposal for criteria for the possible occurrence of true interference in the double-slit experiment. Satisfying these criteria, requires working close to the onset of the Faraday instability, with two spatial conditions favoring slow walkers, and a temporal condition favoring fast walkers. The regions of high velocity, where the walkers bounce periodically, and of very low velocity, with chaotically bouncing walkers, have not been comprehensively investigated so far. We have therefore looked at these regions, probing the limits for interaction with slits. Furthermore, noting that a short transit time is essential to fulfill the criteria, experiments were done using double-slit barriers only 0.5 and 2 mm broad. Nowhere was true interference or a chaotic response found. As the theory has implications for many of the observed quantumlike phenomena involving walkers as, e.g., tunneling and interaction between drops, we have measured the spatial and temporal decay of the wave field. A comparison with the theory shows very good agreement but leads to a reformulation of the above-mentioned criteria.

Mohamed Saladin El Naschie

Gregg S. Jaeger