The momentum problem in the electron double-slit experiment

How is momentum exchanged in the electron double-slit experiment? It may appear that this question should not be asked. After all, the electron double-slit gedanken-experiment was debated already at the fifth Solvay conference in 1927. Einstein suggested that the recoil of the slit structure could be used to determine through which slit the electron went. Bohr countered that the uncertainty principle prohibits such determination of which-way information. Note however, that in this debate, both Einstein and Bohr agreed that the slit structure recoils to conserve momentum. There is thus momentum exchange. Feynman once claimed that one should not attempt the electron double-slit experiment based on its “impossibly small scale.” Nevertheless, experiments were done, and we performed Feynman’s version of the experiment in 2013 with control over the individual slits [1]. In addition, it has already been established that such mechanisms can be investigated. For example, in 2001, we provided the first demonstration of electron diffraction from “slits” of light, the “Kapitza-Dirac” effect [2]. How does the diffracting electron exchange momentum in the Kapitza-Dirac effect? The well-established answer is that one photon is absorbed by the electron and another is stimulated emitted in a QED process called stimulated Compton scattering. The diffraction into the first order is caused by the two-photon momentum recoil that the electron experiences. So, the mechanism is known for the Kapitza-Dirac effect. But how can it be that for two very similar experiments, electron double-slit diffraction and the Kapitza-Dirac effect, we are discouraged to ask the question in one case while in the other case the answer is known? And how can we, in principle, go after this problem experimentally? This is what will be discussed.

[1] Controlled double-slit electron diffraction. R. Bach, D. Pope, S. H. Liou, H. Batelaan, New. J. Phys. 15 033018 (2013).

[2] Observation of the Kapitza-Dirac effect. D. L. Freimund, K. Aflatooni, and H. Batelaan, Nature 413, 142-143 (2001).