On the two-slit interference experiment with electrons: a theoretical prediction of Bohm-de Broglie quantum mechanics different from the prediction of usual Copenhagen quantum mechanics

Resumo

The Bohm-de Broglie quantum mechanics has made possible to calculate the trajectories of electrons in a typical double-slit experiment[C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, the accelerated electrons should, with a certain probabil-ity, emit photons during its movement from the slits to the screen. According to the Copenhagen interpretation we found that this quantity is strictly zero because the electron moves as a free particle along its path after it leaves the slit and before reach the screen. Then, there is no emission of photons. On the other hand, by using the Bohm-de Broglie (BdB) approach we calculate the emission power, giving a general formula and which results, for a concrete real experiment, in a very tiny but not a vanishing value. We give an idea of the type of spectrum that could be measured. Therefore we have shown that the theoretical predictions of the usual quan-tum mechanics and that of Bohm-de Broglie’s interpretation are different. An experiment could determine the correct prediction.