On a new prediction of Causal Quantum Mechanics for the two-slit interference experiment with electrons

TL;DR

This paper derives a general formula for photon emission power in double-slit experiments, showing a potential measurable difference between Copenhagen and causal quantum interpretations based on electron trajectories and quantum potential effects.

Contribution

It introduces a new quantum general formula for photon emission power that applies across interpretations and predicts a tiny but non-zero emission in causal quantum mechanics.

Findings

Copenhagen interpretation predicts zero photon emission power.

Causal interpretation predicts a tiny non-zero emission power.

Proposes an experimental setup to detect the predicted emission spectrum.

Abstract

The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or 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, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum general formula for the emission power of photons, valid independently of the interpretation. Then, according to the Copenhagen interpretation, this formula gives a strictly zero value for the emission power because the electron moves as a free particle after it leaves the slit and before reach the screen. Then, there is no emission of photons. In the case of the causal interpretation, the emission power results, for a concrete real experiment, in a very tiny but not a zero value, driven by the square of the quantum potential gradient. We give an idea of the type of spectrum that could be measured. A brief idea of a possible experimental arrangement in order to detect this effect, is given.