Mass oscillations and matter wave's phase and amplitude modulations of relativistic quantum particles induced by Heisenberg's uncertainty principle.

We present a flip-flop dual-component model to treat quantum dynamics of relativistic particles with a rest mass and investigate the matter waves' phase and amplitude modulations due to Heisenberg's uncertainty principle. Their matter waves behave like a traveling Gaussian-shaped wave packet accompanied by a guiding pilot wave, and the phase modulations result in mass oscillations. These effects are more prominent for light-weighted elementary particles, such as neutrinos and electrons. This mechanism is solely due to the uncertainty principle and has nothing to do with the flavor-mixing of neutrinos. Simulations using neutrinos and electrons are presented, which indicate an oscillation period on the order of ps. This study primarily focuses on the predicted mass oscillations induced by the uncertainty principle. A slit-type interference experiment using neutrinos and electrons from reactors is proposed to test the predicted behaviors.