Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions

The Aharonov-Bohm effect predicts that two parts of the electron wavefunction can accumulate a phase difference even when they are confined to a region in space with zero electromagnetic field. Here we show that engineering the wavefunction of electrons, as accelerating shape-invariant solutions of the potential-free Dirac equation, fundamentally acts as a force and the electrons accumulate an Aharonov-Bohm-type phase-which is equivalent to a change in the proper time and is related to the twin-paradox gedanken experiment. This implies that fundamental relativistic effects such as length contraction and time dilation can be engineered by properly tailoring the initial conditions. As an example, we suggest the possibility of extending the lifetime of decaying particles, such as an unstable hydrogen isotope, or altering other decay processes. We find these shape-preserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin.