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.
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We thank R. L. Jaffe for valuable discussions that considerably contributed to our work. This research was funded by the ICore Excellence Center ‘Circle of Light’, by the Binational USA–Israel Science Foundation BSF, and by a Marie Curie Grant no 328853–MC–BSiCS.
The authors declare no competing financial interests.
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Kaminer, I., Nemirovsky, J., Rechtsman, M. et al. Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions. Nature Phys 11, 261–267 (2015). https://doi.org/10.1038/nphys3196
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