A novel mechanism for probing the Planck scale

The Planck or the quantum gravity (QG) scale, being 16 orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that QG effects via the generalized uncertainty principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies (Villalpando C and Modak S K 2019 Class. Quantum Grav. 36 215016 ; Villalpando C and Modak S K 2019 Phys. Rev. D 100 024054 ). In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the systems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of (Villalpando and Modak 2019 Class. Quantum Grav. 36 215016 ; Villalpando and Modak 2019 Phys. Rev. D 100 024054 ), the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.