Discreteness of Space from GUP in Strong Gravitational Fields

Understand

A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale.

• It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schr\"odinger equation and to the relativistic quantum mechanical equations.
• Some of these corrections give rise to potentially measurable effects in the low-energy laboratory.
• Another prediction of these corrections is that a measured length must be quantized, as seen by studying the solutions of the GUP modified Schr\"odinger, Klein-Gordon, and Dirac equations in a one, two, and three dimensional box.