Strong equivalence principle in polymer quantum mechanics and deformed Heisenberg algebra

The strong equivalence principle (SEP) states that the description of a physical system in a gravitational field is indistinguishable from the description of the same system at rest in an accelerating frame. While this statement holds true in both general relativity and ordinary quantum mechanics, one expects it to fail when quantum gravity corrections are taken into account. In this paper we investigate the possible failure of the SEP in two quantum gravity inspired modifications of quantum mechanics - polymer quantum mechanics and deformed Heisenberg algebra. We find that the SEP fails to hold in both these theories. We estimate the deviation from SEP and find in both cases that it is too small to be measured in present day experiments.