We have recently shown that the very low mechanical energy achieved and measured in the main vibration mode of gravitational wave bar detectors can set an upper limit to possible modifications of the Heisenberg uncertainty principle that are expected as an effect of gravity. Here we give more details on the data analysis procedure that allows one to deduce the energy of the bar mode (i.e., the meaningful parameter for our purpose). Furthermore, we extend the analysis of our results, discussing their implication for physical models that face quantum Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. gravity from different points of view, e.g., proposing modified commutation relations or exploring spacetime discreteness.