>>10956904If you track your center of mass position and average momentum to higher and higher accuracy, you will eventually encounter fluctuations in the values due to thermal vibrations. However, the fact that the HUP minimum is significantly smaller means that we could in principle track these thermal fluctuations to pretty high accuracy without disturbing them much. However, with high enough accuracy you would eventually detect significant deviations in one value as a result of measuring the other. This is at the level of fractions of a proton diameter though, so not very meaningful to us and a long way from detectability.
