If the HUP was a limit then you could try to reach absolute zero by arranging a system where you can’t know anything about the position of a particle, so then the HUP would not prevent you from reaching zero velocity.
The main problem with reaching absolute zero is in how you would get there. You could wait for thermal radiation to lose all the energy, but as you get colder the radiation power drops significantly, and the rate of loss is proportional to the current temperature, so it would basically take infinite time to reach absolute zero.
The other normal way to cool something is to expand a gas or evaporate a liquid into a gas. In order to reach absolute zero you would need to expand the gas to infinite volume, so that won’t work. If you cook a liquid too far it won’t evaporate, so you can’t get low enough that the evaporation temperature change can get you to absolute zero.
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