The uncertainty principle says that $\Delta x\Delta p\geq \frac{\hbar}{2}$. The uncertainty principle is to be viewed as a fundamental fact of nature herself, and the principle has nothing to do with measurement limitations. If such an uncertainty does not show itself in the macroscopic world, it is explained, it is because of the smallness of $\hbar$.
But if one accepts this, then it means that in principle one could make as precise measurements as one wishes by making either $\Delta x$ or $\Delta p$ smaller without bounds. The other will rise without bounds, and at some point must be capable of observation in the macroscopic world, no matter how small $\hbar$ is.
If such a large uncertainty has not been observed in the macroscopic world, how can this be reconciled with the idea described above?
Best Answer
In order to test whether a system is in a state with some wide uncertainty in position or momentum, you would have to do an interference experiment. The smallness of $\hbar$ does not explain why you can't do such an experiment with a macroscopic system.
Rather, what happens is that the system interacts with its environment and undergoes decoherence. Decoherence would select a set of states that are narrow in position and momentum on a macroscopic scale. The system would then exist in each of those states, but the states would be unable to undergo interference as a result of the decoherence. As a result, each version of you would see the system in one of the allowed states, none of which is wide in position and momentum. For more explanation of decoherence see
https://arxiv.org/abs/quant-ph/0306072
https://arxiv.org/abs/1212.3245
and references therein.