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But in practice, is there any measurement that will NOT disturb the system at all? To prove that uncertainty is beyond measurement, we must design a measurement process that does not disturb the system. If such a process cannot be designed then the statement that "uncertainty is beyond measurement" cannot be experimentally tested. Isn't it? I don't know whether the idea of a measurement with zero interaction between the system and the apparatus makes any sense, and if there is non-negligible interaction you cannot get away with disturbance induced by the process. Hence, even the theoretical arguments are logically quite robust in explaining why uncertainty principle has nothing to do with measurement, I think experimentally it is not provable (or better, not a falsifiable claim) if you don't have such an ideal measurement.

But in practice, is there any measurement that will NOT disturb the system at all? To prove that uncertainty is beyond measurement, we must design a measurement process that does not disturb the system. If such a process cannot be designed then the statement that "uncertainty is beyond measurement" cannot be experimentally tested. Isn't it? I don't know whether the idea of a measurement with zero interaction between the system and the apparatus makes any sense, and if there is non-negligible interaction you cannot get away with disturbance induced by the process. Hence, even the theoretical arguments are logically quite robust in explaining why uncertainty principle has nothing to do with measurement, I think experimentally it is not provable (or better, not a falsifiable claim) if you don't have such an ideal measurement.

Addendum : I'm afraid to say something different. We are saying that HUP is a result of the non-commutativity of position and the corresponding momentum in the mathematical formalism of quantum mechanics. Thai is indeed correct. But having said that we have to keep in mind that the formalism of quantum mechanics was built in such a way so that its predictions match with non-classical experimental results and observations. So I personally still have a doubt and I'm not sure. After all the theory is built upon experimental observations. Correct me if I'm being foolish.

But in practice, is there any measurement that will NOT disturb the system at all? To prove that uncertainty is beyond measurement, we must design a measurement process that does not disturb the system. If such a process cannot be designed then the statement that "uncertainty is beyond measurement" cannot be experimentally tested. Isn't it? I don't know whether the idea of a measurement with zero interaction between the system and the apparatus makes any sense, and if there is non-negligible interaction you cannot get away with disturbance induced by the process. Hence, even the theoretical arguments are logically quite robust in explaining why uncertainty principle has nothing to do with measurement, I think experimentally is is not falsifiable if you don't have such an ideal measurement.

But in practice, is there any measurement that will NOT disturb the system at all? To prove that uncertainty is beyond measurement, we must design a measurement process that does not disturb the system. If such a process cannot be designed then the statement that "uncertainty is beyond measurement" cannot be experimentally tested. Isn't it? I don't know whether the idea of a measurement with zero interaction between the system and the apparatus makes any sense, and if there is non-negligible interaction you cannot get away with disturbance induced by the process. Hence, even the theoretical arguments are logically quite robust in explaining why uncertainty principle has nothing to do with measurement, I think experimentally it is not provable (or better, not a falsifiable claim) if you don't have such an ideal measurement.