Is there any mistake in Heisenberg's uncertainty principle?
Yes. It is spelled "Heisenberg" and "Uncertainty".
This is a well accepted feature of quantum mechanics. What would make you doubt it?
It is often mistakenly stated.
Technically no, as it's a consequence of the mathematical structure of quantum theory.
That said, real particles are under no obligation to obey quantum theory.
It's just that we've never seen any disagreement between what experimental tests show and what quantum theory predicts.
That's not to say that there aren't better uncertainty principles out there.
For example, the entropic uncertainty principle:
[itex]h(x) + h(p/\hbar) \geq \log(\pi e)[/itex]
is better than the Heisenberg uncertainty principle:
In that you can get the Heisenberg principle as a special case of the entropic principle, but not the other way around.
Also, entropy is a better measure of uncertainty, if you think of uncertainty as how many square meters you have to search rather than within what meter radius you have to look.
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