Heisenberg’s Uncertainty Principle UP is a cornerstone of quantum mechanics stating that there is a limit to the precision both position and velocity of a particle like an electron, can be determined. The standard hand-waving argument is that precise measurement of position changes velocity and vice versa, and so precise measurement of both to arbitrary precision is impossible. This makes quantum mechanics fundamentally different from classical mechanics, where there is no such limit to measurement precision, in principle.
The other cornerstone is Schrödinger's wave function, which does not contain UP even if it is supposed to tell everything there is to say about the system. UP is thus an add-on to standard Quantum Mechanics stdQM based on Schrödinger’s equation, and then connected to measurement.
Is there any UP in RealQM? We recall that RealQM describes an atomic system as a collection of non-overlapping extended electronic charge densities which do not have particle character. For an extended body (on macro or microscale) there is no unique point position and velocity describing the state of the body and so there is a certain fuzziness or certain uncertainty depending on size if only one point, such as the center of gravity is to be used. RealQM thus, just like classical continuum mechanics for extended elastic bodies, comes with a form of UP depending on size, but this is perfectly normal and no mystery.
In RealQM there is no built-in limit to possible measure precision. The charge densities of an atom in ground state are stationary in space and shift around under radiation and so come with the usual fuzziness of extended bodies, which on microscale of course can be very real making it very difficult to point-wise determine the electron charge density in an atom, but there is no mystery like that of Heisenberg.
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