Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.
Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.
— Wikipedia on Quantum indeterminacy
Quantum indeterminacy is the inability to predict the behaviour of the system with 100% accuracy, even in principle.
If everything is connected
, quantum indeterminacy is due to the logical fact that, by definition, a “part” cannot contain (all the information of) the “whole”.
An observer (A) cannot separate itself from the system (B) that it wants to observe, because an observation is an interaction between the observer and the observed
In order to get a perfect prediction of a measurement result, observer (A) must have all the information of the present state of the whole system (A+B). However, there are two logical difficulties.
First, observer A cannot have all the information about (A+B).
Second, observer A cannot observe itself to get (all of) its present state information, since an observation is an interaction between two entities. Logically, it is impossible for something to interact with itself directly. Just as logically, it is impossible for your right hand to hold your right hand itself.
So the information observer A can get (to the greatest extent) is all the information about B, which is only part of the system (A+B) it (A) needs to know in order to get a prefect prediction for the evolution of the system B.
— Me@2015-09-14 08:12:32 PM
2015.09.15 Tuesday (c) All rights reserved by ACHK