Charles Wesley Cowany and Roderich Tumulka write:
Since science provides us with knowledge, it may seem surprising that it sometimes sets limitations to knowledge. By a “limitation to knowledge” we mean that certain facts about the world cannot be discovered or confirmed in an empirical way, no matter how big our effort, including possible future technological advances. For example, a limitation to knowledge is in place if a quantity cannot be measured although it has a well defined value. A limitation to knowledge means that there is a fact, and we cannot know what it is, nor even guess with much of a chance of guessing correctly. Nature knows and we do not.
The very idea of a limitation to knowledge may seem to go against the principles of science. If there is no way of measuring a quantity X, then this may suggest that X does not actually have a well-de fined value, i.e., that nature does not know either what X is.
However, the existence of limitations to knowledge is a fact, as it is a simple consequence of quantum mechanics, independently of which interpretation of quantum mechanics we prefer.
These limitations to knowledge arise as a consequence of the defining equations of the theories. They are not further, ad hoc postulates; and they do not require carefully contrived, or conspiratorial, initial conditions. Instead, they are dictated by the physical laws.
What is upsetting about limitations to knowledge is that they conflict with key ideas of (what may be called) positivism: That a statement is unscientific or even meaningless if it cannot be tested experimentally, that an object is not real if it cannot be observed, and that a variable is not well-de fined if it cannot be measured. We conclude that this form of positivism is exaggerated; it is inadequate.
Read more here.