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At the risk of confusing you even more: the value "that would be if the measurement was not made" simply does not exist. Take a your favourite simple quantum system, e.g., the spins of two electrons. The values of the various components and combinations of their spin do not exist before you decide which observables you will measure. It is simply impossible ...

The answer to this question comes from the very definition of measurement. In plain words, by definition, when you measure the state of a system you interact with that system and therefore perturb its state. This is known and is very well documented. Take the double-slit experiment for example: Your setup is an electron beam that you fire towards a wall ...