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Most physicists today believe that quantum mechanics is correct, and that the EPR paradox is a " paradox " only because classical intuitions do not correspond to physical reality.
How EPR is interpreted regarding locality depends on the interpretation of quantum mechanics one uses.
In the Copenhagen interpretation, it is usually understood that instantaneous wave function collapse does occur.
However, the view that there is no causal instantaneous effect has also been proposed within the Copenhagen interpretation: in this alternate view, measurement affects our ability to define ( and measure ) quantities in the physical system, not the system itself.
In the many-worlds interpretation locality is strictly preserved, since the effects of operations such as measurement affect only the state of the particle that is measured.
However, the results of the measurement are not unique — every possible result is obtained.

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