An extension of "Popper's experiment" can test interpretations of quantum mechanics

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics - namely that the state of a particle is merely an expression of "what is known" about the system is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called "Extension step 1") - which fully serves its original purpose - is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the "many-worlds" interpretation (MWI) is correct are shown to be identical. Only after a further modification (called "Extension step 2") (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because "what is known" by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus - within the CI - for H they are "known not to exist" Yet H can infer their existence by studying the evolution of the ion.