The Everettian, aka Many Worlds, interpretation of Quantum Mechanics states that the wave function of the universe never collapses and evolves according to the plain Schrodinger equation.
When a measurement of a quantum system occurs, instead of having wave function collapse, the system gets entangled with the measuring device and with the environment.
As a consequence, measurement always puts the state of the universe in a superposition of states each of which describes a "copy" of our macroscopic world, and these copies (the "branches") differ by the output of the measurement itself.
A physical phenomenon called decoherence implies that in MWI it is impossible to empirically establish the existence of the other branches (the ones "we don't live in" in a given moment).
In MWI every quantum measurement outcome is realized in a branch, and has 100% probability of happening in the universe (by "universe" it's meant the whole set of degrees of freedom, comprising all the branches). The usual probabilistic picture of QM is retrieved by the fact that each observer splits into copies of itself along with the rest of the macroscopic world it lives in. Probability is now translated into the indexical uncertainty that each future copy of the observer is subject to before peering at the measuring device and seeing the measurement result.
The role of probability in MWI is not universally accepted. But in this question I'm not asking about this.
Karl Popper is famous for his demarcation criterion, falsificationism, for distinguishing scientific theories from non-scientific ones.
Q. On the surface, it could seem that MWI fails Popper's criterion, because we can't empirically access the branches (worlds) we don't live in. Is this really true? What did Karl Popper think about the MWI of quantum mechanics? Did he write anything about that?