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From what I have read on it, I like the idea of a wavefunction which evolves solely according to Schroedinger's equation and does not collapse during observations. However, I was under the impression that the Copenhagen interpretation's collapse of the wavefunction was a necessary outcome of experiments. If an electron is observed to be at a particular location, then one femtosecond later, if observed again, it will not have strayed far. Measurements repeated in very quick succession, return nearly the same value for the electron's location. Is that true?

If so, then I don't see how the MWI can work. Let's say one observation of the electron finds it in an unlikely location. If the wavefunction did not collapse and still obeys Schroedinger's law, then a second observation is likely to find it in an entirely different spot.

If I'm wrong and the quickly taken electron measurements do not need to be consistent, then why was the wavefront collapse added to the Copenhagen interpretation?