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I am afraid that the problem with the superposition may be harder. In fact, the superposition problem must be consider as a part of the problem of the which way information. The problem stays in the fact that the existence resp. not existence of the which way information can influence the real physical processes. The superposition is only one side of this problem. I am almost sure that there exists only one rational explanation which is based on the concept of a context introduced in my paper attached below. This explanation is based on the following considerations: there are incompatible events, which cannot be observed simultaneously in the given experiment; events observable in the given experiment make together the context of this experiment (the experimental setting defines the context); thus the existence (resp. not existence) of the which way information defines the context of the eperiment; thus with the which way information we observe different events then in the situation when the which way information is not available. Then when we have not available the which way information we can observe the interference. This means that the phenomenon of the interference is primarily associates with the context of the experiment. All this is explained in details in my paper on the extended probability theory and quantum mechanics attached to this note. In conclusion I think that the problem of interference is only a part of the larger problem of understanding well the role of the which way information (of information in general) in quantum physics.
Your Jiri Soucek