''When a measurement is made, it means that the differential system has to change, since an interaction, depending on the type of measurement, is inevitable. This introduces a change in the differential formulation of the problem. Thus after the measurement a different wave function will describe the set up, as the measurement changed the system. This is the famous collapse, that that specific wave function no longer holds, a new one has to be calculated.
Since the wave function leads to a probability distribution, which is a classical concept too, not distinguishable from the quantum, contemplate the probability distribution of a young person to enter the university after exams. There exists a geographic probability distribution over the country of how many succeed and how many fail . This means that a multitude of data has been used from previous exams to create the distribution. If a specific young person is successful, does this change the probability distribution in general? It just changes his/her probability to 1 and he/she has to face a new situation with new probability distributions that will shape his/her future.
In a similar way the "collapse" means that the probability is 1 after the measurement that the particle was in that specific (x,y,z,t) etc and a new probability distribution has to apply to a new situation from a new wave function. The old wave function still mathematically exists, but is irrelevant to the evolution of the situation.
In any theory that is consistent with quantum mechanical postulates the above holds so if the many world interpretation is consistent with quantum mechanics, it will have no problem from the semantics of "collapse", which sounds a lot more drastic than it is.
EDIT: The people who are saying there is no collapse are saying what I am discussing above, that collapse is a semantic for describing probability distributions and their use in measurements in the microcosm. It is the Copenhagen interpretation.''
