The theory of quantum mechanics predicts probabilities. This should not be troubling, because all other scientific theories do the same thing.
Belief in the many-worlds interpretation (MWI) is based on a belief in time reversal symmetry, followed by a rejection of probability. The MWI advocates don't really believe in probability, because they believe that if there are many possibilities of events occurring in the past, then there must similarly be all those possibilities in the future. Their theory is then untestable, because they refuse to make probabilistic predictions, and say that all possibilities occur in some worlds and it is meaningless to say that some worlds are more likely than others.
You could take any theory with probabilistic predictions, and hypothesize that each probability is really a branch into a parallel universe. Thus you could believe in MWI without even mentioning quantum mechanics. Usually the MWI arguments are couched in quantum technicalities, but they are mainly just a misunderstanding of probability.
Lubos Motl writes:
The very meaning of "probability" violates the time-reversal symmetryHe is right about this, and the MWI folks are hung up on this simple point.
An exchange with the reader reminded me that I wanted to dedicate a special blog post to one trivial point which is summarized by the title. This trivial issue is apparently completely misunderstood by many laymen as well as some low-quality scientists such as Sean Carroll.
This misunderstanding prevents them from understanding both quantum mechanics and classical statistical physics, especially its explanation for the second law of thermodynamics (or the arrow of time). ...
This logical arrow of time is a simple, elementary, and irreducible part of our existence within Nature. But it has consequences. If you think about the comments above and recognize that all these things are as clear as you can get, you should also understand that there is no "measurement problem" in quantum mechanics – the existence of the "a measurement" is tautologically an inseparable part of any statement about the corresponding "probabilities".
Confusion about probability leads to other faulty conclusions. For example, some say that quantum mechanics proves that nature is inherently probabilistic, and hence there must be some underlying reality of all the possibilities that can be represented by hidden variables. No, quantum experiments have proven that wrong.
Physicists should take a math class in probability before they start trying to rewrite the foundations of quantum mechanics.