  The splitting-worlds reading of Everett faces a number of challenges. First, supporters of the Everett interpretation frequently motivate their interpretation by arguing that it postulates the existence of neither a controversial wave collapse nor hidden variables, and it leaves the simple and elegant mathematical structure of quantum mechanics intact. But, the splitting-worlds interpretation adds extra structure to no-collapse orthodox quantum mechanics. Further, this interpretation marks a radical shift from orthodox quantum mechanics. A scientific theory is not constituted only by its mathematical formalism, but also by the ontology it postulates, the way it depicts the physical realm and the way it accounts for our experience. The many parallel worlds ontology of the splitting-worlds interpretation and its account of our experience are radically different from the ontology of the intended interpretation of orthodox quantum mechanics and its account for our experience. Second, relative states are well defined in any basis, and the question arises as to which basis should be preferred and the motivation for selecting one particular basis over others.  Third, in the splitting-worlds interpretation each of the worlds in the universe may split into two or more worlds, and the problem is that (similarly to the collapse in orthodox collapse quantum mechanics) there are no clear criteria for when a splitting occurs and how long it takes. Fourth, there is the question of how the splitting-worlds interpretation accounts for the statistical predictions of the orthodox theory. In the Everett-like interpretations in general, and in the splitting-worlds interpretation in particular, all the possible measurement outcomes in the EPR/B experiment are realized and may be observed.  Thus, the question arises as to the meaning of probabilities in this interpretation. For example, what is the meaning of the statement that in the state |ψ10&gt; (see section 5.3.2) the probability of the L-measurement apparatus pointing to the outcome ‘up’ in an earlier z-spin measurement on the L-particle is (approximately) ½? In the splitting-worlds interpretation the probability of that outcome appears to be 1! Furthermore, setting aside the problem of interpretation, there is also the question of whether the splitting-worlds interpretation, and more generally Everett-like interpretations, can account for the particular values of the quantum probabilities of measurement outcomes. Everett claimed to derive the Born probabilities in the context of his interpretation. But this derivation has been controversial. (For discussions of the meaning of probabilities, or more precisely the meaning of the coefficients of the various terms in quantum states, in Everett-like interpretations, see Butterfield 1996, Lockwood 1996a,b, Saunders 1998, Vaidman 1998, Barnum et al. 2000, Bacciagaluppi 2002, Gill 2003, Hemmo and Pitowsky 2003, 2005, Wallace 2002, 2003, 2005a,b, Greaves 2004 and Saunders 2004, 2005.) 