  The Many Worlds Interpretation (MWI) famously avoids the issue of wave
function collapse. Different MWI trees representing the same quantum events can
have different topologies, depending upon the observer. However, they are all
isomorphic to the group of block universes containing all of the outcomes of
all of the events, and so, in that sense, the group of block universes is a
more fundamental representation. Different branches of the MWI tree,
representing different universes in MWI, ultimately share the same quantum
state in a common ancestor branch. This branching topology is incompatible with
that of the Minkowski block universe; the resolution is to replace the branches
with discrete, parallel block universes, each of which extends from the trunk
to the outermost twigs. The number of universes in a branch is proportional to
its thickness which, in turn, depends upon the absolute square of the
probability amplitude for the state in that branch. Every quantum event may be
represented by a kernel of universes, which is the smallest group of universes
that will reproduce the quantum probabilities of the outcomes of that event. By
considering the ratios of the probabilities of the outcomes of any event, it
can be shown that the number of universes in every kernel must finite, as must
be the total number of universes in the multiverse. Further, every universe in
the multiverse must be finite both in space and time. Another consequence is
that quantum probabilities must be rational, which suggests that quantum
mechanics is only an approximation to a discrete theory. A corollary is that
not every conceivable universe exists in the multiverse, no doubt to the
disappointment of those who enjoy alternate-history novels.
