  The basic mathematical structure, QM-A, of the many worlds interpretation
consists solely of the linear mathematics plus the Hilbert space properties of
the state vectors. There is no collapse and there are no particles or hidden
variables. It is remarkable that QM-A alone can account for all our
observations except probability. There is no need for particles, hidden
variables or collapse to explain perception of only one classical version of
reality, the photoelectric effect, localized effects from a spread-out wave
function in scattering and interference experiments, wave-particle duality, and
so on. But probability cannot be defined within QM-A. Nevertheless, because of
its astonishing success, it seems reasonable to require (1) that the
mathematics of an interpretation be limited to the highly successful QM-A and
(2) that "matter" be composed of state vectors alone. But the probability law
requires, in essence, that one version of the observer be singled out. The most
straightforward way to accomplish this under (1) and (2) is to assume there is
an aspect of the observer-the Mind-which is outside the laws of quantum
mechanics and perceives just one version of reality. Under that assumption, the
probability law can then be derived. Thus we have an interpretation, QM-A plus
"outside" observer, which explains all our perceptions.
