  A non-relativistic quantum mechanical theory is proposed that describes the
universe as a continuum of worlds whose mutual interference gives rise to
quantum phenomena. A logical framework is introduced to properly deal with
propositions about objects in a multiplicity of worlds. In this logical
framework, the continuum of worlds is treated in analogy to the continuum of
time points, both "time" and "world" are considered as mutually independent
modes of existence. The theory combines elements of Bohmian mechanics and of
Everett's many-worlds interpretation, it has a clear ontology and a set of
precisely defined postulates from where the predictions of standard quantum
mechanics can be derived. Probability as given by the Born rule emerges as a
consequence of insufficient knowledge of observers about which world it is that
they live in. The theory describes a continuum of worlds rather than a single
world or a discrete set of worlds, so it is similar in spirit to many-worlds
interpretations based on Everett's approach, without being actually reducible
to these. In particular, there is no splitting of worlds, which is a typical
feature of Everett-type theories. Altogether, the theory explains (1) the
subjective occurrence of probabilities, (2) their quantitative value as given
by the Born rule, and (3) the apparently random "collapse of the wavefunction"
caused by the measurement, while still being an objectively deterministic
theory.
