Reconstruction of Schrödinger's Cat in Many Worlds 4; The Emergent Structure of Many-Worlds Interpretation and Its Self-Consistency Foundation

This paper constructs a logically self-consistent emergent structural framework
for the Many-Worlds Interpretation (MWI) based on decoherence theory, quan
tum information geometry, and self-referential dynamics. Within this framework,
a ”world” is rigorously defined as a quasi-classical branch formed in Hilbert space
through environmental decoherence and information-geometric boundaries. Its in
dependence is quantitatively characterized by the branch separation degree Dab de
fined by the quantum relative entropy between branches. When Dab exceeds a crit
ical value Dc determined jointly by the energy scale of environmental fluctuations
and the decoherence time, the branches separate irreversibly in the information
geometric sense, constituting independent ”worlds”. Furthermore, by introducing
the concept of a self-consistent observer, this paper demonstrates the dynamic selec
tion mechanism of cosmological laws within the string theory landscape: only those
vacuum branches that can support self-consistent observers (satisfying conditions
such as the memory decoherence time being much greater than the cognitive oper
ation time) have their wavefunction weights effectively preserved during evolution,
thereby acquiring physical reality. Finally, combining Zurek’s envariance argument
with the requirement of observer memory stability, we show that the Born rule
P(i) = |⟨i|ψ⟩|2 is not an additional assumption but a necessary consequence for
the stable existence of self-consistent observers. This framework provides an opera
tional mathematical foundation for the many-worlds interpretation, transforms the
anthropic principle into a dynamic selection problem, and offers an explanation for
the origin of probability based on quantum information principles.