Because quantum mechanics prevents the initial state from being specified with arbitrary precision, and SDIC amplifies any such uncertainty exponentially, unique evolution must fail for nonlinear chaotic systems.
Complex systems where the rules don't follow simple straight-line logic, and tiny changes can produce completely unpredictable, seemingly random outcomes.
Quantum mechanics(the scientific framework being discussed)
The science of how the tiniest things in the universe (atoms, electrons, photons) behave—which turns out to work very differently than everyday objects.
SDIC(Used in the context of whether quantum interactions with such systems contribute indeterministically to their outcomes)
Sensitivity to initial conditions — a property of nonlinear macroscopic (chaotic) systems whereby small differences in initial state lead to divergent outcomes
Unique evolution(as used in determinism and physics)
The idea that given a starting state, there is only one possible way a system will develop over time—that the future is fully determined by the present.
Premise (A) makes clear that SD is the operative definition for characterizing chaotic behavior in this argument, invoking exponential growth characterized by the largest global Lyapunov exponent. Premise (B) expresses the precision limit for the state of minimum uncertainty for momentum and position pairs in an \(N\)-dimensional quantum system (note, the exponent is \(2N\) in the case of uncorrelated electrons).[8] The conclusion of the argument in the form given here is actually stronger than