  Various versions of "independence" are actively inverstigated in quantum
probability. In the context of relativistic QFT, we show here that the physical
origin of "independence" can be sought in the asymptotic condition through
which asymptotic fields and states exhibiting the independence emerge from the
non-independent interacting Heisenberg fields in a kind of "central limit".
From the algebraic viewpoint, this condition is equivalent to the on-shell
condition to pick up free one-particle modes, which also reduces to Einstein's
famous formula $E=mc^{2}$. A scenario to reconstruct interacting Heisenberg
fields as Micro-objects from these "independent" =free Macro-objects
intertwined by an S-matrix as a measurable quantity is formulated according to
the Micro-Macro Duality associated with a new notion of a \textit{cocycle of
K-T operators}.
