for it. It is possible that there does not exist anything in nature that is described by higher order Gamow vectors and first order resonance poles is all there is. But since there is no theoretical reason against higher order poles of the $S$-matrix and these higher order Gamow “states” emerge naturally from the poles, it is worthwhile to investigate their properties further [@R7]. The only place that we can think to look for effects of these higher order Gamow states are the high-multiplicity events in high energy hadronic and nuclear collisions. That a quantum mechanically rather pure initial state of two hadrons can result in a high multiplicity event could have its origin in the highly impure “resonance” state associated with the ${\cal N}$-dimensional subspace of higher order Gamow kets.

Reversed time evolution and time reversal transformation
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An irreversible time evolution on the microphysical level immediately leads to the question as to the time reversal transformation $A_T$. In the usual reversible time evolution (\[G6\]) one always has with a state $W(t)$ also a state $W(-t)$ (or with the state vector $\phi(t)$ also a state vector $\phi(-t)=\mbox{e}^{-i(-2t)H}\phi(t)$). The time reversed state defined by $W^T(t)\equiv A_T^{-1}W(t)A_T$ or $\phi^T=A^{-1}_T\phi$ can therefore 