## 9 Additional Remarks and Discussion
A nearer consideration of this issue shows that this \"absence\" is not due to some mathematical \"error\", but only due to the simple fact that conventional theory is based on the formalism of first-order perturbation theory. In this approximation, the degrees of freedom of neutron and H (or any other nucleus) are formally decoupled; so no neutron-H quantum correlation effects do appear here. In other terms, text-book non-relativistic neutron scattering theory treats the neutron as a classical mass point [8,10,11]; i.e., this theory contains only \(c\)-numbers referring to neutron's properties (e.g., the scattering length \(b_{A}\) or the cross-section \(\sigma_{A}\)). The excess energy transfer, and the associated effective-mass reduction of the scattering particle \(H\) in the presented INS experiments, are sometimes considered as violating the energy and momentum conservation laws of basic physics. However, this is not the case because \(H\), and also \"neutron + H\" are _not_ closed quantum systems, but open systems. It is helpful to write down explicitly the conservation relations for the complete closed system \"neutron + H + \(\mathcal{E}\) (environment)\"  
\[E_{H+\mathcal{E}}=-E_{n}\quad\text{and}\quad\hbar K_{H+\mathcal{E}}=-\hbar K_{ n}, \tag{33}\]  
which express the correct energy and momentum conservations for a closed system. Obviously, these are in contrast to the following (often assumed) equations  
\[E_{H}=-E_{n}\quad\text{and}\quad\hbar\mathbf{K}_{H}=-\hbar\mathbf{K}_{n}, \tag{34}\]  
which however are (in various cases only crude) approximations. Clearly, if one neglects \(\mathcal{E}\) (or over-simplifies its quantum character), the conservation laws seem artificially violated. Thus we can say that the quantum dynamics of \(\mathcal{E}\) is indispensable for the interpretation of the considered INS effect from H.  
In the light of these remarks, the following (for conventional theory: highly perplexing) conclusion follows as a corollary: The time evolution of any neutron-H dynamical process (like, e.g., INS), in which H belongs to a hydrogenous material (and thus one cannot neglect \(\mathcal{E}\)), is not unitary. The striking INS results from H\({}_{2}\) in C-nanotubes [28] and metal-organic materials [29], discussed in Section 4, may appear contradictory because: (i) the \(J=0\to 1\) rotational excitation reveals the conventional value \(M_{eff}\approx 1\) a.m.u., see Equation (10). But (ii) the \(M_{eff}\) of the translational motion of H\({}_{2}\) is not 2 a.m.u. as conventionally expected, but only \(M_{eff}\approx 0.64\) a.m.u. However, this \"contradiction\" is an artifact that just disappears in the light of the QTD theoretical treatment. Namely, this difference only implies that the quantum environments of H are qualitatively different in these two cases. In other words: the QTD theoretical frame allows us to reveal novel quantum effects of \"system-environment\" interactions that are beyond the predictive power of present-day quantum chemistry. It should be emphasized that both \"system\" and \"environment\" represent quantum objects, the quantum dynamics of which must be treated on equal footing. In simple words, environment is not a passive object that just restricts (or confines) the system's dynamics. Based on the INS experimental effect under consideration (and in particular of the striking reduction of effective mass of H), a speculative idea arises, which concerns the possible practical and/or technological relevance of QTD and quantum information theory: A more mobile H atom, or H\({}^{+}\) ion, due to a suitably chosen nanostructured fuel cell material, would cause an improved cell's efficiency. Last but not least, it should be mentioned that the considered \"anomalous\" INS effect has recently found an additional theoretical interpretation [26,40] based on \"quantum mechanisms\" (rather than on quantum correlations), which is based on the fundamental theory of Weak Values (WV) and Two-State Vector Formalism (TSVF) by [PERSON] and collaborators, cf.