## 9 Additional Remarks and Discussion  
Some additional considerations provided below may contribute to the clarification of the preceding theoretical and experimental results. It may be pointed out that only non-relativistic theory has been considered in this paper. In view of the striking INS findings considered above, one may ask in which other potential systems similar scattering anomalies could be observed. Indeed, another interesting system is given by single H\({}_{2}\)O molecules in oriented nanoscale channels of a solid material, as firstly presented and analyzed in reference [17]; see also [18]; here, a large \"anomaly\" (about \(-45\) %) of the effective mass of H in the OH-stretching vibrational motion was found. Moreover, several more such systems are already known, which however exhibit significantly smaller anomalies, and therefore they are less convincing, e.g., the same effect was originally found (in the electron-Volt energy-transfer range) in liquid D\({}_{2}\)[38], and in liquid H\({}_{2}\)[39]. Additionally, also scattering from H of solid polyethylene--a solid polymer, (-CH\({}_{2}\)-)\({}_{n}\)--was found to exhibit the same small anomaly; see, e.g., [26]. The corresponding anomalies were in the range of a few percent, and thus they could be experimental artifacts caused by a wrong calibration of the spectrometer; for a related discussion, see Appendix A. These observations lead to the following critical remarks. Although we showed that all usual, classical mechanisms cannot explain the INS anomalous results, coming with a plausible explanation based on the negative conditional entropy does not make it necessarily the cause of the observed discrepancies between INS experiments and conventional theory. From that point of view, one needs some explanation of why this happens in the particular INS problems considered above. Therefore, here it seems appropriate to stress the following point: The succinct specifics of the studied materials that give rise to the considered \"anomalous\" quantum correlation effects are not known until now. These specifics certainly concern, or are related with, the specifics of the H-\(\mathcal{E}\) quantum-correlation dynamics (see Section 7), which however are beyond the reach of present-day quantum chemistry of H-\(\mathcal{E}\) interactions--the latter dealing with quantum statics (i.e., time-independent problems), rather than with quantum dynamics (i.e., time-dependent processes). All considerations and results in this paper are related to concrete INS experiments, which is incoherent. In simple terms, \"incoherent\" means that the impinging neutron collides with, and scatters from, a single particle (nucleus, atom, etc.). In the case of neutron scattering from protons (conventionally also referred to as H-atoms), the scattering is incoherent in a very good approximation, due to the spin-flip mechanism accompanying the neutron-proton collision [8]. This is tantamount to the gain of a \"which-path information\" [32] which destroys coherence between possible neutron paths. A clear first-principles explanation of this effect, and of coherent versus incoherent scattering, is presented in the well-known \"Feynman Lectures\" [7], in particular Section 3.3 therein. Contrary to the viewpoint of this paper, in standard neutron scattering theory, quantum correlations between distinguishable particles are assumed to play no role; cf. [8; 10; 11]. Namely, although neutron is a quantum particle and, in general, will become even entangled with a scattering nucleus, this quantum effect is absent in the standard theory. Moreover, the neutron's quantum degrees-of-freedom are absent in any basic scattering expression or formula (e.g., the dynamic structure factor; or the van Hove correlation functions). Instead, only \(c\)-numbers referring to a neutron appear in these formulas.