Abstract
The notions of Weak Value (WV) and Two-State Vector Formalism (TSVF), firstly introduced by Aharonov and collaborators, provide a quantum-theoretical formalism of extracting new information from a system in the limit of small disturbances to its state. Here, we explore two applications to the case of non-relativistic two-body scattering with one body weakly interacting with its environment. We present a physically compelling analysis of a new quantum effect: momentum transfer deficit and an accompanying enhanced energy transfer; or, equivalently, an apparent mass-deficit of the struck body. First, incoherent inelastic neutron scattering (INS) from protons of H 2 molecules in C-nanotubes is investigated. The data of the H 2 translational motion along the nanotube shows that the neutron apparently exchanges energy and momentum with a fictitious particle with mass of 0.64 atomic mass units (a.m.u.), which is in blatant contradiction with the expected value of 2 a.m.u. Second, the same theory is applied to neutron reflectivity—which is elastic and coherent—from the interface of (single crystal) Si with H 2 O-D 2 O liquid mixtures. The data shows a striking enhanced reflectivity in a wide range of momentum transfers, which is tantamount to a momentum-transfer deficit with respect to conventional expectations. However, these effects find a natural interpretation within the WV-TSVF theoretical analysis under consideration. In summary, both scattering effects contradict conventional theoretical expectations, thus also supporting the novelty of the theoretical framework of WV and TVSF. Additionally, it should be pointed out that the two dynamical variables in the interaction Hamiltonian of the theoretical model belong to two different physical bodies.
Highlights
The counter-intuitive Elitzur–Vaidman effect [1] concerning interaction-free measurements revealed, among other facts, the ability to experimentally obtain information about an object’s presence in some spatial region without ever “touching” it
Universe 2019, 5, 58 results of actual measurements as obtained with real instruments. (For a quite different opinion, see the fundamental time-inversion symmetry of the Schrödinger equation was shown to be a crucial feature in the novel theory of Weak Values (WV) and the Two-State Vector Formalism (TSVF) of Aharonov and collaborators; cf. [2,3,4,5,6,7] and references therein
In summary: these short derivations show that the novel features of WV and TSVF are caused by the interference between the post-selected state and another quantum state, which is orthogonal to the pre-selected state [15]
Summary
The counter-intuitive Elitzur–Vaidman effect [1] concerning interaction-free measurements (popularly known as “bomb tester”) revealed, among other facts, the ability to experimentally obtain information about an object’s presence in some spatial region without ever “touching” it. The revealed effect is as follows: the photons (particles) collide with the considered mirror only from the inside of the MZI, they do not push the mirror outwards, but rather they somehow succeed to pull it in [8]; see Section 2 Inspired by this remarkable theoretical result, we recently started investigating a possible experimental application of this theory in the context of (non-relativistic) incoherent neutron scattering off atoms and molecules in condensed matter [10]. (in Section 5), we investigate an effect of surface physics, i.e., neutron reflectivity—which is elastic and coherent—from the interface of a single-crystal Si wafer with H2 O-D2 O liquid mixtures These measurements show a striking increased neutron reflectivity in a wide range of momentum transfers, which is tantamount to a momentum transfer deficit with respect to conventional expectations. The present paper does not consider interpretational issues; instead, it proposes a new family of effects related with momentum-energy transfers, contributing to the connection between the “theory”-community and the community of experimental scattering physics
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