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.
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.
Recently, the notions of Weak Measurement (WM), Weak Value (WV) and Two-State-Vector Formalism (TSVF), firstly introduced by Aharonov and collaborators, have extended the theoretical frame of standard quantum mechanics, thus providing a quantum-theoretical formalism for extracting new information from a system in the limit of small disturbance to its state. Here we provide an application to the case of two-body scattering with one body weakly interacting with its environment — e.g. a neutron being scattered from a H 2 molecule physisorbed in a carbon nanotube. In particular, we make contact with the field of incoherent inelastic neutron scattering from condensed systems. We provide a physically compelling prediction of a new quantum effect — a momentum transfer deficit; or equivalently, an enhanced energy transfer; or an apparent reduction of the mass of the struck particle. E.g., when a neutron collides with a H 2 molecule in a C-nanotube and excites its translational motion along the nanotube, it apparently exchanges energy and momentum with a fictitious particle with mass of 0.64 atomic mass units. Experimental results are shown and discussed in the new theoretical frame. The effect under consideration has no conventional interpretation, thus also supporting the novelty of the quantum theoretical framework of WV and TVSF. Some speculative remarks about possible applications being of technological interest (fuel cells and hydrogen storage; Li + batteries; information and communication technology) are shortly mentioned.
Abstract Weak Values (WV) and Two-State-Vector Formalism (TSVF) provide novel insights in various quantum physical and technological fields. In the first part of the paper we consider a new quantum effect of scattering accompanying an elementary collision of two quantum systems A and B, in which the latter interacts with a quantum environment. In clear contrast to a classical environment, the quantum case can exhibit counter-intuitive effects of momentum- and energy-transfer which contradict conventional expectations. Experimental evidence of a new effect—deficit of momentum transfer (equivalently: reduced effective mass) in a neutron-atom collision—is presented and theoretically interpreted. Here, non-relativistic incoherent inelastic neutron scattering (INS) is applied. INS on single H2 molecules confined in multi-walled carbon nanotube channels has been experimentally investigated. Interpreted within conventional theory, the results reveal a counter-intuitive reduced effective mass of the recoiling H2 molecule, i.e. M = 0.64 a.m.u. (atomic mass units). In contrast, this finding has a simple qualitative interpretation within WV and TSVF theory. In the second part of the paper we report on current experimental and theoretical investigations in the field of X-ray diffraction (XRD), which belongs to coherent scattering. Preliminary XRD results from cubic crystalline materials show a surprising variation of the measured lattice parameter (usually called “lattice constant”) with momentum transfer. A first theoretical model of the effect in the light of the new theory is presented. These findings give further evidence for the broad character and significance of the novel WV and TSVF theory.
The concepts of Weak Values (WV) and Two-State Vector Formalism (TSVF) appear to motivate new experiments and to offer novel insights into dynamical processes in various materials of several scientific and technological fields. To support this view, here we consider the dynamics of hydrogen atoms and/or molecules in nanostructured materials like e.g., carbon nanotubes. The experimental method applied is incoherent scattering of thermal (i.e., non-relativistic) neutrons (INS). In short, the main finding consists in the following effect: the measured energy and momentum transfers are shown to contradict even qualitatively the associated expectations of conventional scattering theory. This effect was recently observed in INS experiments, e.g., in H2 adsorbed in carbon nanotubes, where a large momentum transfer deficit was found. Due to the broad abundance of hydrogen, these findings may be also of technological importance, since they indicate a considerably enhanced H mobility in specific structured material environments. A new INS experiment is proposed concerning the H mobility of an ultra-fast proton conductor (H3OSbTeO6) being of technological relevance. Further neutron scattering investigations on other systems (metallic hydrides and H2 encapsulated inside C60) are proposed. As concerns theoretical implications, the analysis of the experimental results strongly supports the view that the wavefunction (or state vector) represents an ontological physical entity of a single quantum system.
The notions of weak measurement, weak value, and two-state-vector formalism provide a new quantum-theoretical frame for extracting additional information from a system in the limit of small disturbances to its state. Here, we provide an application to the case of two-body scattering with one body weakly interacting with an environment. The direct connection to real scattering experiments is pointed out by making contact with the field of impulsive incoherent neutron scattering from molecules and condensed systems. In particular, we predict a new quantum effect in neutron-atom collisions, namely an observable momentum transfer deficit; or equivalently, a reduction of effective mass below that of the free scattering atom. Two corroborative experimental findings are shortly presented. Implications for current and further experiments are mentioned. An interpretation of this effect and the associated experimental results within conventional theory is currently unavailable. Quanta 2016; 5: 61–84.
Current developments of non-relativistic quantum mechanics appear to predict, and reveal, counter-intuitive dynamical effects of hydrogen in nanostructured materials that are of considerable importance for basic research as well as for technological applications. In this review, the experimental focus is on H2O and H molecules in carbon nanotubes and other nanocavities that have been experimentally investigated using the well-established technique of incoherent inelastic neutron scattering (INS). For instance, the momentum and energy transfers, as obtained from the commonly used standard data analysis techniques, from a (I) H2 molecule in a C-nanotube resulting in a roto-translational motion along the nanotube axis seems to (1) either violate the standard conservation laws or (2) to attribute to the H molecule undergoing translation the effective mass a.m.u. (atomic mass units) instead of the expected 2 a.m.u. A similar striking anomalous effect has been found in the neutron-H scattering from the (II) H2O molecules in nano-channels of some solid materials, in which O-H stretching vibrations along the channel axis are created. The results of this scattering process seem to once again either violate the standard conservation laws or to attribute to the effective mass of the struck H2 molecule as a.m.u. instead of the expected value of 1 a.m.u. We show that these counterintuitive observations from the INS studies have no conventional interpretation within the standard non-relativistic scattering theory. However, they can be qualitatively interpreted "from first principles" within the framework of modern theories of (III) time-symmetric quantum dynamics, as provided by the weak values (WV) and two-state- vector formalism (TSVF), and/or (IV) quantum correlations, especially quantum discord (QD) and quantum thermodynamics (QTD). The theoretical analysis provides an intuitive understanding of the experimental results, gives strong evidence that the nano-structured cavities do represent quantum systems which participate significantly in the dynamics of the neutron-H scattering, and, surprisingly, shows that new physical information can be derived from the experimental data. This latter point may also have far-reaching consequences for technology and material sciences (e.g., fuel cells, H storage materials, etc.). Moreover, novel insights into the short-lived quantum dynamics and/or quantum information theory can be gained.
Abstract The conventional theory of non-relativistic neutron beam scattering from many-body systems treats the beam essentially as a classical system, because the neutron dynamical variables are captured in the main theoretical formulas (e.g. time-correlation functions) not as quantum mechanical operators but as c-numbers only. This simplification results in the full decoupling of the probe particles’ dynamics from the quantum dynamics of the scatterer. Further, neutrons’ wavefunctions are represented with plane waves, and thus the concept of neutron’s finite coherence length in momentum space becomes irrelevant. Making contact with modern quantum theoretical approaches (e.g., quantum entanglement, Feynman paths, “which-path information” versus interference, Weak Values theory) new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, such as a surprising intensity deficit in neutron Compton scattering (NCS) of epithermal neutrons from protons of H-containing materials. Here, the NCS-intensity deficit observed in scattering from liquid C6H6 is discussed and interpreted from first principles, in the general frame of Weak Values theory. Moreover, based on Feynman’s didactical argument that there isn’t any interference between distinguishable neutron paths, we show that this NCS-effect cannot be interpreted as being caused by destructive interference of neutron paths scattered from entangled (two or a few) protons, as was earlier proposed by some authors.