The one-dimensional Levinson’s theorem is derived and used to study zero-energy resonances in a double-potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound-state solutions.

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the ‘marginal laws’, in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the presence of entanglement not only at the level of the states, but also at the level of the measurements. However, at the “local” level of a specific joint measurement, a description where entanglement is only incorporated in the state remains always possible, by adopting a fine-tuned tensor product representation. But contextual tensor product representations should only be considered when there are good reasons to describe the outcome-states as (non-entangled) product states. This will not in general be true, hence, the entanglement resource will have to generally be allocated both in the states and in the measurements. In view of the numerous violations of the marginal laws observed in physics’ laboratories, it remains unclear to date if entanglement in micro-physical systems is to be understood only as an ‘entanglement of the states’, or also as an ‘entanglement of the measurements’. But even if measurements would also be entangled, the corresponding violation of the marginal laws (also called ‘no-signaling conditions’) would not for this imply that a superluminal communication would be possible.

The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approaches to the foundations of quantum physics. The deep analogies between the foundations of physics and cognition lead us to investigate the validity of quantum theory as a general and unitary framework for cognitive processes, and the empirical success of the Hilbert space models derived by such investigation provides a strong theoretical confirmation of this validity. However, two situations in the cognitive realm, `question order effects' and `response replicability', indicate that even the Hilbert space framework could be insufficient to reproduce the collected data. This does not mean that the mentioned operational-realistic approach would be incorrect, but simply that a larger class of measurements would be in force in human cognition, so that an extended quantum formalism may be needed to deal with all of them. As we will explain, the recently derived `extended Bloch representation' of quantum theory (and the associated `general tension-reduction' model) precisely provides such extended formalism, while remaining within the same unitary interpretative framework.

An extended Bloch representation of quantum mechanics was recently derived to offer a possible (hidden-measurements) solution to the measurement problem. In this article we use this representation to investigate the geometry of superposition and entangled states, explaining interference effects and entanglement correlations in terms of the different orientations a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), which we show to be particularly suitable for the description of multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description where sub-entities can remain in well-defined states, even when entangled. This means that the completed version of quantum mechanics provided by the extended Bloch representation, where density operators are also considered to be representative of genuine states (providing a complete description), not only offers a plausible solution to the measurement problem but also to the lesser-known entanglement problem. This is because we no longer need to give up the general physical principle saying that a composite entity exists and therefore is in a well-defined state, if and only if its components also exist and therefore are also in well-defined states.

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a conceptuality interpretation about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place.

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.