## Articles

**The Extended Bloch Representation of Quantum Mechanics for Infinite-Dimensional Entities**

*(with Diederik Aerts) - PDF*

**Towards a Quantum World Wide Web**

*(with Diederik Aerts,*

*Jonito Aerts Arguëlles, Lester Beltran,*

*Lyneth Beltran*,

*Isaac Distrito,*

*Sandro Sozzo and*

*Tomas Veloz*

*)*

**Multiplex Realism ***(with Diederik Aerts) **- **To be presented at the 2nd International Congress of Consciousness**, **to be held in Miami, Florida, USA, from May 19th to 21st, 2017**.*

*multiplex realism*, which will be presented and motivated in this article, our three-dimensional Euclidean theater is only one among many theaters that can be conceived and constructed, to stage the whole of our reality. The view of a ‘multiplex reality’ has consequences not only for our understanding of the nature of the physical world, particularly when we consider the relation between classical and non-classical (quantum and relativistic) entities, but also for our understanding of the manifestations of consciousness.

**Context and Interference Effects in the Combinations of Natural Concepts**

*(with Diederik Aerts,*

*Jonito Aerts Arguëlles, Lester Beltran,*

*Lyneth Beltran*,

*Sandro Sozzo and*

*Tomas Veloz*

*)*

*- Submitted to the Tenth International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT-17)*

*-*The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the 'conceptual combinations problem' of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts 'interfere' when they combine to form more complex conceptual entities, and they also exhibit a 'quantum-type context-dependence', which are responsible of the 'over- and under-extension' that are systematically observed in experiments on membership judgments.

**T****esting Quantum Models of Conjunction Fallacy on the World Wide Web ***(with Diederik Aerts, **Jonito Aerts Arguëlles, **Lyneth Beltran*,* Sandro Sozzo and **Tomas Veloz**) - Int. **J . Theor. Phys. *

*doi:10.1007/s10773-017-3288*

*-8*

*(IQSA 2016) -*

The 'conjunction fallacy' has been extensively debated by scholars in cognitive science and, in recent times, the discussion has been enriched by the proposal of modeling the fallacy using the quantum formalism. Two major quantum approaches have been put forward: the first assumes that respondents use a two-step sequential reasoning and that the fallacy results from the presence of 'question order effects'; the second assumes that respondents evaluate the cognitive situation as a whole and that the fallacy results from the 'emergence of new meanings', as an 'effect of overextension' in the conceptual conjunction. Thus, the question arises as to determine whether and to what extent conjunction fallacies would result from 'order effects' or, instead, from 'emergence effects'. To help clarify this situation, we propose to use the World Wide Web as an 'information space' that can be interrogated both in a sequential and non-sequential way, to test these two quantum approaches. We find that 'emergence effects', and not 'order effects', should be considered the main cognitive mechanism producing the observed conjunction fallacies.

**The extended Bloch Representation of Entanglement and Measurement in Quantum Mechanics***(with Diederik Aerts and Sandro Sozzo**)** **- Int. J. Theor. Phys. (2016). doi:10.1007/s10773-016-3257-7 (IQSA 2016) - PDF*

The quantum formalism can be completed by assuming that a density operator can also represent a pure state. An 'extended Bloch representation' (EBR) then results, in which not only states, but also the measurement-interactions can be represented. The Born rule is obtained as an expression of the subjective lack of knowledge about the measurement-interaction that is each time actualized. Entanglement can also be consistently described in the EBR, as it remains compatible with the principle according to which a composite entity exists only if its components also exist, and therefore are in pure states.

**Quantum Cognition Beyond Hilbert Space: Fundamentals and Applications***(with Diederik Aerts, Lyneth Beltran, Sandro Sozzo and Tomas Veloz) - **Quantum Interaction, **L**ecture Notes in Computer Science, Volume 10106, p. 81, 2017;** 10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016, Revised Selected papers, Editors: Jose Acacio de Barros, Bob Coecke, Emmanuel Pothos**. DOI: 10.10007/978-3-319-52289-0 - PDF1 & PDF2 (two-part article on the arXiv)*

The 'quantum cognition' paradigm was recently challenged by its proven impossibility to simultaneously model 'question order effects' and `response replicability'. In the present article we describe sequential dichotomic measurements within an operational and realistic framework for human cognition, and represent them in a quantum-like 'extended Bloch representation', where the Born rule of quantum probability does not necessarily hold. We then apply this mathematical framework to successfully model question order effects, response replicability and unpacking effects, thus opening the way toward `quantum cognition beyond Hilbert space'.

**Theoretical and conceptual analysis of the celebrated 4π-symmetry neutron interferometry experiments***Foundations of Science - First online: 04 March 201**6 - PDF*

In 1975, two experimental groups have independently observed the 4π-symmetry of neutrons' spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach–Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical 4π-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron's phase change, when passing through the magnetic field, is due to a longitudinal Stern-Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is 2π rotated, but strongly indicate that the latter, like any other elementary "particle," would be a genuinely non-spatial entity.

**Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective***(with **Diederik Aerts**) - **International Journal of Quantum Foundations, Vol. 3, Issue 1, January 2017, pp. 1-16* *- PDF *

The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient transactions, no specific mechanism was actually provided to explain why the weights of such symmetry breaking are precisely those given by the Born rule. In other words, PTI, similarly to decoherence theory, provides a physical basis for the transition from a pure state to a fully reduced density matrix state, but doesn't explain a quantum measurement in a complete way. On the other hand, the recently derived extended Bloch representation (EBR) - a specific implementation the HMI - precisely provides such missing piece of explanation, i.e., a qualitative description of the WSB as a process of actualization of hidden measurement-interactions and, more importantly, a quantitative prediction of the values of the associated weights that is compatible with the Born rule of probabilistic assignment. Therefore, from the PTI viewpoint, the EBR provides the missing link for a complete description of a quantum measurement.

**On the Foundations of the Brussels Operational-Realistic Approach to Cognition***(with **Diederik Aerts and Sandro Sozzo**) - Frontiers in Physics 4:17. doi: 10.3389/fphy.2016.00017*

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.

**The GTR-model: a universal framework for quantum-like measurements***(with **Diederik Aerts**) - **In: "Probing the Meaning of Quantum Mechanics. Superpositions, Dynamics, Semantics and Identity.," pp. 91-140. Eds. D. Aerts, C. De Ronde, H. Freytes and R. Giuntini, World Scientific Publishing Company, Singapore (2016) ** - PDF*

We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable fluctuations in the experimental context, in accordance with the 'hidden-measurements interpretation' of quantum mechanics. When the structure of the state space is Hilbertian, and measurements are of the 'universal' kind, i.e., are the result of an average over all possible ways of selecting an outcome, the GTR-model provides the same predictions of the Born rule, and therefore provides a natural completed version of quantum mechanics. However, when the structure of the state space is non-Hilbertian and/or not all possible ways of selecting an outcome are available to be actualized, the predictions of the model generally differ from the quantum ones, especially when sequential measurements are considered. Some paradigmatic examples will be discussed, taken from physics and human cognition. Particular attention will be given to some known psychological effects, like question order effects and response replicability, which we show are able to generate non-Hilbertian statistics. We also suggest a realistic interpretation of the GTR-model, when applied to human cognition and decision, which we think could become the generally adopted interpretative framework in quantum cognition research.

**Beyond-quantum modeling of question order effects and response replicability in psychological measurements***(with **Diederik Aerts**) - Preprint, 2015 - PDF - Submitted to: J. Math. Psychology*

A general tension-reduction (GTR) model was recently considered (Aerts & Sassoli de Bianchi, 2015a,b) to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations, and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in the ambit of quantum models of cognition and decision. Yet, this result also highlighted the possibility of observing violations of the predictions of the Born rule, in those situations where the averaging would not be large enough, or would be altered because of the combination of multiple measurements. In this article we show that this is indeed the case in typical psychological measurements exhibiting question order effects, by showing that their statistics of outcomes are inherently non-Hilbertian, and require the larger framework of the GTR-model to receive an exact mathematical description. We also consider another unsolved problem of quantum cognition: response replicability. It is has been observed that when question order effects and response replicability occur together, the situation cannot be handled anymore by quantum theory. However, we show that it can be easily and naturally described in the GTR-model. Based on these findings, we motivate the adoption in cognitive science of a hidden-measurements interpretation of the quantum formalism, and of its GTR-model generalization, as the natural interpretational framework explaining the data of psychological measurements on conceptual entities.

**The Extended Bloch Representation of Quantum Mechanics. Explaining Superposition, Interference and Entanglement***(with **Diederik Aerts**) - Preprint, 2015 - **PDF - **J. Math. Phys*. *57, 122110 (2016). DOI: 10.1063/1.4973356 *

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

**A possible solution to the second entanglement paradox***(with **Diederik Aerts**) - **In: "Probing the Meaning of Quantum Mechanics. Superpositions, Dynamics, Semantics and Identity.," pp. 351-359. Eds. D. Aerts, C. De Ronde, H. Freytes and R. Giuntini, World Scientific Publishing Company, Singapore (2016) - PDF*

Entangled states are in conflict with a general physical principle which expresses that a composite entity exists if and only if its components also exist, and the hypothesis that pure states represent the actuality of a physical entity, i.e., its `existence'. A possible way to solve this paradox consists in completing the standard formulation of quantum mechanics, by adding more pure states. We show that this can be done, in a consistent way, by using the extended Bloch representation of quantum mechanics, recently introduced to provide a possible solution to the measurement problem. Hence, with the solution proposed by the extended Bloch representation of quantum mechanics, the situation of entangled states regains full intelligibility.

**Do spins have directions?***(with **Diederik Aerts**) - **Soft Computing. **March 2017, Volume 21, Issue 6, pp 1483-1504.** - PDF*

The standard Bloch sphere representation has been recently generalized to describe not only systems of arbitrary dimension, but also their measurements, in what has been called the \emph{extended Bloch representation of quantum mechanics}. This model, which offers a solution to the longstanding measurement problem, is based on the \emph{hidden-measurement interpretation of quantum mechanics}, according to which the Born rule results from our lack of knowledge of the measurement interaction that each time is actualized between the measuring apparatus and the measured entity. In this article we present the extended Bloch model and use it to investigate, more specifically, the nature of the quantum spin entities and of their relation to our three-dimensional Euclidean theater. Our analysis shows that spin eigenstates cannot generally be associated with directions in the Euclidean space, but only with generalized directions in the Blochean space, which apart from the special case of spin one-half entities, is a space of higher dimensionality. Accordingly, spin entities have to be considered as genuine non-spatial entities. We also show, however, that specific vectors can be identified in the Blochean theater that are isomorphic to the Euclidean space directions, and therefore representative of them, and that spin eigenstates always have a predetermined orientation with respect to them. We use the details of our results to put forward a new view of realism, that we call multiplex realism, providing a specific framework with which to interpret the human observations and understanding of the component parts of the world. Elements of reality can be represented in different theaters, one being our customary Euclidean space, and another one the quantum realm, revealed to us through our sophisticated experiments, whose elements of reality, in the quantum jargon, are the eigenvalues and eigenstates. Our understanding of the component parts of the world can then be guided by looking for the possible connections, in the form of partial morphisms, between the different representations, which is precisely what we do in this article with regard to spin entities.

**Fisica quantistica e coscienza: come prenderle sul serio e quali sono le conseguenze?***AutoRicerca, Numero 10, Anno 2015*

In questo articolo presenterò alcune idee di base sulla cosiddetta interpretazione a misure nascoste (hidden-measurement interpretation) della meccanica quantistica, che offre una soluzione al problema della misura senza richiedere l’intervento deus ex machina di un “ego astratto”. In cambio, ci chiede di accettare che la nostra realtà fisica è per lo più non-spaziale, quindi molto più vasta di quanto ci potevamo aspettare sulla base della nostra esperienza ordinaria della stessa. Sottolineerò altresì che, similmente alla meccanica quantistica, i dati oggi a nostra disposizione sui fenomeni psichici e spirituali relativi alla coscienza, se presi sul serio, ci intimano di accettare, anch’essi, l’esistenza di un “altrove” non-spaziale, dove la coscienza è in grado di manifestarsi. In altri termini, sia la fisica quantistica che lo studio della coscienza ci indicano l’esistenza di realtà più dilatate, che si estendono oltre i limiti del nostro teatro spaziale, o spaziotemporale. Ciò non significa, tuttavia, che queste realtà siano necessariamente le stesse, come spesso si ipotizza sulla base di pregiudizi di stampo materialista e riduzionista. In questo articolo spiegherò anche come il nuovo campo di ricerca denominato cognizione quantistica ci ha fornito, inaspettatamente, un modello molto significativo della natura non-spaziale delle entità microscopiche, in quella che è stata definita l’interpretazione concettualistica (conceptuality interpretation) della meccanica quantistica, e come la sorprendente ipotesi alla base di questa nuova interpretazione possa anche far luce sulla natura di quelle realtà non-ordinarie che noi esseri umani siamo in grado di sperimentare quando ci troviamo in stati di coscienza più dilatati.**Taking quantum physics and consciousness seriously: ****What does it mean and what are the consequences?***PDF - To appear in the proceedings of the 1st **International Congress of Conscientiology*

In this article we present some of the foundational ideas of the so-called *hidden-measurement interpretation* of quantum mechanics, whose proposed solution to the measurement problem does not require any *deus ex machina* intervention from an abstract ego, but asks us in exchange to accept that our physical reality is mostly*non-spatial*, and therefore much larger than what we could expect from our ordinary experience of it. We also emphasize that, similarly to quantum mechanics, the data available today from the study of psychic and spiritual phenomena about the consciousness, if taken seriously, require us to accept, as well, the existence of a non-spatial “elsewhere” where the consciousness is able to manifest. In other terms, both quantum physics and consciousness point to the existence of larger realities extending beyond the limits of our spatial theatre. This doesn’t mean, however, that they would necessarily be the same, as is often assumed, due to prejudices rooted in materialism. In this article we also explain how the new research domain called *quantum cognition *has provided us with a new thought-provoking model for the non-spatial nature of the microscopic entities, in what has been called the *conceptuality interpretation* of quantum mechanics, and how the astonishing hypothesis underlying this new interpretation can possibly shed some light also on the nature of those non-ordinary realities that we humans are able to experience when in more expanded states of consciousness.

**Many-Measurements or Many-Worlds? A Dialogue**

*(with*

*Diederik Aerts*

*) - Foundations of Science 20 (2015), pages 399-427*

*-*

Many advocates of the Everettian interpretation consider that their approach is the only one taking quantum mechanics really seriously, and that by doing so a fantastic scenario for our reality can be deduced, made of infinitely many and continuously branching parallel worlds. In this article, written in the form of a dialogue, we suggest that quantum mechanics can be taken even more seriously, if the 'many-worlds' view is replaced by a 'many-measurements' view. In this way, not only the Born rule can be derived, thus solving the measurement problem, but a one-world 'non-spatial' reality can also be deduced, providing an even more fantastic scenario than that of the multiverse.

**The unreasonable success of quantum probability II: Quantum measurements as universal measurements***(with **Diederik Aerts**) - Journal Mathematical Psychology, Volume 67, August 2015, pages 76-90 - **PDF*

In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the rho-model, able to describe general quantum-like measurements with an arbitrary number of outcomes, and we have used it as a general theoretical framework to study the most general possible condition of lack of knowledge in a measurement, so defining what we have called a universal measurement. In this second part, we present the formal proof that universal measurements, which are averages over all possible forms of fluctuations, produce the same probabilities as measurements characterized by uniform fluctuations on the measurement situation. Since quantum probabilities can be proven to arise from the presence of such uniform fluctuations, we have proven that they can be interpreted as the probabilities of a first-order non-classical theory, describing situations in which the experimenter lacks complete knowledge about the nature of the interaction between the measuring apparatus and the entity under investigation. This same explanation can be applied - mutatis mutandis - to the case of cognitive measurements, made by human subjects on conceptual entities, or in decision processes, although it is not necessarily the case that the structure of the set of states would be in this case strictly Hilbertian. We also show that universal measurements correspond to maximally robust descriptions of indeterministic reproducible experiments, and since quantum measurements can also be shown to be maximally robust, this adds plausibility to their interpretation as universal measurements, and provides a further element of explanation for the great success of the quantum statistics in the description of a large class of phenomena.

**The unreasonable success of quantum probability I: Quantum measurements as uniform fluctuations***(with **Diederik Aerts**) - Journal Mathematical Psychology, Volume 67, August 2015, pages 51-75 - **open access*

We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation as it appears in different domains of science - form cognitive science to physics - and use it to explain the emergence of quantum probabilities (the Born rule) as uniform fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states both of the system and the measuring apparatus, in a way that the measurement probabilities can be derived as the Lebesgue measure of suitably defined convex subregions of the simplex under consideration. Although this Lebesgue-model is an abstract construct, it admits physical realizations. In this article we consider a very simple and evocative one, using a material point particle which is acted upon by special elastic membranes, which by breaking and collapsing are able to produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of a measurement process, be it from a measurement associated with a situation in cognitive science or in physics, or in any other domain. We also show that the Lebesgue-model can be further generalized into a model describing conditions of lack of knowledge generated by non-uniform fluctuations, which we call the rho-model. In this more general framework, which is more suitable to describe typical experiments in cognitive science, we define and motivate a notion of universal measurement, describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. And more specifically, also providing a possible explanation for the success of quantum cognition, a research field in cognitive science employing the quantum formalism as a modeling tool. This is the first part of a two-part article. In the second part, the proof of the equivalence between universal measurements and uniform measurements, and its significance for quantum theory as a first order approximation, is given and further analyzed.

**God may not play dice, but human observers surely do***PDF - **Foundations of Science**: Volume 20, Issue 1 (2015), Page 77-105*

We investigate indeterminism in physical observations. For this, we introduce a distinction between genuinely indeterministic (creation-1 and discovery-1) observational processes, and fully deterministic (creation-2 and discovery-2) observational processes, which we analyze by drawing a parallel between the localization properties of microscopic entities, like electrons, and the lateralization properties of macroscopic entities, like simple elastic bands. We show that by removing the randomness incorporated in certain of our observational processes, acquiring over them a better control, we also alter these processes in such a radical way that in the end they do not correspond anymore to the observation of the same property. We thus conclude that a certain amount of indeterminism must be accepted and welcomed in our physical observations, as we cannot get rid of it without also diminishing our discriminative power. We also provide in our analysis some elements of clarification regarding the non-spatial nature of microscopic entities, which we illustrate by using an analogy with the process of objectification of human concepts. Finally, the important notion of relational properties is properly defined, and the role played by indeterminism in their characterization clarified.

**Corrispondenze astrologiche: una prospettiva multiesistenziale***AutoRicerca, **Numero 8**, Anno 2014*

Per alcuni individui l’astrologia sembra costituire un valido strumento di autoricerca e autosviluppo. Eppure, a livello statistico non appare in grado di produrre correlazioni significative. In questo articolo si propone una possibile soluzione di questo apparente paradosso, sulla base del cosiddetto paradigma coscienziale.

**A speculative solution to the astrological paradox***PDF - To be published in the Journal of Consciousness *

So far, astrology has not been able to produce significant statistical correlations. However, certain individuals could use it with some benefit in their self-research and selfdevelopment. In this article, I propose a tentative speculative solution to this paradox, based on the consciential (multidimensional, multimaterialistic) paradigm.

**The Extended Bloch Representation of Quantum Mechanics and the Hidden-Measurement Solution to the Measurement Problem***(with **Diederik Aerts**) - Annals of Physics** 351**, Pages 975–1025 (**2014)* - *PDF** (open access). See also the Erratum, **Annals of Physics** ** 366, 2016, Pages 197–198*

A generalized Poincare-Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it allows to derive the Born rule as an average over hidden-variables, describing not the state of the quantum entity, but its interaction with the measuring system. According to this modelization, a quantum measurement is to be understood, in general, as a tripartite process, formed by an initial deterministic decoherence-like process, a subsequent indeterministic collapse-like process, and a final deterministic purification-like process. We also show that quantum probabilities can be generally interpreted as the probabilities of a first-order non-classical theory, describing situations of maximal lack of knowledge regarding the process of actualization of potential interactions, during a measurement.

**Solving the Hard Problem of Bertrand's Paradox***(with **Diederik Aerts**) - J. Math. Phys. 55, 083503 (2014) - **PDF*

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article we show that Bertrand's paradox contains two different problems: an "easy" problem and a "hard" problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible "ways of selecting" an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible "ways of selecting" an interaction, which we call a 'universal average'. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.

**A remark on the role of indeterminism and non-locality in the violation of Bell's inequality***PDF - **Annals of Physics**, Volume 342, March 2014, Pages 133–142*

Some years ago Aerts et al. presented a macroscopic model in which the amount of non-locality and indeterminism could be continuously varied, and used it to show that by increasing non-locality one increases, as expected, the degree of violation of Bell's inequality (BI), whereas, more surprisingly, by increasing indeterminism one decreases the degree of the violation of BI. In this note we propose a different macroscopic model in which the amount of non-locality and indeterminism can also be parameterized, and therefore varied, and we find that, in accordance with the model of Aerts et al., an increase of non-locality produces a stronger violation of BI. However, differently from their model, we also find that, depending on the initial state in which the system is prepared, an increase of indeterminism can either strengthen or weaken the degree of violation of BI.

**Quantum dice***PDF - **Annals of Physics**, **Volume 336, September 2013, Pages 56–75*

In a letter to Born, Einstein wrote: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the old one. I, at any rate, am convinced that He does not throw dice." In this paper we take seriously Einstein's famous metaphor, and show that we can gain considerable insight into quantum mechanics by doing something as simple as rolling dice. More precisely, we show how to perform measurements on a single die, to create typical quantum interference effects, and how to connect (entangle) two identical dice, to maximally violate Bell's inequality.

**Quantum "fields" are not fields. Comment on "There are no particles, there are only fields," by Art Hobson***PDF - **Am. J. Phys. 81 , 707 (2013)*

We comment on a recent paper by Hobson, explaining that quantum "fields" are no more fields than quantum "particles" are particles, so that the replacement of a particle ontology by an all-field ontology cannot solve the typical interpretational problems of quantum mechanics.

**Elementi teorico-pratici di esplorazione extracorporea**

*AutoRicerca,*

*Numero 5*

*, Anno 2013*

La proiezione della coscienza è un fenomeno naturale, conseguenza della para-anatomia e parafisiologia del nostro olosoma. Scopo principale dello studio di questo fenomeno, e delle tecniche in grado di favorirlo, è poterne assumere il controllo, trasformando quella che solitamente è un’esperienza vissuta in modo inconsapevole in un’esperienza pienamente lucida e rimembrata. In questo modo, non solo possiamo sollevare un lembo del grande velo, che non ci consente di scorgere la natura propriamente multidimensionale e multiesistenziale della nostra esistenza, ma altresì possiamo accedere a informazioni di prima mano circa la nostra storia personale, gli obiettivi che ci siamo prefissati quando abbiamo deciso di assumere questo corpo fisico, su questo specifico pianeta, e la natura della realtà entro la quale, da tempi immemori, ci evolviamo. In questo lavoro presenteremo in modo sintetico, ma nondimeno completo, le principali informazioni disponibili sull’argomento della proiezione della coscienza, così da offrire al lettore uno strumento teorico-pratico che gli consenta di avvicinarsi con conoscenza di causa e discernimento all’esplorazione di questo importante tema dell’autoricerca, al di fuori dei dogmatismi religiosi e dei riduzionismi della visione monomaterialista della scienza contemporanea.

**Subtle energies or subtle matters? A conceptual clarification **

*Journal of Conscientiology, Volume 16, Issue 55, July 2013 - PDF*

The concept of energy is central in all of modern science, and is obviously of great importance also in the study of the psychoenergetic phenomena. However, both among conventional physicists and less conventional researchers of parapsychic phenomena, there still is some confusion about a proper understanding of this concept. The purpose of the present article, mainly educational in nature, is to provide a correct interpretation of the concept of energy, and of its transport in the different physical systems. This is in order to facilitate the formulation of scientifically well-posed questions, especially in the study of the energetic dynamics associated to the still controversial subtle paramatters.**Energie sottili o materie sottili?** **Una chiarificazione concettuale***Autoricerca, **Numero 6**, Anno 2013*

Il concetto di energia è centrale in tutta la scienza moderna, ed è ovviamente di grande rilevanza anche nello studio dei fenomeni psicoenergetici. D’altra parte, sia tra i fisici convenzionali che tra gli studiosi dei fenomeni parapsichici, permangono alcune confusioni circa una corretta comprensione di questo concetto. Scopo del presente articolo, essenzialmente di natura didattica, è quello di fornire una corretta interpretazione del concetto di energia, e del suo trasporto nei diversi sistemi fisici. Questo alfine di favorire la formulazione di domande scientificamente ben poste, soprattutto nello studio delle dinamiche energetiche che riguardano le controverse paramaterie di natura più sottile.

**Quantum measurements are physical processes. Comment on "Consciousness and the double-slit interference pattern: Six experiments," By Dean Radin et al.***PDF** - **Physics Essays**, March issue, Vol. 26, No. 1 (2013) *

The validity of the assertion that some recent double-slit interference experiments, conducted by Radin et al., would have tested the possible role of the experimenter's mind in the collapse of the quantum wave function, is questioned. It is emphasized that quantum mechanics doesn't need any psychophysical ingredient to explain the measurement processes, and therefore parapsychologists shouldn't resort to the latter to support the possibility of psychokinesis, but search for more convincing explanations.

**Using simple elastic bands to explain quantum mechanics: a conceptual review of two of Aerts' machine-models***PDF - * *Central European Journal of Physics**, Volume 11, Issue 2, pp 147-161 (2013)*

From the beginning of his research, the Belgian physicist Diederik Aerts has shown great creativity in inventing a number of concrete machine-models that have played an important role in the development of general mathematical and conceptual formalisms for the description of the physical reality. These models can also be used to demystify much of the strangeness in the behavior of quantum entities, by allowing to have a peek at what's going on - in structural terms - behind the "quantum scenes," during a measurement. In this author's view, the importance of these machine-models, and of the approaches they have originated, have been so far seriously underappreciated by the physics community, despite their success in clarifying many challenges of quantum physics. To fill this gap, and encourage a greater number of researchers to take cognizance of the important work of so-called *Geneva-Brussels school*, we describe and analyze in this paper two of Aerts' historical machine-models, whose operations are based on simple breakable elastic bands. The first one, called the *spin quantum-machine*, is able to replicate the quantum probabilities associated with the spin measurement of a spin-1/2 entity. The second one, called the \emph{connected vessels of water model} (of which we shall present here an alternative version based on elastics) is able to violate Bell's inequality, as coincidence measurements on entangled states can do.

**The observer effect**

*PDF -*

*Foundations of Science*

*, June issue, Volume 18,*

*Issue 2*

*, pp 213-243 (*

*2013)*

Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; in the first case, it is a purely invasive process, which can involve either creation or destruction aspects. An entity can also be observed with or without a full control over the observational process. In the latter case, the observation can be described by a symmetry breaking mechanism, through which a specific deterministic observational process is selected among a number of potential ones, as explained in Aerts' hidden measurement approach. This is what is called a product test, or product observation, whose consequences are that outcomes can only be predicted in probabilistic terms, as it is the case in typical quantum measurements. We also show that observations can be about intrinsic (stable) properties of the observed entity, or about relational (ephemeral) properties between the observer and observed entities; also, they can be about intermediate properties, neither purely classical, nor purely quantum. Our analysis allows us to propose a general conceptual characterization of quantum measurements, as observational processes involving three aspects: (1) product observations, (2) pure creation aspects and (3) ephemeral relational properties. We also discuss the important concept of non-spatiality and emphasize some of the differences and similarities between quantum and classical/relativistic observations.

**The delta-quantum machine, the k-model, and the non-ordinary spatiality of quantum entities***PDF - **Foudations of Science**, March issue, Volume 18, Issue 1, pp 11-41 (2013)*

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts' creation-discovery view and hidden measurement approach: a fundamental explanatory framework whose importance, in this author's view, has been seriously underappreciated by the physics community, despite its success in clarifying many conceptual challenges of quantum physics. Secondly, it aims to introduce a new quantum-machine - that we call the delta-quantum-machine - which is able to reproduce the transmission and reflection probabilities of a one-dimensional quantum scattering process by a Dirac delta-function potential. The machine is used not only to demonstrate the pertinence of the above mentioned explanatory framework, in the general description of physical systems, but also to illustrate (in the spirit of Aerts' epsilon-model) the origin of classical and quantum structures, by revealing the existence of processes which are neither classical nor quantum, but irreducibly intermediate. We do this by explicitly introducing what we call the k-model and by proving that its processes cannot be modelized by a classical or quantum scattering system. The third purpose of this work is to exploit the powerful metaphor provided by our quantum-machine, to investigate the intimate relation between the concept of potentiality and the notion of non-spatiality, that we characterize in precise terms, introducing for this the new concept of weak actuality.

**Parapsychology needs paraphysics***Journal of Nonlocality**, Vol. II, Nr. 1, June 2013*

I have been invited to participate in a multi-disciplinary dialogue on the experimental evidence for nonlocal bio-communication, its emergent characteristics, impact on mainstream sciences and future research directions. In that ambit, I have more specifically commented a key question addressed by physicist Jean Burns, regarding the possibility of using what we already know from physics to explain the available abundant evidence that ESP can travel without apparently any physical signal to carry it. My suggestioni is that, most probably, such explanation will not come from physics, but from *paraphysics*.

**Searching, researching, self-researching... ***Journal of Consciousness**, Volume 14, Issue 52, Page 75 - January 2012 - **PDF*

The main scope of this essay is to inform the new generations of scientific researchers about the possibility of adopting a new integral approach in science, which is the one of scientific self-research. By doing so, I will also explain why self-research is still not promoted on a large scale on this planet, despite being a key element in the construction of a more advanced, self-aware and peaceful humanity.**Cercare, ricercare, autoricercare...**

*AutoRicerca,*

*Numero 4*

*, Anno 2012*

Scopo principale di questo articolo, scritto in uno stile informale, è quello di informare le nuove generazioni di ricercatori circa la possibilità di adottare un approccio nuovo – e allo stesso tempo assai antico – alla conoscenza: l’

*autoricerca*. Nel fare questo, tenterò di spiegare non solo cosa sia l’autoricerca, ma anche perché tale disciplina non sia ancora oggi promossa su vasta scala sul nostro pianeta, nonostante la sua importanza strategica nel costruire una società umana più avanzata, consapevole e pacifica.

**L’arte dell'osservazione nella ricerca interiore***AutoRicerca, **Numero 3**, Anno 2012*

We present a step by step introduction to the notion of time-delay inclassical and quantum mechanics, with the aim of clarifying its foundation at aconceptual level. In doing so, we motivate the introduction of the concepts of"fuzzy" and "free-flight" sojourn times, that we use to provide the mostgeneral possible definition for the quantum time-delay, valid for simple andmultichannel scattering systems, with or without conditions on the observationof the scattering particle, and for incoming wave packets whose energy can besmeared out or sharply peaked (fixed energy). We conclude our conceptualanalysis by presenting what we think is the right interpretation of theconcepts of sojourn and delay times in quantum mechanics, explaining why, inultimate analysis, they shouldn't be called "times".*In questo lavoro presentiamo alcuni elementi di base dell’arte osservativa, così come descritti ed esplorati nel corso di un seminario teorico-pratico tenutosi presso il “Laboratorio di Autoricerca di Base” (**www.autoricerca.ch**), nei giorni 8-9 ottobre 2011. A sua volta, il presente scritto trae buona parte della sua ispirazione da quanto è stato presentato da Walter Ferrero e Andrea di Terlizzi nel coso del loro “Laboratorio sperimentale di tecnologia interiore,” tenutosi a Tropolach – Carinzia, nei giorni 17-21 novembre 2010. Ogni errore tecnico, o di interpretazione, delle idee qui esposte è da imputare unicamente allo scrivente, e non ai summenzionati autori. Il lettore è incoraggiato ad approfondire tali idee non solo prendendo conoscenza dei testi originali (vedi bibliografia), ma anche partecipando ai numerosi seminari formativi proposti dai summenzionati autori, nell’ambito della loro accademia per lo sviluppo del potenziale umano (**www.accademiahorus.it**).*

**Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition***PDF - **Central European Journal of Physics**, Vol. 10, No. 2, pp. 282–319 (2012)*

We present a step by step introduction to the notion of time-delay inclassical and quantum mechanics, with the aim of clarifying its foundation at aconceptual level. In doing so, we motivate the introduction of the concepts of"fuzzy" and "free-flight" sojourn times, that we use to provide the mostgeneral possible definition for the quantum time-delay, valid for simple andmultichannel scattering systems, with or without conditions on the observationof the scattering particle, and for incoming wave packets whose energy can besmeared out or sharply peaked (fixed energy). We conclude our conceptualanalysis by presenting what we think is the right interpretation of theconcepts of sojourn and delay times in quantum mechanics, explaining why, inultimate analysis, they shouldn't be called "times".

**From permanence to total availability: a quantum conceptual upgrade***PDF - **Foundations of Science**, Vol. 17, Issue 3, pp. 223-244 (2012)*

We consider the classical concept of time of permanence and observe that itsquantum equivalent is described by a bona fide self-adjoint operator. Itsinterpretation, by means of the spectral theorem, reveals that we have toabandon not only the idea that quantum entities would be characterizable interms of spatial trajectories but, more generally, that they would possess thevery attribute of spatiality. Consequently, a permanence time shouldn't beinterpreted as a "time" in quantum mechanics, but as a measure of the totalavailability of a quantum entity in participating to a creative process ofspatial localization.

**Ephemeral properties and the illusion of microscopic particles***PDF - **Foundations of Science**, Vol. 16, Issue 4, pp. 393-409 (2011)*

Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of non-spatial and non-local entities.*Versione Italiana: AutoRicerca, **Numero 2**, Anno 2011*

Fondando la nostra analisi sull’approccio alla meccanica quantistica della scuola di Ginevra-Brussel, ci lasceremo guidare da alcuni esempi di oggetti macroscopici convenzionali, alfine di chiarire il contenuto di due importanti risultati dell’inizio del ventesimo secolo: il criterio di realtà di Einstein-Podolsky-Rosen e il principio di indeterminazione di Heisenberg. Combinando questi due risultati, mostreremo che la credenza diffusa nell’esistenza delle particelle microscopiche è solo il risultato di un’illusione cognitiva, in quanto le particelle microscopiche non sono particelle, bensì la manifestazione spaziale e locale, di natura effimera, di entità non-spaziali e non-locali.

**Comment on "The quantum mechanics of electric conduction in crystals," by R. J. Olsen and G. Vignale***PDF** - Am. J. Phys. 79, p. 546-549, 2011*

In this note we use the notion of time-delay to explain the physical content of the transformation properties of the transmission and reflection amplitudes, as a result of a displacement of the potential. We then reconsider the derivation in the above mentioned paper of Olsen and Vignale, to obtain the condition for total reflection, in the limit of an infinite number of cells composing the finite-periodic potential. In doing so, we also obtain an expression of Hartman's effect, showing that the group velocity of the transmitted particle inside the chain can become arbitrary large, as the number of cells tends to infinity. [*See also the **reply** of the authors*]

After having emphasized some fundamental analogies between Yoga and Conscientiology, we propose to combine the practice of a specific pranayama, called *Circular Breathing* (CB), with the technique of the *Voluntary Energetic Longitudinal Oscillation* (VELO), to promote a procedure as gradual and effective as possible in achieving the*Vibrational State* (VS). We also present an ultra simplified mechanical model, to highlight a possible mechanism underlying the functioning of these particular energetic (inner) technologies.

O artigo destaca algumas analogias fundamentais entre o Yoga e a Conscienciologia e, em seguida, propõe a combinação da prática de um *pranayama* específico, chamado *Respiração Circular* (RC), com a técnica da *Oscilação Longitudinal Voluntária das Energias* (OLVE), a fim de oferecer um procedimento o mais gradual e efetivo possível para se alcançar o *Estado Vibracional* (EV). O artigo também apresenta um modelo mecânico ultrassimplificado para ilustrar o mecanismo subjacente ao funcionamento de tais tecnologias energéticas pessoais específicas.**Dal pranayama dello Yoga all’OLVE della Coscienziologia: proposta per una tecnica integrativa**

*AutoRicerca,*

*Numero 1*

*, Anno 2011*

Dopo aver tracciato alcuni paralleli fondamentali tra Yoga e Coscienziologia, proponiamo di combinare la pratica di uno specifico pranayama, detto della Respirazione Circolare (RC), con la tecnica dell’Oscillazione Longitudinale Volontaria delle Energie (OLVE); questo alfine di promuovere un procedimento che sia il più possibile graduale ed efficace per il raggiungimento dello Stato Vibrazionale (SV). Presenteremo altresì un modello ultra semplificato, in grado di suggerire un possibile meccanismo alla base del funzionamento di queste particolari tecniche respiratorie ed energetiche.

**Comment on “Generalized composition law from 2x2 matrices," by R. Giust, J.-M. Vigoureux, and J. Lages***Am. J. Phys. **78**, p. 645-646, 2010*

We point out that the result derived by R. Giust, J.-M. Vigoureux, and J. Lages was previously obtained by different authors and different methods, in a more compact form, and comment on the utility of the factorization formula in relation to Levinson's theorem.

**Comment on a letter by David Lindsay, addressing Massimiliano Sassoli de Bianchi's two-parts paper "A Dialogue About Science, Reality and the Consciousness" **

*-*

*Journal of Consciousness*

*, Vol. 12, No. 45, July 2009*

I reply to an interesting letter from David Lindsay, about the content of the mentioned paper, particularly for what concerns his proposal of a direct observation of the process of materialization of microscopic entities, by means of specifically designed OBE experiments.

**Interdimensional Energy Transfer: a Simple Mass Model***PDF** - **Journal of Consciousness**, Vol. 11, No. 43, 2009*

A simple mass model is presented to explain the energetic separation between the physical and extraphysical dimensions. The model is also used to understand the function of the holochakra as a mediator structure which can considerably increase the efficiency of interdimensional energy transfer.

Um modelo simples de massa é apresentado para explicar a separação energética entre a dimensão intrafísica e a dimensão extrafísica. O modelo é utilizado para entender a função do holochacra como estrutura intermediadora, que pode aumentar consideravelmente a eficiência da transferência energética interdimensional.

**Trasferimento interdimensionale di energia: un modello semplice di massa***Autoricerca, **Numero 6**, Anno 2013*

Un semplice modello di massa viene presentato per spiegare la separazione energetica tra la dimensione fisica e le dimensioni extrafisiche. Il modello può essere utilizzato anche per comprendere il funzionamento dell’olochakra (energosoma), nel suo ruolo di struttura mediatrice in grado di accrescere considerevolmente l’efficienza del trasferimento energetico interdimensionale.

**Comment on “The role of mediation in collisions and related analogs,” by E. Bashkansky and N. Netzer***PDF** - Am. J. Phys. 75, p. 1166, 2007*

We show that the result derived by Bashkansky and Netzer is more general and not limited to the specific choice of a geometric sequence chosen for the mediator masses.

**A Dialogue About Science, Reality and the Consciousness – Part II***Journal of Consciousness, **Vol. 9, No. 34, 2006*

This paper is the continuation and conclusion of a Socratic dialogue between a lecturer and a student, whose first part appeared in the previous issue of the *J*of*C* (Sassoli de Bianchi, 2007). In a non-technical style, the dialogue presents some elements for a general and operational description of reality. In this second part, the reader is introduced to concepts such as: *separation, existence, possibility, personal reality* and *personal experience, creation* and *discovery, time, change* and *permanence, structure* and *complexity, distinction* and *connection*, and many others as well. The role played by these concepts in our understanding of reality and the consciousness is explored.

Este artigo é a continuação e conclusão do diálogo socrático entre professor e aluno, cuja primeira parte foi publicada na edição prévia do JofC (Sassoli de Bianchi, 2007). Escrito em estilo não técnico, o diálogo apresenta alguns elementos para a descrição geral e operacional da realidade. Nesta segunda parte, alguns conceitos serão introduzidos ao leitor. São eles: separação, existência, possibilidade, realidade pessoal e experiência pessoal, criação e descoberta, tempo, mudança e permanência, estrutura e complexidade, distinção e conexão, dentre outros. Será também explorado o papel destes conceitos na compreensão sobre realidade e consciência.

*Italian version: AutoRicerca, Numero 7, Anno 2014*

**A Dialogue About Science, Reality and the Consciousness – Part I***Journal of Consciousness, **Vol. 9, No. 33, 2006*

This paper is written as a Socratic dialogue between a lecturer and a student. In a non-technical style, it presents some elements for an operational description of reality. Following a brief introductory discussion about the main characterizing ingredients of a scientific approach to reality, the reader is introduced to a number of important, but unexpectedly puzzling, concepts which are at the roots of our scientific language. More specifically, using a number of simple examples, the dialogue explores the meaning of concepts such as: *experimental test, property, attribute, actuality *and* potentiality, entity, state, certainty, identity, evolution, classical *and* quantum probabilities, energy, space *and* non-locality,* and many others as well. The old questions of determinism and dualism will also be addressed, and the role played by the participatory consciousnesses in our operational understanding of reality considered

*experimental test, property, attribute, actuality*and

*potentiality, entity, state, certainty, identity, evolution, classical*and

*quantum probabilities, energy, space*and

*non-locality,*and many others as well. The old questions of determinism and dualism will also be addressed, and the role played by the participatory consciousnesses in our operational understanding of reality considered.

Este artigo foi escrito como o diálogo Socrático entre professor e aluno. Escrito em estilo não-técnico, apresenta alguns elementos para a descrição operacional da realidade. Seguindo uma breve discussão introdutória sobre os principais ingredientes relacionados à abordagem científica da realidade, é introduzida ao leitor uma série de importantes, mas inesperadamente enigmáticos, conceitos que estão nas raízes da linguagem científica. Mais especificamente, usando uma série de simples exemplos, o diálogo explora a definição de conceitos tais como: teste experimental, propriedade, atributos, atualidade e potencialidade, entidade, estado, certeza, identidade, evolução, probabilidades clássicas e quantum, energia, espaço e nãolocalidade dentre outros. A velha questão do determinismo e dualismo será abordada, sendo considerado o papel representado pela consciência participativa no entendimento operacional da realidade.

*Part I and Part II of this long article have been republished in book form. To purchase the printed version of the book, click*

*here*

*. To purchase the electronic version, click*

*here*

*.*

*Italian version: AutoRicerca, Numero 7, Anno 2014*

**Comment on "The Quest for Proof of Out-of-Body Experiences and Allied Phenomena," by Michael Ross***PDF** **- **Journal of Consciousness, Vol. 8, No. 29, July 2005*

In his article, Michael Ross invited us to consider the following question: “Why are OBE’s (and psychic/spiritual events and talents in all their manifestations) so difficult to empirically prove under scientifically valid conditions?”. Ross presents possible answers to his interrogative, asking the readers to respond and share their opinions. This is precisely what I try to do in this comment of mine.

**Theorice and the global structure of the evolving reality***PDF** - Journal of Consciousness**, Volume 8, No. 29, July 2005*

This article is a conceptual speculative statement about the origin and structure of our reality. We propose to view the consciousnesses’ holosomas as living holotheories of reality, evolving through the instrument of theorice and producing a fractal structuring of reality as a whole. We hypothesised that the fractal structuring process is responsible, through the phenomenon of morphoconnection, for the condition of cosmoconsciousness. The concept of cosmocompletism is introduced and its consequences for a global evolutionary scenario discussed.**Speculazioni su origine e struttura del reale***AutoRicerca, **Numero 4**, Anno 2012*

In questo lavoro presentiamo una tesi speculativa su origine e struttura della nostra realtà. Equiparando gli *olosomi* delle coscienze a delle *oloteorie* viventi della realtà, in grado di evolversi per mezzo dello strumento della *teatica* (teoria + pratica), deduciamo l’esistenza di un processo di *frattalizzazione* in atto del reale, che sarebbe all’origine della condizione di *cosmocoscienza*. Introduciamo inoltre i concetti di *morfoconnessione* e *cosmocompletismo*, e discutiamo della loro rilevanza nell’ambito di uno scenario evolutivo globale.

**A Simple semiclassical derivation of Hartman’s effect***PDF** - Eur. J. Phys., 21, 2000, pp. L1-L4*

We present a very simple semiclassical derivation of Hartman's effect valid for potential barriers of general shape. The derivation also gives some insight into the tunnelling time phenomenon.

**A remark on the high-energy limit of the one-dimensional scattering problem with position dependent mass***(with M. Di Ventra) - Solid State Communications., **106**, No. 5, 1998, pp. 249-251*

We show that, contrary to what would be expected on the basis of the mass barrier model, the transmission probability for the one-dimensional scattering problem with position-dependent mass normally tends to unity as energy goes to infinity, provided the mass is a continuous function of position.

**Comment on "Factorization of scattering matrices in one-dimensional Schrödinger-type equations" by T. Aktosun, M. Klaus, and C. van der Mee***PDF** - J. Math. Phys., **38**, 1997, pp. 4882-4883*

We point out a recent proof of the factorization formula using an adaptation of the variable phase method, and present a third alternative proof that uses integral equations instead of Schroedinger differential equations.

**On the One-Dimensional Scattering by Time-Periodic Potentials: General Theory and Application to Specific Models***(with D. Saraga) - PDF - Helv. Phys. Acta 70, 1997, pp. 751-779*

A comprehensive introduction to the basic formalism of the one-dimensional scattering by time-periodic short-ranged potentials is presented. The fundamental objects of the theory (transmission and reflexion probabilities, sidebands and time delays) are defined, and a generalized Born expansion derived. Particular emphasis is given to the connection between the time-dependent approach and the quasi-stationary one. In particular, the independence of the scattering process of the choice of time-origin, in the limit of a monoenergetic wave packet, is clearly established. The generalized Born expansion is applied to two archetypical models: the square barrier with modulated height (the celebrated Büttiker-Landauer model) and the square barrier with oscillating position. For these two models, the full transmission probability is calculated up to the first non-vanishing correction in the time-dependent perturbation.

**Dynamical capture in quantum mechanics***(with Ph. A. Martin) - **PDF** - J. Phys. A: Math. Gen., **30**, 1997, pp. 1011 - 1015*

Using simple time-dependent methods, we study the phenomenon of dynamical capture in non relativistic quantum mechanics. We show that for time-dependent potentials asymptotically constant in time, the probability for an incoming particle to be trapped in the interaction region is in general non-zero. Capture in a stationary beam is also discussed.

**Quelques aspects de la diffusion quantique: temps de retard, théorème de Levinson et potentiels dépendant du temps (PhD thesis)***PDF** - Thèse N° 1438 (1995) présentée au département de physique (EPFL), pour l’obtention du grade de docteur ès sciences*

In this Thesis we study several aspects of potential scattering in non-relativistic quantum mechanics. In the first part, we study the concept of time delay. More precisely, after an elementary introduction to the theory (chapter I), we clarify in chapter II the role played by the localizing regions in the definition of global time delay. In chapter III, we generalize the concept to arbitrary conditions of observation for the scattered particle (conditional time delay). In chapters IV and V, we address the problem of the measure of time delay by physical clocks and, more specifically, by the Larmor clock which exploit the mechanism of precession of a spin in a magnetic field. In the second part, we are interested in the spectral property of time delay, its connection with Levinson's theorem, and the application of the latter to one-dimensional systems. We derive Levinson's theorem in chapter VI, using as a single ingredient the completeness of physical states. In chapter VII, we apply Levinson's result to determine the number of bound-states of a finite periodic potential, as a function of its period. For this, we use the the factorization property of the scattering matrix which we derive in chapter VIII in the more general situation of a particle with position-dependent mass. In the third part, we are concerned by time-dependent potentials. In chapter IX, we generalize the concept of time delay, and for the particular case of a periodic variation we derive a Levinson theorem. In chapter X, we consider potentials with very slow or very rapid variations in time. The low and high frequency limits are derived as well as their first corrections, and their physical significance discussed.

Dans cette thèse on aborde divers aspects de la diffusion par potentiel en mécanique quantique non-relativiste. Dans la première partie, nous étudions le concept de temps de retard. Plus précisément, après une introduction élémentaire à la théorie (chapitre I), nous clarifions au chapitre II le rôle joué par les régions de localisation dans la définition du temps de retard global. Au chapitre III, nous généralisons le concept à des conditions d'observation arbitraires pour la particule diffusée (temps de retard conditionnel). Aux chapitres IV et V, nous abordons le problème de la mesure du temps de retard par des horloges physiques et, plus particuliérement, par l'horloge de Larmor qui exploite le mécanisme de précession d'un spin dans un champ magnétique. Dans la deuxième partie nous nous intéressons à la propriété spectrale du temps de retard, à son lien avec le théorème de Levinson, et à l'application de ce dernier à des systèmes unidimensionnels. Nous dérivons le théorème de Levinson au chapitre VI, en utilisant comme seul ingrédient la complétude des états physiques. Au chapitre VII, nous appliquons le résultat de Levinson pour déterminer le nombre d'états liés d'un potentiel périodique fini, enfonction de sa période. Pour cela, nous utilisons la propriété de factorisation de la matrice de diffusion que nous dérivons au chapitre VIII dans le cadre plus général d'une particule avec masse dépendante de la position. Dans la troisième partie, nous sommes concernés par les potentiels dépendant du temps. Au chapitre IX, nous généralisons le concept de temps de retard, et pour le cas particulier d'une variation périodique nous dérivons un théorème de Levinson. Au chapitre X, nous considérons des potentiels qui varient très lentement ou très rapidement au cours du temps. Les limites basse et haute fréquence sont dérivées ainsi que les premières corrections, et leur interprétation physique est discutée.

**Levinson's theorem for time-periodic potentials***(with Ph. A. Martin) - **PDF** - Europhys. Lett., 34 (9), 1995, pp. 639 - 643*

Levinson's theorem is generalized to quantum scattering with time-periodic potentials. The zero-energy limit of the phase shift in the elastic channel is linked to the number of bound (cyclic) states of the time-dependent potential by the same relation as in the static case.

**How many bound-states does a one-dimensional finite superlattice have?***(with **M. Di Ventra**) - Superlattices and Microstructures, 20, No 2, 1996, pp. 149-153*

We give a simple and general description of the bound-state structure of a one-dimensional finite superlattice as a function of its period d and some quantities characterizing the single unit cell*.*

**Differential équations and factorization property for the one-dimensional Schrödinger equation ****with position-dependent mass***(with **M. Di Ventra**) - Eur. J. Phys. **16**, 1995, pp. 260 - 265*

The variable phase method is applied to the one-dimensional Schrödinger equation with position-dependent (effective) mass, to derive first-order differential equations for the transmission and reflection amplitudes, and bound-state energies, which are particularly convenient for numerical computations. When the mass and potential have the same asymptotic at both ends of the real line, the method also allows to prove a factorization property of the scattering matrix.

Il metodo della fase variabile è applicato all’equazione di Schrödinger unidimensionale, con massa (efficace) dipendente dalla posizione, allo scopo di derivare equazioni differenziali del primo ordine per le ampiezze di trasmissione, riflessione e per le energie degli stati legati, che siano particolarmente adatte per calcoli numerici. Per una massa ed un potenziale aventi lo stesso andamento asintotico a destra e a sinistra, il metodo permette anche di dimostrare una proprietà di fattorizzazione della matrice di diffusione.

**On the low- and high-frequency limit of quantum scattering by time-dependent potentials***(with Ph. A. Martin) - **PDF** - J. Phys. A, **28**, 1995, pp. 2403-2427*

Using time-dependent methods, we study the scattering of a quantum mechanical particle by short-range potentials with very slow or very fast periodic variations in time. The low- and high-frequency limits are derived as well as their first non-vanishing corrections, and their physical significance discussed.

**On the number of states bound by one-dimensional finite periodic potentials***(with **M. Di Ventra**) - PDF - J. Math. Phys., 36, 1995, pp. 1753-1764*

Bound-states and zero-energy resonances of one-dimensional finite periodic potentials are investigated, by means of Levinson's theorem. For finite range potentials supporting no bound states, a lower bound for the (reduced) time delay at threshold is derived.

**Spin precession revisited***(with Ph. A. Martin) - **PDF** - Found. Phys., **24**, 1994, pp. 1371-1378*

The passage of a spin 1/2 neutral particle through a region of uniform magnetic field and the corresponding precession mechanism is analyzed from the view point of scattering theory, with particular consideration on the role of the field boundaries.

**Levinson's theorem, zero-energy resonances, and time delay ****in one-dimensional scattering systems***PDF - J. Math. Phys., 35, 1994, pp. 2719-2733*

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, we show that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound-state solutions.

**Conditional time-delay in scattering theory**

*PDF - Helv. Phys. Acta 66, 1993, pp. 361-377*

We give a general and mathematically precise definition of the notion of conditional time delay in scattering theory i.e., a notion of time delay for a given condition of observation of the scattered particle. A formula, generalizing the Eisenbud-Wigner time delay formula, is derived. The basic concept entering in the definition of the conditional time delay is that of conditional sojourn time. Although conditional sojourn times cannot be uniquely defined in quantum mechanics because of the uncertainty principle, we show that conditional time delays admit a well defined probabilistic interpretation in the limit of infinitely extended spatial regions. Some comments are presented in relation with the tunneling time problem.

**On the definition of time-delay in scattering theory** *(with Ph. A. Martin) - PDF - Helv. Phys. Acta 65, 1992, pp. 1119-1126*

We show that the time delay of a scattering process, defined as the difference of interacting and free sojourn times for increasing spatial regions, can only exist for sequences of dilated balls. The transformation properties of the Eisenbud-Wigner formula under translations are discussed.

**On the theory of the Larmor clock and time-delay** *(with Ph. A. Martin) - **PDF** - J. Phys. A, 25, 1992, pp. 3627-3647*

Using the time dependent scattering theory we prove that, in any spatial dimension and for arbitrary spin, the reading of the Larmor clock agrees with the global (Eisenbud-Wigner) time delay in the limit of an infinitesimal magnetic field. We show that convergence is also achieved at fixed energy (without oscillating terms) in the limit where the spatial switching on of the field occurs on distances much larger than the de Broglie wave length of the particle. Finally, we investigate the functioning of the spin clock beyond the linear response regime.