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# Divergence from “neutral” to “absorbent” states with a number of experimenters ≥ 2. Small changes in the probability of concordant pairs (related to microscopic random fluctuations) have crucial consequences if the number of experimenters who do the same experiment is ≥ 2. The elementary change of probability of concordant pairs is very -15 small in this simulation: from –0.5 to +0.5 × 10 (the smallest

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In previous articles, we proposed to describe the results of Benveniste’s experiments using a theoretical framework based on quantum logic. This formalism described all characteristics of these controversial experiments and no paradox persisted. This interpretation supposed to abandon an explanation based on a classical local causality such as the...

## Contexts in source publication

**Context 1**

... same calculation is repeated several times by reinjecting at each step the updated common probability of A and B. In Figure 4, the evolution of Pquant (ACP) is shown after several calculation steps with a very small random variation of Pquant (ACP) at each step ([-0.5; 0.5] × 10 -15 ). ...

**Context 2**

... × 10 -15 ). We see that a divergence occurs after several iterations with two possible outcomes: all pairs are concordant with Pquant (ACP) = 1 or all pairs are discordant with Pquant (ACP) = 0. Therefore, the probability amplitudes associated with each state of A (or B, C, etc) dramatically change during joint observations with other experimenters Eq. 4 can be easily adapted for three or more experimenters and the divergence occurs after a lower number of iterations when the number of experimenters increases (Figure 4). If many teams of two, three or more experimenters perform the experiments, the overall mean of probability for concordant pairs remains equal to 0.5, but two populations appear: experimenters X with Pquant (XCP) = 1 and experimenters Y with Pquant (YCP) = 0. ...

**Context 3**

... many teams of two, three or more experimenters perform the experiments, the overall mean of probability for concordant pairs remains equal to 0.5, but two populations appear: experimenters X with Pquant (XCP) = 1 and experimenters Y with Pquant (YCP) = 0. In other words, the random outcomes of concordant pairs and discordant pairs are distributed in two populations of experimenters: those who "turn down" and those who "turn up" as depicted in Figure 4. However, for symmetry reasons, nothing in the formalism allows choosing one of the two solutions for a given team of experimenters. ...

**Context 4**

... a single observer, there is no significant change of the probability of concordant pairs; for each sample that is observed by a "neutral" experimenter, the probabilities to be associated with concordant or discordant pairs are equal and each reduced state is obtained randomly (Figure 4). Indeed, with a single experimenter, the intersubjective agreement has no consequence (the experimenter is always in agreement with him/herself). ...

**Context 5**

... have now a hypothesis on the origin of the relationship between labels of samples and concordance of pairs. A strong constraint emerges as clearly depicted in Figure 4 if we take into account both the intersubjective agreement and random microscopic fluctuations. Nevertheless, for symmetry reasons, nothing in the formalism favors one relationship over the other one ("all concordant" vs. "all discordant"). ...

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Extensions of the Kochen–Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single context is epistemic. A remark by Gleason about the ad hoc construction of probability measures in Hilbert spaces...

## Citations

... If the plausibility of this model is assumed, one could hypothesize that the consciousness of the practitioners in the production and application of homeopathic treatment/ experiment could play a role; it means that we might consider the interaction of their cognitive states using the same quantum-like logic. 3,[62][63][64][65][66] Despite some quantum phenomena, such as entanglement, being counterintuitive, they are extremely useful constructs in theoretical and experimental physics. Entanglement is accepted as a fact of nature and is actively being explored as a resource for future technologies including quantum computers, quantum communication networks, and high-precision quantum sensors. ...

Introduction There are two critical pillars of homeopathy that contrast with the dominant scientific approach: the similitude principle and the potentization of serial dilutions. Three main hypotheses about the mechanisms of action are in discussion: nanobubbles-related hormesis; vehicle-related electric resonance; and quantum non-locality.
Objectives The aim of this paper is to review and discuss some key points of such properties: the imprint of supramolecular structures based on the nanoparticle-allostatic, cross-adaptation-sensitization (NPCAS) model; the theory of non-molecular electromagnetic transfer of information, based on the coherent water domains model, and relying (like the NPCAS model) on the idea of local interactions; and the hypothesis of quantum entanglement, based on the concept of non-locality.
Results and Discussion The nanoparticles hypothesis has been considered since 2010, after the demonstration of suspended metal nanoparticles even in very highly diluted remedies: their actual action on biological structures is still under scrutiny. The second hypothesis considers the idea of electric resonance mechanisms between living systems (including intracellular water) and homeopathic medicines: recent findings about potency-related physical properties corroborate it. Finally, quantum theory of ‘non-local’ phenomena inspires the idea of an ‘entanglement’ process among patient, practitioner and the remedy: that quantic phenomena could occur in supra-atomic structures remains speculative however.
Conclusion Further studies are needed to ascertain whether and which of these hypotheses may be related to potential cellular effects of homeopathic preparations, such as organization of metabolic pathways or selective gene expression.

... I described these experiments in details in a book [23] (now translated into English [10]), more particularly the experiments that were designed as proofs of concept. Then I tempted to decipher the logic of these experiments in a series of articles [21,[24][25][26][27]. The purpose of these articles was also to show that these results were consistent and deserved to be considered from a fresh point of view, even though the price to pay was an abandon of the initial hypothesis (namely, a molecular-like effect without molecules). ...

Background:
Benveniste's biology experiments suggested the existence of molecular-like effects without molecules ("memory of water"). In this article, it is proposed that these disputed experiments could have been the consequence of a previously unnoticed and non-conventional experimenter effect.Methods:A probabilistic modelling is built in order to describe an elementary laboratory experiment. A biological system is modelled with two possible states ("resting" and "activated") and exposed to two experimental conditions labelled "control" and "test", but both are biologically inactive. The modelling takes into account not only the biological system, but also the experimenters. In addition, an outsider standpoint is adopted to describe the experimental situation.Results:A classical approach suggests that, after experiment completion, the "control" and "test" labels of biologically-inactive conditions should both be associated with the "resting" state (i.e., no significant relationship between labels and system states). However, if the fluctuations of the biological system are also considered, a quantum-like relationship emerges and connects labels and system states (analogous to a biological "effect" without molecules).Conclusions:No hypotheses about water properties or other exotic explanations are needed to describe Benveniste's experiments, including their unusual features. This modelling could be extended to other experimental situations in biology, medicine, and psychology.

... I described these experiments in details in a book [23] (now translated in English [10]), more particularly the experiments that were designed as proofs of concept. Then I tempted to decipher the logic of these experiments in a series of articles [21,[24][25][26][27]. The purpose of these articles was also to show that these results were consistent and deserved to be considered from a fresh point of view, even though the price to pay was an abandon of the initial hypothesis (namely, a molecular-like effect without molecules). ...

Background: Benveniste’s biology experiments suggested the existence of molecular-like effects without molecules (“memory of water”). In this article, it is proposed that these disputed experiments could have been the consequence of a previously unnoticed and non-conventional experimenter effect. Methods: A probabilistic modelling is built in order to describe an elementary laboratory experiment. A biological system is modelled with two possible states (“resting” and “activated”) and exposed to two experimental conditions labelled “control” and “test”, but both biologically inactive. The modelling takes into account not only the biological system, but also the experimenters. In addition, an outsider standpoint is adopted to describe the experimental situation. Results: A classical approach suggests that, after experiment completion, the “control” and “test” labels of biologically-inactive conditions should be both associated with “resting” state (i.e. no significant relationship between labels and system states). However, if the fluctuations of the biological system are also considered, a quantum-like relationship emerges and connects labels and system states (analogous to a biological “effect” without molecules). Conclusions: No hypotheses about water properties or other exotic explanations are needed to describe Benveniste’s experiments, including their unusual features. This modelling could be extended to other experimental situations in biology, medicine and psychology.

Introduction
Fundamental research into the scientific basis of the manufacture of ultra-high dilutions and their working in applications has evolved over the past twenty years since our last critical analysis of the field was published in 1994 [1]. New contenders from the realm of physics (entanglement, non-locality) have entered the scene. The vast majority within the community of the application of ultra-high dilutions are not physicists. This paper attempts to elucidate the concepts of entanglement, non-locality and their application in ultra-high dilution research (UHD).
Method
A selected study on the activity of fundamental research into UHD is performed to gain insight into trends of development activity of fundamental research in this area. In an attempt to nurture further development of theoretical models in fundamental research in UHD, an attempt is made to made recent theoretical concepts more accessible to the larger community including practitioners, policy makers and beneficiaries of UHD.
Results
Fundamental research in UHD had a period of prolific activity and recognition at the turn of the millennium until about ten years ago. Since then, research output as well as its recognition receded sharply suggesting that a period of reflection and consolidation may be in progress.
Conclusion
The study and the knowledge gained from more recent theoretical models in UHD and entanglement suggest that there may be some benefit in stocktaking of what we really know about the fundamental workings of UHD as well as identifying or developing models that include measurable predictors that go beyond metaphorical descriptors.