Benveniste’s experiments – known in the lay press as the “water memory” phenomenon – are generally considered to be a closed case. However, the amount of data generated by twenty years of well-conducted experiments prevents closing the file so simply. An issue, which has been little highlighted so far, merits to be emphasized. Indeed, if Benveniste failed to persuade his peers of the value of his experiments, it was mainly because of a stumbling block, namely the difficulty of convincingly proving the causal relationship between the supposed cause (“informed water”) and the experimental outcomes in different biological models. To progress in the understanding of this phenomenon, we abandon the idea of any role of water in these experiments (“water memory” and its avatars). In other words, we assume that “controls” and “tests” that were evaluated were all physically identical; only their respective designations (labels) differentiated them. Since we state that there is no causal link between labels (“controls” vs. “tests”) and corresponding states of the biological system (no change vs. change), these variables are independent. Therefore, the key question is: “Is it possible to observe a correlation between independent variables that mimics a causal relationship but is itself not causal?” In this article, we show how simple considerations based on probability theory lead to describe non-classical correlations involving the experimenter. This probabilistic modelling allows to propose an alternative explanation to Benveniste’s experiments where water plays no role and where the place of the experimenter is central.

The “memory of water” experiments suggested the existence of molecular-like effects without molecules. Although no convincing evidence of modifications of water – specific of biologically-active molecules – has been reported up to now, consistent changes of biological systems were nevertheless recorded. We propose an alternate explanation based on classical conditioning of the experimenter. Using a probabilistic model, we describe not only the biological system, but also the experimenter engaged in an elementary dose-response experiment. We assume that during conventional experiments involving genuine biologically-active molecules, the experimenter is involuntarily conditioned to expect a pattern, namely a relationship between descriptions (or “labels”) of experimental conditions and corresponding biological system states. The model predicts that the conditioned experimenter could continue to record the learned pattern even in the absence of the initial cause, namely the biologically-active molecules. The phenomenon is self-sustained because the observation of the expected pattern reinforces the initial conditioning. A necessary requirement is the use of a system submitted to random fluctuations with autocorrelated successive states (no forced return to the initial position). The relationship recorded by the conditioned experimenter is, however, not causal in this model because blind experiments with an “outside” supervisor lead to a loss of correlations (i.e., system states randomly associated to “labels”). In conclusion, this psychophysical model allows explaining the results of “memory of water” experiments without referring to water or another local cause. It could be extended to other scientific fields in biology, medicine and psychology when suspecting an experimenter effect.

By definition, a placebo has no biological effect. Therefore, besides classical non-specific effects, the outcome associated to a placebo rests on its “meaning”. Meaning is always for someone and understanding the effects attributed to placebo requires to describe the expectations and interpretations of the agents involved in the experiment. We present a probabilistic modeling of the “placebo effect” that has its roots in the act of measuring and – in contrast with other hypotheses such as patient’s expectation or conditioning – is centered on experimenters and not only on patients. Therefore, this modeling potentially applies to any biology experiment aimed to demonstrate a causal relationship. Its originality is the description of the experimental situation from the point of view of an uninvolved participant who does not interact with the experimenters and the biological system. When probability fluctuations inherent to any measurement are taken into account, a counterintuitive result emerges: two placebos with different “meanings” can be associated with different “effects” after measurement of a biological system. In clinical trials, this “meaning effect” due to the experimenters could add to the drug effect and contribute to the “placebo effect”. This simple modeling suggests that the act of measuring is not always neutral and some correlations between apparent causes and observed outcomes may emerge, thus contributing to conclude for obvious – but false – causal relationship. These results could have consequences in the design and interpretation of experiments in life sciences, medicine and psychology.

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.

Background. In experimental sciences, conception of an experiment and record of the outcomes must be strictly separated. Although many possible pitfalls have been described, particularly in biological sciences, one cannot exclude unknown loopholes. Methods. A simple probabilistic modeling is constructed in order to describe experimenters testing the hypothesis of a relationship between some experimental conditions (supposed causes) and states of a biological system (observed effects). The modeling rests on two preliminary remarks. First, after assessment of a relationship, the outcome is not a property of the system alone, but is a property of the experimenters and the system taken as a whole. Second, as a consequence, the outcome does not preexist to measurement. Results. A biological system with two possible states (“resting” and “activated”) exposed to two control conditions distinguished only by their “labels” is modeled. A classical approach suggests that the two control conditions are both associated with the “resting” state (i.e. no relationship). Nevertheless, if the fluctuations of the system are considered, the hypothesis of a significant relationship between “labels” and system states is confirmed. In contrast, if the outcomes are not globally recognized as a relationship, but remains unconnected by the experimenters, no significant relationship emerges. Conclusion. This probabilistic modeling suggests that, despite precautions, the strict separation of biological systems and experimenters is an ideal not necessarily achieved when the hypothesis of a relationship is tested. The consequences could be wrong conclusions about causal relationships. Specific blind procedures are proposed to prevent unwanted correlations involving the experimenters.

Background: Factors that participate in the biological changes associated with a placebo are not completely understood. Natural evolution, mean regression, concomitant procedures and other non specific effects are well-known factors that contribute to the "placebo effect". In this article, we suggest that quantum-like correlations predicted by a probabilistic modeling could also play a role.Results: An elementary experiment in biology or medicine comparing the biological changes associated with two placebos is modeled. The originality of this modeling is that experimenters, biological system and their interactions are described together from the standpoint of a participant who is uninvolved in the measurement process. Moreover, the small random probability fluctuations of a "real" experiment are also taken into account. If both placebos are inert (with only different labels), common sense suggests that the biological changes associated with the two placebos should be comparable. However, the consequence of this modeling is the possibility for two placebos to be associated with different outcomes due to the emergence of quantum-like correlations.Conclusion: The association of two placebos with different outcomes is counterintuitive and this modeling could give a framework for some unexplained observations where mere placebos are compared (in some alternative medicines for example). This hypothesis can be tested in blind trials by comparing local vs. remote assessment of correlations.

In previous articles, a description of 'unconventional' experiments (e.g. in vitro or clinical studies based on high dilutions, 'memory of water' or homeopathy) using quantum-like probability was proposed. Because the mathematical formulations of quantum logic are frequently an obstacle for physicians and biologists, a modified modeling that rests on classical probability is described in the present article. This modeling is inspired from a relational interpretation of quantum physics that applies not only to microscopic objects, but also to macroscopic structures, including experimental devices and observers. In this framework, any outcome of an experiment is not an absolute property of the observed system as usually considered but is expressed relatively to an observer. A team of interacting observers is thus described from an external view point based on two principles: the outcomes of experiments are expressed relatively to each observer and the observers agree on outcomes when they interact with each other. If probability fluctuations are also taken into account, correlations between 'expected' and observed outcomes emerge. Moreover, quantum-like correlations are predicted in experiments with local blind design but not with centralized blind design. No assumption on 'memory' or other physical modification of water is necessary in the present description although such hypotheses cannot be formally discarded.In conclusion, a simple modeling of 'unconventional' experiments based on classical probability is now available and its predictions can be tested. The underlying concepts are sufficiently intuitive to be spread into the homeopathy community and beyond. It is hoped that this modeling will encourage new studies with optimized designs for in vitro experiments and clinical trials.

The case of the “memory of water” was an outstanding scientific controversy of the end of the twentieth century which has not been satisfactorily resolved. Although an experimenter effect has been proposed to explain Benveniste’s experiments, no evidence or convincing explanation supporting this assumption have been reported. One of the unexplained characteristics of these experiments was the different outcomes according to the conditions of blinding. In this article, an original probabilistic modeling of these experiments is described that rests on a limited set of hypotheses and takes into account measurement fluctuations. All characteristics of these disputed results can be described, including their “paradoxical” aspects; no hypothesis on changes of water structure is necessary. The results of the disputed Benveniste’s experiments appear to be a misinterpreted epiphenomenon of a more general phenomenon. Therefore, this reappraisal of Benveniste’s experiments suggests that these results deserved attention even though the hypothesis of “memory of water” was not supported. The experimenter effect remains largely unexplored in biosciences and this modeling could give a theoretical framework for some improbable, unexplained or poorly reproducible results.

Benveniste’s experiments were at the origin of a scientific controversy that has never been satisfactorily resolved. Hypotheses based on modifications of water structure that were proposed to explain these experiments (“memory of water”) were generally considered as quite improbable. In the present paper, we show that Benveniste’s experiments violated the law of total probability, one of the pillars of classical probability theory. Although this could suggest that quantum logic was at work, the decoherence process is however at first sight an obstacle to describe this macroscopic experimental situation. Based on the principles of a personalist view of probability (quantum Bayesianism or QBism), a modeling could nevertheless be built that fitted the outcomes reported in Benveniste’s experiments. Indeed, in QBism, there is no split between microscopic and macroscopic, but between the world where an agent lives and his internal experience of that world. The outcome of an experiment is thus displaced from the object to its perception by an agent. By taking into account both the personalist view of probability and measurement fluctuations, all characteristics of Benveniste’s experiments could be described in a simple modeling: change of the biological system from resting state to “activated” state, concordance of “expected” and observed outcomes and apparent “jumping” of “biological activities” from sample to sample. No hypothesis on change of water structure was necessary. In conclusion, a modeling of Benveniste’s experiments based on a personalist view of probability offers for the first time a logical framework for these experiments that have remained controversial and paradoxical till date.

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 “memory of water hypothesis. In the present article, we describe with the same formalism the cognitive states of different experimenters who interact together. In this quantum - like model, the correlations observe d in Benveniste’s experiments appear to be the consequence of the intersubjective agreement of the experimenters.

The “memory of water” was a major international controversy that remains unresolved. Taken seriously or not, this hypothesis leads to logical contradictions in both cases. Indeed, if this hypothesis is held as wrong, then we have to explain how a physiological signal emerged from the background and we have to elucidate a bulk of coherent results. If this hypothesis is held as true, we must explain why these experiments were difficult to reproduce by other teams and why some blind experiments were so disturbing for the expected outcomes. In this article, a third way is proposed by modeling these experiments in a quantum-like probabilistic model. It is interesting to note that this model does not need the hypothesis of the “memory of water” and, nevertheless, all the features of Benveniste’s experiments are taken into account (emergence of a signal from the background, difficulties faced by other teams in terms of reproducibility, disturbances during blind experiments, and apparent “jumps of activity” between samples). In conclusion, it is proposed that the cognitive states of the experimenter exhibited quantum-like properties during Benveniste’s experiments.

"Memory of water" experiments (also known as Benveniste's experiments) were the source of a famous controversy in the contemporary history of sciences. We recently proposed a formal framework devoid of any reference to "memory of water" to describe these disputed experiments. In this framework, the results of Benveniste's experiments are seen as the consequence of quantum-like interferences of cognitive states. Design: In the present article, we describe retrospectively a series of experiments in physiology (Langendorff preparation) performed in 1993 by Benveniste's team for a public demonstration. These experiments aimed at demonstrating "electronic transmission of molecular information" from protein solution (ovalbumin) to naive water. The experiments were closely controlled and blinded by participants not belonging to Benveniste's team. Results: The number of samples associated with signal (change of coronary flow of isolated rodent heart) was as expected; this was an essential result since, according to mainstream science, no effect at all was supposed to occur. However, besides coherent correlations, some results were paradoxical and remained incomprehensible in a classical framework. However, using a quantum-like model, the probabilities of the different outcomes could be calculated according to the different experimental contexts. Conclusion: In this reassessment of an historical series of "memory of water" experiments, quantum-like probabilities allowed modeling these controversial experiments that remained unexplained in a classical frame and no logical paradox persisted. All the features of Benveniste's experiments were taken into account with this model, which did not involve the hypothesis of "memory of water" or any other "local" explanation.

Background: The randomized controlled trial (RCT) is the 'gold standard' of modern clinical pharmacology. However, for many practitioners of homeopathy, blind RCTs are an inadequate research tool for testing complex therapies such as homeopathy.Methods: Classical probabilities used in biological sciences and in medicine are only a special case of the generalized theory of probability used in quantum physics. I describe homeopathy trials using a quantum-like statistical model, a model inspired by quantum physics and taking into consideration superposition of states, non-commuting observables, probability interferences, contextuality, etc.Results: The negative effect of blinding on success of homeopathy trials and the 'smearing effect' ('specific' effects of homeopathy medicine occurring in the placebo group) are described by quantum-like probabilities without supplementary ad hoc hypotheses. The difference of positive outcome rates between placebo and homeopathy groups frequently vanish in centralized blind trials. The model proposed here suggests a way to circumvent such problems in masked homeopathy trials by incorporating in situ randomization/unblinding.Conclusion: In this quantum-like model of homeopathy clinical trials, success in open-label setting and failure with centralized blind RCTs emerge logically from the formalism. This model suggests that significant differences between placebo and homeopathy in blind RCTs would be found more frequently if in situ randomization/unblinding was used.

Benveniste’s experiments (also known as “memory of water” or “digital biology” experiments) remain unresolved. In some research areas, which have in common the description of cognition mechanisms and information processing, quantum-like statistical models have been proposed to address problems that were “paradoxical” in a classical frame. Therefore, the outcomes of the cognitive state of the experimenter were calculated for a series of Benveniste’s experiments using a quantum-like statistical model (i.e. a model inspired by quantum physics and taking into consideration superposition of quantum states, non-commutable observables, and contextuality). Not only were the probabilities of “success” and “failure” of the experiments modeled according to their context, but the emergence of a signal from background was also taken into account. For the fi rst time, a formal framework devoid of any reference to “memory of water” or “digital biology” describes all the characteristics of these disputed results. In particular, the diffi culties encountered by Benveniste (reproducibility of the experiments, disturbances after blinding) are simply explained in this model without additional ad hoc hypotheses. It is thus proposed that we see Benveniste’s experiments as the result of quantum-like probability interferences of cognitive states.

After more than 20 years, the case of the "memory of water" still has not been resolved satisfactorily. After the affair with the journal Nature, Benveniste extended his results on high dilutions to an "electromagnetic biology" and then to a "digital biology," where electromagnetic signals supposed to be emitted from biologically active solutions were said to be stored on magnetic memories. Although the results obtained by Benveniste and coworkers were obvious, the difficulties in reproducibility by other teams created doubt of the reality of the alleged phenomenon. In a first step, we analyzed a set of experiments obtained by Benveniste's team in the 1990s. We quantified the relationship between "expected" effects (ie, labels of the tested samples) and apparatus outcomes, and we defined the experimental conditions to observe significant correlations. We concluded that the results of these experiments were related to experimenter-dependent correlations, which did not support the initial "memory of water" hypothesis. The fact that a signal emerged from background noise, however, remained puzzling. Therefore, in a second step, we described Benveniste's experiments according to the relational interpretation of quantum physics of C. Rovelli. In this interpretation, the state of a system is observer-dependent and the collapse of the wave function appears only in the states relative to a given observer. This interpretation allowed us to elaborate a model describing Benveniste's experiments in which the emergence of a signal from background noise was described by the entanglement of the experimenter with the observed system. In conclusion, the pursuit of the experimental "proof" to support the "memory of water" hypothesis has prevented other interpretations. Although our hypothesis does not definitely dismiss the possibility of "memory of water," the experimenter-dependent entanglement could be an attractive alternative interpretation of Benveniste's experiments.

In previous articles, a description of 'unconventional' experiments (e.g. in vitro or clinical studies based on high dilutions, 'memory of water' or homeopathy) using quantum-like probability was proposed. Because the mathematical formulations of quantum logic are frequently an obstacle for physicians and biologists, a modified modeling that rests on classical probability is described in the present article. This modeling is inspired from a relational interpretation of quantum physics that applies not only to microscopic objects, but also to macroscopic structures, including experimental devices and observers. In this framework, any outcome of an experiment is not an absolute property of the observed system as usually considered but is expressed relatively to an observer. A team of interacting observers is thus described from an external view point based on two principles: the outcomes of experiments are expressed relatively to each observer and the observers agree on outcomes when they interact with each other. If probability fluctuations are also taken into account, correlations between 'expected' and observed outcomes emerge. Moreover, quantum-like correlations are predicted in experiments with local blind design but not with centralized blind design. No assumption on 'memory' or other physical modification of water is necessary in the present description although such hypotheses cannot be formally discarded.In conclusion, a simple modeling of 'unconventional' experiments based on classical probability is now available and its predictions can be tested. The underlying concepts are sufficiently intuitive to be spread into the homeopathy community and beyond. It is hoped that this modeling will encourage new studies with optimized designs for in vitro experiments and clinical trials.

Analysing cluster aggregates is an important problem in clonogenic assays. This measurement has to be carried out on 3D populations and, as far as possible, automatically. The method described in this paper is based on a 3D reconstruction of some serial slices. Different analyses techniques are used to measure cell organisation in 2D images. An efficient reconstruction method for this kind of problem is proposed, and tests for characterising cell distribution in a 3D medium are made. These preliminary results are discussed, showing the possibility of solving the initial problem using this kind of technique.