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IJRRAS 23 (3) ● June 2015

www.arpapress.com/Volumes/Vol23Issue3/IJRRAS_23_3_06.pdf

221

OBSERVER-CENTERED DESCRIPTION OF MISINTERPRETED

RESULTS IN BIOLOGY

Francis Beauvais

91, Grande Rue, 92310 Sèvres, France

ABSTRACT

Benveniste’s experiments have been the subject of an international scientific controversy (known as the case of the

“memory of water”). We recently proposed to describe these results in a modeling in which the outcome of an

experiment is considered personal property (named cognitive state) of the observer and not an objective property of

the observed system. As a consequence, the correlations between “expected” results and observed results in

Benveniste’s experiments could be considered the consequence of quantum-like interferences of the possible

cognitive states of the experimenters/observers.

In the present paper, we evidence that small random fluctuations from the environment together with intersubjective

agreement force the “expected” results and the observed results experienced by the observers into a noncommuting

relationship. The modeling also suggests that experimental systems with enough compliance (e.g., biological

systems) are more suitable to evidence quantum-like correlations. No hypothesis related to “memory of water” or

other elusive modifications of water structure is necessary.

In conclusion, a quantum-like interpretation of Benveniste’s experiments offers a logical framework for these

experiments that have remained paradoxical to now. This quantum-like modeling could be adapted to other areas of

research for which there are issues of reproducibility of results by other research teams and/or suspicion of nontrivial

experimenter effect.

Keywords: Quantum-like probabilities; Quantum cognition; Experimenter effect; Memory of water; Scientific

controversy.

1. INTRODUCTION

In any scientific controversy, there are both sound and dubious arguments from each side. The “memory-of-water”

controversy is no exception and we will show in this article that a third way is possible, one that dissolves the

“paradoxical” results of these disputed experiments. The research of Benveniste’s team on high dilutions (dubbed

the “memory of water”) became famous in June 1988 when Nature published an article suggesting that specific

information on compounds of biological interest could be stored in water after serial high dilutions [1]. Although no

molecule could be present in the samples containing the highest dilutions of the initial compound, changes of a

parameter of a biological system were observed. After the investigation performed in Benveniste’s laboratory and

the resulting conflict, Benveniste’s team explored new biological models and set up new devices [2].

In the years that followed, Benveniste claimed that electromagnetic waves emitted from a solution containing a

molecular compound could be captured with an electromagnetic coil and then transmitted via an electronic device to

a second coil containing a sample of water. He then reported that this “biological information” could be digitized

and stored in a computer memory and then played to samples of water, which thus could induce specific biological

effects. Other biological models were developed by Benveniste’s team after the Nature article to evidence the reality

of “high dilutions” and “digital biology”. More particularly, two biological systems were developed with success.

These were the isolated guinea pig heart, a classical model in physiology, and the in vitro plasma coagulation, which

had the advantage to be possibly automated [3-12].

In the present article, we describe in detail neither the biological models nor the devices that were used to

supposedly “imprint” molecular information in water. Details can be found elsewhere [2, 13]. Giving many

technical descriptions in this article would miss the point. Indeed, the important issue is to decipher the logic of

these experiments that tell us a coherent – but paradoxical – story. The thesis that we defend is that water does not

play any role in these experiments [14]. First, there was a circular reasoning in the usual description of these

experiments: 1) modifications of water induced changes of a biological model and 2) biological changes were the

consequence of modifications in water structure. Second, no modification of water has ever been evidenced that

could explain how the huge amount of information necessary to describe any biological macromolecule could be

coded and stored in liquid structures. In the next section, we describe what is precisely paradoxal in these

experiments.

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2. WHAT ARE THE SCIENTIFIC FACTS IN BENVENISTE’S EXPERIMENTS?

First, we define a change of a biological parameter above background noise as “signal” and no change as “no signal”

(i.e. change not different than background noise). In the experiments reported by Benveniste, the “expected” results

(materialized by “inactive” or “active” samples) and the observed results (“no signal” or “signal”) were correlated

and, at first sight, this relationship was causal as any pharmacological effect. Samples supposed to be “inactive”

were associated with “no signal”; samples supposed to be “active” were associated with “signal”. Therefore, it was

tempting and almost unavoidable that the “cause” of the biological change would be attributed to the procedure

supposed to “imprint” information in water. Note that the change of a biological parameter was in itself an

unexpected result according to mainstream science because no signal at all was supposed to be observed either with

“inactive” or “active” samples.

Public demonstrations with the active participation of colleagues to the experiments were repeatedly organized by

Benveniste [2]. These meetings were occasions for Benveniste to present his results and to involve other scientists in

order to convince them of the validity of his theories; one of these demonstrations has been recently analyzed in

depth [15]. These public experiments were designed as a proof-of-concept and were generally performed in two

steps. In the first step, samples expected to be “inactive” or “active” on the biological system were prepared in

another laboratory. These samples could be water samples or in last experiments were computer files. Blind samples

received a code from a scientist not belonging to Benveniste’s team. A series of “inactive” and “active” samples was

nevertheless kept unblinded. In the second step, all samples were transported into Benveniste’s laboratory, and the

corresponding activity was tested on the biological model. When all measurements were done, the results were sent

to the scientist that supervised and controlled the experiment, and that scientist could assess the rate of concordance

(i.e., the rate of “success”) between “expected” and observed results.

For these demonstrations, the results with the blind samples were not better than random: some samples supposed to

be “active” were associated with no signal and conversely other samples supposed to be “inactive” were associated

with signal. The most puzzling was that “success” was systematically obtained with samples prepared and assessed

in parallel but kept open-label even though they were in-house blinded in Benveniste’s laboratory.

These “failures” were interpreted by Benveniste as “jumps of activity” from one sample to another. These apparent

“jumps” were not considered by Benveniste as a “falsification” (in the sense of Popper) of his hypotheses on

“memory of water” and “digital biology”. In consequence, these weird results induced only head-long technological

rush of Benveniste’s team to “improve reproducibility” and to protect the samples and/or the biological model from

external disturbances such as electromagnetic waves, water contamination, etc. However, despite various

improvements of the experimental conditions, the weirdness continued to be repeatedly observed and was the main

stumbling block that prevented Benveniste’s hypothesis to be convincing [2, 13, 16-18].

We defend the idea that the different outcomes according to the experimental conditions (inside vs. outside first

assessment of “success” rate) is the only scientific fact, if any, that emerges from the story of “memory of water”.

3. WHY AN OBSERVER-CENTERED QUANTUM-LIKE MODELING?

If there was really “something”, physical or chemical, in water samples, as in classical pharmacology, modifications

in blinding should not disturb the outcomes. Assessment of success firstly by outside observer or firstly by inside

observer should not change the rate of samples with “success”. Suppose now that there was no specific information

in water samples and that these latter were all physically equivalent. In this case, we have no reason to expect

differences in outcomes. How explain then that biological changes did occur? Tackling these outstanding results

requires getting off the beaten track.

The formalism that we use is inspired by quantum cognition [19], relational quantum physics [20] and quantum

Bayesianism [21, 22]. In these interpretations of quantum physics, what is described is not the physical world in

itself but what each observer experiences (Figure 1). Therefore, the outcome considered in the present formalism to

describe Benveniste’s experiments is not the change of an experimental parameter in itself, but the experience

elicited in the experimenter that records this change (or absence of change).

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Figure 1. Different observers can have different reports of the same experimental situation.

Alice is the experimenter; she performs an experiment that has two possible outcomes: +1 or -1. For Eve, who is outside the

laboratory without information on the outcome of the experiment, the cognitive state of each observer inside the laboratory is in

a superposed state (“observer having experienced the outcome +1” and “observer having experienced the outcome -1”).

However, when Alice performs an experiment, she experiences either +1 or -1 on her measurement device. In other words, her

cognitive state is not in a superposed state, but in a “reduced” state. Bob is an observer inside the laboratory and he observes

also that Alice is not in a superposed state. Moreover, Alice and Bob agree on their observations, either +1 or -1 (intersubjective

agreement).

We define the cognitive state A as all possible experiences (with their respective probabilities) elicited in an observer

who observes/measures an experimental device. Mathematically, A is represented by the vector of

A in a Hilbert

vector space. Therefore, the cognitive state of one observer is depicted as the vector sum (i.e. the “superposition”) of

the possible experiences of the observer. This does not mean that the cognitive state of the observer is “really” in a

superposed state. The wave function is simply a predictive statistical tool. Another important point is that the

outcome does not preexist to the act of measurement for a given observer; the outcome is created by the

measurement and an experiment has no outcome before being experienced [22].

Thus, the state vector of

A of the cognitive state A is the superposition of the two states A-1 and A+1, which are the

two possible outcomes of a measurement:

11

Ψ AbAa

A

The norm a of the vector, which is obtained after projection of

A on the axis of the state A+1, is assimilated to a

probability amplitude. Therefore, the probability of the cognitive state being associated with A+1 is a2. Because the

total of probabilities is equal to one, a2 + b2 = 1.

An observer has no access to the “internal state” of another observer, but these observers nevertheless construct a

common reality by sharing their experiences; “reality” emerges as a consequence of intersubjective agreement.

4. OBSERVER-CENTERED DESCRIPTION OF BENVENISTE’S EXPERIMENTS

4.1 First step: Description of a relationship between “expected” and observed results

This first step has been previously described and will be briefly summarized [14]. Appendix 1 provides details of the

calculations.

In this formalism, “expected” results and observed results are experienced by the experimenter, and we describe the

relationship between these two sets of observables. We define the first set of observables (“expected” results) as

AIN/AAC, which corresponds to the observation of “inactive”/“active” labels, and the second set of observables

(observed results) as ACP/ADP , which corresponds to the observation of concordant/discordant pairs.

The observed biological system has two possible states: no signal or signal. “Success” is defined by the observation

of a “concordant” pair (ACP): AIN associated with no signal or AAC associated with signal. “Failure” is defined as the

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observation of a “discordant” pair (ADP): AIN associated with signal or AAC associated with no signal. We define

Probquant and Probclass as quantum and classical probability, respectively.

The cognitive state A of the experimenter is described from an outside point of view (Figure 1). The aim of these

experiments is to contrast the states AIN and AAC for the respective probabilities of “success”. Therefore, the

cognitive state A is described as a superposition of the eigenvectors of the first observable:

2

ACIN

A

AA

ψ

(Eq. 1)

The eigenvectors of the first observable (AIN/AAC) are developed on the eigenvectors of the second observable

(ACP/ADP):

DPCPIN AμAμA1211

(Eq. 2)

DPCPAC AAA 2221

(Eq. 3)

There are some mathematical constraints (

1

2

12

2

11

,

1

2

22

2

21

and Probquant (ACP) + Probquant (ADP) = 1). The

calculations in Appendix 1 show that there are two solutions for the relationship between the two observables

corresponding to two rotation matrices. Only for one solution, do observed results fit with “expected” results

(Figure 2).

As calculated in Appendix 1, the corresponding solutions for probability of “success” or “failure” are:

2

)sin(cos

)(Prob 2

θθ

ACPquant

(Eq. 10)

2

)sin(cos

)(Prob 2

θθ

ADPquant

(Eq. 11)

The rate of “success” is optimal if sin θ = cos θ (θ = +π/4). In this case, Prob (ACP) = 1 and Prob (ADP) = 0. Classical

probabilities are obtained with θ = 0; in this case, Prob (ACP) = 1/2 and Prob (ADP) = 1/2. Note that there is no signal

when θ = 0 because concordant pairs are associated with “inactive” labels (no signal) and discordant pairs are

associated with active labels (no signal). When θ ≠ 0, the two bases are said to be noncommuting.

In conclusion, the relationship between “expected” and observed results can be modeled as the consequence of the

superposition of the possible cognitive states of the experimenter. The passage from classical to quantum-like logic

rests on a unique parameter (angle θ).

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Figure 2. Relationship between the cognitive states for “expected” results and observed results. This figure summarizes the

relationship between the two observables, namely the cognitive states for “expected” results (AIN/AAC) and for observed results

(ACP/ADP). The state vector of A can be described according to two orthogonal bases AIN/AAC or ACP/ADP. The probabilities for A

to be associated with IN, AC, CP, or DP is obtained by squaring the projection of

A on the corresponding axis (probability

amplitude) and by squaring the value. The probability to be associated with IN or AC is fixed and equal to 1/2; the probability to

be associated with CP or DP depends on the value of θ. For example, the concordance between expected results and observed

results is optimal for θ = +π/4. When θ = 0, the observables are said commuting and noncommuting when θ ≠ 0.

Abbreviations: IN, “inactive” expected value; AC, “active” expected value; CP, concordant pair (“expected” result associated

with observed value); DP, discordant pair (“expected” result not associated with observed value).

4.2 Second step: Why are the observables noncommuting?

In the first step, we have seen that θ ≠ 0 allows describing a relationship between the two observables. We have to

explain however why θ ≠ 0 (noncommuting observables). To understand how noncommuting observables could

emerge from formalism, we consider now that the experimenter obtains information on the state of the experimental

device either “directly” or through other sources such as the interaction with another observer (Figure 1). Interaction

must be understood as the “measurement” of the actual state of A by B and the actual state of B by A. The following

demonstration rests on the following propositions: 1) The information gained on the outcome of an experiment is

through macroscopic environment; 2) The macroscopic environment is submitted to microscopic fluctuations

(related to thermal fluctuations, electromagnetic waves, etc); 3) Different cognitive states that gain information on

the outcome of the same experiment must agree on this outcome (intersubjective agreement).

We first define two experimenters, Alice and Bob with cognitive states A and B, respectively, who perform

experiments together. The observables are supposed to be initially commuting, that is θ = 0 (i.e. there is no

relationship between the observables). The state vectors that describe the cognitive states A and B separately with

θ = 0 are (see Appendix 1):

A

ψ

(1)

(2)

AIN

AAC

ACP

ADP

Angle θ

(1):

)sin(cos2/1 θθ

(2):

)sin(cos2/1 θθ

Angle θ

21

21

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2

DPCP

A

AA

ψ

(Eq. 9a for A with θ = 0)

2

DPCP

B

BB

ψ

(Eq. 9b for B with θ = 0)

The tensor product of the two state vectors describes the cognitive states A and B together:

22

DPCPDPCP

BA

BBAA

ψψ

(Eq. 12)

2222

DPDPCPDPDPCPCPCP BABABABA

When they compare their observation of the same experiment, Alice and Bob agree that their observations fit. For

example, if Alice reports that she observed a concordant pair, Bob must also observe a concordant pair

(intersubjective agreement). As a consequence, the states

DPCP BA

and

CPDP BA

are not possible states. The

vector that describes A and B becomes:

22

DPDPCPCP

AB

BABA

ψ

(Eq. 13)

(Total probability is equal to 1 and probability amplitudes of the state vectors in Eq. 9 have therefore been divided

by

2

).

Because

CPCP BA

and

DPDP BA

define an orthogonal basis, one could suggest that classical probabilities would

be sufficient to calculate probabilities. In the “real world”, however, the experimental device and the observers are

not isolated but influenced by microscopic random fluctuations of various origins. In classical physics, these

microscopic fluctuations induce small variations around the mean value of a measurement. We will explore the

consequences of these fluctuations in the quantum-like modeling. If we take into account the random microscopic

fluctuations, Eq. 9 must be modified. We first complete Eq. 9a and Eq. 9b with positive or negative ε random

numbers << 1/2.

DPCPAAεAεψ 11 2121

(Eq. 14)

DPCPBBεBεψ 22 2121

(Eq. 15)

The portions of environment corresponding to A and B are different; therefore, the random microscopic fluctuations

associated with A and B are independent. The state vector that describes both A and B is therefore:

DPDPCPCPAB BA

εε

BA

εε

ψΔ

2121

Δ

2121 2121

(Eq. 16)

Δ

)21)(21(

)(Prob 21 εε

ABCPquant

(Eq. 17)

(with ∆ =

2121 21212121 εεεε

since total probability must be equal to 1).

The successive probabilities associated with A and B are computed step by step, each step corresponding to one

infinitesimal random fluctuation. Thus, after the first random microscopic fluctuation, the probability associated

with concordant pairs for the two cognitive states are Probquant (ACP) = (1/2 + ε1) and Probquant (BCP) = (1/2 + ε2)

(Eq. 14 and Eq. 15). The intersubjective agreement must be guaranteed and the common probability Probquant (ABCP)1

is calculated according to Eq. 17. After the next random microscopic fluctuations (ε3 for A and ε4 for B),

Probquant (ABCP)2 associated with A and B is calculated. At each computing step, the common Probquant (ABCP)n is

updated and reinjected for the calculation of Probquant (ABCP)n+1.

The evolution of Probquant (ABCP) after a series of random microscopic fluctuations is computed in Figure 3. We see

that only two positions are stable. Even with tiny random changes of probabilities at each step ([-0.5; 0.5] × 10-15), a

transition occurs after several iterations that model fluctuations of the environment. One of two different outcomes

are obtained: either Probquant (ABCP) = 1 (i.e. all pairs are concordant) or Probquant (ABCP) = 0 (i.e. all pairs are

discordant). In both cases, signal is selected/filtered from background noise and order is introduced. Thus, suppose

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that “expected” results are ↓↓↓↓↑↑↑↑. Before transition, the observed results are ↓↓↓↓↓↓↓↓ (i.e., no signal; 50% of

concordant pairs and 50% of discordant pairs). After transition, the observed results are ↓↓↓↓↑↑↑↑ (100% of

concordant pairs) or ↑↑↑↑↓↓↓↓ (0% of concordant pairs). Note that modeling with Alice alone does not lead to

transition of Probquant (ACP) toward 1 or 0.

Figure 3. Consequence of the interaction of two cognitive states for the same experiments.

Cognitive states gain information on the outcome of an experiment always through the macroscopic environment. The

macroscopic environment is submitted to tiny fluctuations in the interval. The experimenter obtains information on the state of

the experimental device either “directly” or through other sources such as the interaction with another observer Nevertheless

agreement between these different sources must be respected. It can be demonstrated that only two positions are stable:

“expected” results and observed results are either always concordant (θ = +π/4) or always discordant (θ = -π/4). See text for

details on calculations. Eight examples of computing of the probability to observed concordant pairs are shown in this figure (at

each iteration, a very small elementary change of probability of concordant pairs is applied in this computer simulation: from –

0.5 to +0.5 × 10-15).

Therefore, taking into account both fluctuations of the environment and intersubjective agreement forces the

observables (ABIN/ABAC and ABCP/ABDP) into a noncommuting relationship.

4.3 Third step: How asymmetry is introduced in favor of “expected” results?

As depicted in the previous section, two stable states were obtained after transition (with θ = +π/4 or θ = -π/4)

(Figure 3). Nothing in the formalism allows favoring one of the two solutions. Nevertheless, in practice, asymmetry

is actually introduced by the biological model. Indeed, when the biological model is “at rest” (between two

measurements), the state “↓” (no signal) is observed because the experimental conditions are equivalent to an

“inactive” sample. Therefore one can consider that an “inactive” sample with the outcome “↓” is inserted between

each measurement. After transition, the relationships of “labels” and their respective outcomes must be either all

concordant or all discordant. Since the association of “↓” with inactive sample is a concordant pair, the asymmetry

introduced by the biological system at rest permits only the solution corresponding to θ = +π/4 (Figure 3).

ΔProb at each iteration: ε = random [-0.5 ; +0.5] × 10-15

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

010 20 30 40 50 60 70 80 90 100

Calculation steps

Prob (concordant pairs)

θ = +π/4

θ = -π/4

θ = 0

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5. THE STUMBLING BLOCK OF BENVENISTE’S EXPERIMENTS EXPLAINED

We now have the tools to describe the stumbling block of Benveniste’s experiments, namely the disturbance

observed in some blind experiments. Any description or interpretation of Benveniste’s experiments must be able to

take into account this puzzling phenomenon that prevented the success of experiments designed as proof-of-concept.

Simply put, when Bob or Eve controlled the experiments made by Alice (Figure 1) using blind designs and then

assessed the rate of “success”, the results were quite different: statistically significant concordance of “expected”

and observed labels with Bob and concordance not better than random with Eve.

We can summarize the issue in a concise manner. Suppose that the “expected” results are ↓↓↓↓↑↑↑↑ in that order,

i.e. we expect 8 outcomes: 4 with no signal and 4 with signal. With the controller Bob who participates to the blind

experiment by assessing the rate of “success”, the results are: ↓↓↓↓↑↑↑↑, i.e. complete “success” with this series of

samples (100% of concordant pairs). With Eve replacing Bob, the results become ↓↑↑↓↑↑↓↓, i.e. not better than

random (50% of concordant pairs and 50% of discordant pairs). Signal is nevertheless observed after control by Eve,

but not at the correct place (i.e. “expected” place). The fact that a signal is nevertheless present is an experimental

fact that has been repeatedly observed but that remained unexplained according to classical logic. The presence of

signal at unexpected places was interpreted by Benveniste’s team as “jumps” of biological activity between samples

due to various external disturbances. The idea of local cause (“memory of water”) was not called into question at

this time by Benveniste’s team.

When an “outside” controller (Eve in Figure 1) assesses the rate of “success”, she compares the successive items of

two lists: labels (“expected” results) and experimental outcomes (observed results). For Eve, the cognitive state of

the experimenter is superposed. However, when Eve compares “expected” results and observed results, the

information she has on the “expected” results must be taken into account for the calculation of the probability for A

to be associated with concordant pairs. This is formally equivalent to a “which-path” measurement in quantum

physics. The “path” information must be taken into account for the calculation of the probability of “success” or

“failure”; therefore classical probabilities (conditional probabilities) apply:

)|(Prob)(Prob )|(Prob)(Prob)(Prob ACCPACINCPINCPclass AAAAAAA

(Eq. 18)

)|(Prob)(Prob)|(Prob)(Prob)(Prob INDPINACDPACDPclass AAAAAAA

(Eq. 19)

According to Eq. 7 and Eq. 8, Prob (ACP | AAC) = Prob (ADP | AIN) = sin2 θ = 1/2 (for θ = +π/4). This means that the

probability of signal is the same for both “inactive” and “active” labels (signal is associated either with “inactive”

labels in discordant pairs or with “active” labels in concordant pairs).

We now consider the general case of an experiment with a proportion p = Prob (AIN) of “inactive” labels and a

proportion q = Prob (AAC) of “active” labels (p + q = 1). In this case, the conditional probability of signal or no

signal is q or p, respectively:

Prob (ADP | AIN) = Prob (ACP | AAC) = q for signal,

Prob (ACP | AIN) = Prob (ADP | AAC) = p for no signal.

We can now calculate:

Probclass (ACP) = p2 + q2 (Eq. 20)

Probclass (ADP) = qp + pq (Eq. 21)

There are two components in each of these two equations: one is related to “inactive” labels and the other is related

to “active” labels. The terms in bold letters in these equations are those as

sociated with signal. The probability of observing a signal in experiments with an “outside” controller like Eve is

equal to pq + q2 = q × (p + q) = q (Figure 4). The probability of observing a signal remains the same, without or

with control by Eve, and is equal to q. The chief difference is that without Eve’s control the samples with a signal

are at the expected places and with Eve’s control, they are positioned at random.

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“Inactive” labels

“Active” labels

“Expected” results

according to labels

○

○

○

○

○

○

●

●

●

●

Prob (●) = q

Observed results

without “outside”

controller*

○

○

○

○

○

○

●

●

●

●

Prob (●) = q

Observed results

with “outside”

controller*

○

●

○

○

●

○

○

●

○

●

Prob (●) = (1 – q) × q if “inactive”

Prob (●)= q2 if “active”

Prob (●) = q

○: No signal (background noise); ●: Signal.

* “Outside” controller is personified by Eve in Figure 1; for Eve, the cognitive state A of the experimenter Alice is in a

superposed state. As an “outside” controller who participates to blind experiment, Eve assesses if “signal” (●) is at the correct

(i.e. “expected”) places. This is formally equivalent to a “wave function collapse” of the cognitive state A, and classical

probabilities apply. When Alice and Eve meet, Eve communicates to Alice the places (labels) where a signal is present and they

both agree, despite the presence of signal, that the experiment is a “failure” because the places observed with signal are not

better than random.

Figure 4. Description of the seemingly “jumping” activities from one sample to another. The quantum-like modeling

predicts that random concordance between “expected” results and observed results are obtained when the experiments are

checked by an “outside” controller (Eve in Figure 1). Benveniste’s team reasoned into a classic frame and interpreted these

“failed” experiments as “jumping of biological activity” from one sample to another. See text for details on calculations.

In conclusion, in the quantum-like formalism, the cognitive state of Alice is superposed for Eve; in contrast, for Bob

the cognitive state of Alice is not superposed (they are both on the same “branch” of the reality). The consequence is

an apparent causal relationship between labels and outcomes if Eve does not control the experiments. This

relationship is broken, however, if Eve controls the experiments. The quantum-like modeling easily describes the

apparent “jumps” of signal that disturbed so much the interpretation of Benveniste’s experiments.

6. ARE ALL EXPERIMENTAL MODELS SUITABLE TO EVIDENCE QUANTUM-LIKE

CORRELATIONS OF COGNITIVE STATES?

To observe quantum-like correlations between “expected” and observed results, the formalism suggests that two

conditions are necessary: 1) small random fluctuations of θ around zero and 2) “compliance” of the experimental

model, thus allowing transition from mean θ = 0 to θ = +π/4 (or θ = –π/4). Therefore, the question is: With which

experimental models could quantum-like correlations between “expected” results and observed results be

established?

Suppose an experimental model based on radioactive decay. Nucleus disintegration is not influenced by fluctuations

of the environment. As a consequence, such a model would not be suitable. A beam splitter that randomly reflects or

transmits incident photons is submitted to tiny random environmental noise. The probability for a photon to be

transmitted is submitted to infinitesimal variations around a mean value. Condition #1 is thus fulfilled. However,

these variations remain centered on the mean value because the random fluctuations are not sufficiently large to

change the fixed average rate of transmission. The same reasoning applies for the spin of an electron measured in a

Stern-Gerlach apparatus; the intensity of the random fluctuations is too small to change the fixed orientation of the

magnets. Although submitted to external fluctuations, these devices are not “compliant”.

Therefore, what was so special in Benveniste’s experimental models? Although this is obvious, we must underscore

that Benveniste’s experiments were performed in the context of a laboratory dedicated to biological sciences. The

experimental models used in these experiments resulted in a selection among other ones that were assayed for

optimal evidence of correlations between “expected” and observed results. Indeed, many biological models fulfill

the conditions required by the formalism: 1) they are submitted to environment fluctuations (e.g. thermal

fluctuations) and 2) many molecules in living systems are submitted to Brownian motion. Movements of molecules

in solution confer a large plasticity to these systems. The mean values of a parameter can vary (under some range)

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thus fulfilling also condition #2. Moreover, biological systems are generally asymmetric with a “resting” state (See

Section 4.3); this is not the case with the above physical system.

In conclusion, models such as biological models, which are both randomly influenced by the fluctuations of

environment and composed of elements with many degrees of freedom, could be sufficiently compliant to evidence

quantum-like correlations.

7. DISCUSSION

It appears that a crucial issue in the present quantum-like modeling is as follows: Who is the first to compare

“expected” results and observed results of a series of experiments? In other words, who is aware of the rate of

“success”? The fact that the order of the assessments (outside observer first vs. inside observer first) leads to

different results is a property of noncommuting observables.

Our modeling gives logic to the paradoxical results that messed up Benveniste every time he seemed near to succeed

with proof-of-concept experiments. How a simple modification of experimental conditions (inside vs. outside

assessment of rate of “success”) could have such consequences remained incomprehensible according to the logic of

the classical experimental sciences. The apparent causal relationship between observables (interpreted as “success”)

and the “spreading” of the signal into “inactive” samples (interpreted as “failure”) are both simply described by the

formalism. The emergence of a signal from the background noise of the biological system is also easily explained.

Overall, this formalism fits the corpus of the experimental data gained by Benveniste’s team over the years [2, 13,

15, 23]. Moreover, in this modeling, no physico-chemical explanation such as “memory of water” is necessary.

The formalism proposed in this article is observer-centered. What an observer perceives cannot be directly

experienced by another observer. By definition, the “qualia” of an observer belong to personal experience and only

language in its different forms (or direct observation of the state of the observer) allows transmitting information on

perception from one observer to another. Acquiring information on perceptions of an observer is actually a

“measurement”. In the quantum-like modeling, the outcome does not preexist to the “measurement”; the act of

questioning/measuring literally creates the answer (but which answer is produced cannot be controlled). This

indeterminacy for Eve on what Alice “really” perceives concerning the relationship of two observables is central in

our modeling (Figure 1). The perception of one observer is formalized by a vector, which is the sum of the possible

perceptions of the “reality”. For one observable, there is no difference for the classic versus the quantum-like

approaches because, mathematically speaking, (x + 0)2 = x2 + 02 (the square of the sum is equal to the sum of the

squares in this case). For two observables, however, the classic and quantum-like approaches diverge because two

pathways with probability amplitudes x and y lead to the same outcome and therefore in the general case, (x + y)2 ≠

x2 + y2; the difference between the two sides of this equation is the “interference term”.

The fact that different cognitive states interact with one another through the macroscopic world (which is submitted

to infinitesimal fluctuations) with the constraint of intersubjective agreement has important consequences: the

observables are forced into a noncommuting relationship. Therefore, the correlations between “expected” results and

observed results in Benveniste’s experiments could be understood as the consequence of quantum-like interferences

of the possible cognitive states of the experimenters/observers.

The formalism used in this article is reminiscent of Bayesian logic. Indeed, the probabilities of the two observables,

“expected” results and observed results, could be equated to a priori probabilities and a posteriori probabilities,

respectively. Probabilities are updated according to the “reality” shared by the observers as defined by

intersubjective agreement. In quantum Bayesianism, the quantum state is not a property of the external world, but of

the observer: quantum states are thus states of knowledge of each observer [24]. Therefore, for a given event, there

are as many wave functions as there are observers. After sharing the outcomes of measurements and accordingly

modifying their respective cognitive states, a coherent modeling of the reality, common to all observers, emerges

[22].

This quantum-like modeling has similarities with modelings of quantum cognition on information processing by

human brain for decision making, judgment, memory, etc. [19]. Until now however the objective of the modeling in

quantum cognition was to describe psychological processes. Our modeling is the first to our knowledge to propose

the use of a quantum-like formalism to describe the perception of macroscopic events outside human brain. The

decision to study some observables and to explore their possible relationships is subjective and is dependent on our

capacity to discriminate between our perceptions coming from the “outside” world and to describe “objects”.

Despite the subjective nature of the observables, the formalism shows that they are forced into a noncommuting

relationship in a manner reminiscent of a decoherence process. In other words, the formalism describes a subjective

“potential” that is the consequence of the interaction of the cognitive state with the objective macroscopic world

(exactly as any quantum entity interacts with a macroscopic device). This “potential” is necessary but is not

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sufficient. Indeed, nothing guarantees that the macroscopic objects will be perceived according to these constraints.

The formalism itself suggests that experimental devices with many freedom degrees submitted to random

fluctuations appear more suitable for establishing quantum-like correlations because they are possibly more

compliant. Biological models are more likely to fulfill these requirements.

Demonstrating causal relationships is a daily exercise for many bench scientists with their experimental models.

Therefore one could expect that such quantum-like correlations would be more frequently reported. It is well known

that some experiments, more particularly in biology, are not reproduced by other teams and conversely that some

teams are more “gifted” than other ones in getting “successful” results. Of course, trivial explanations must be first

identified. Nevertheless, it is also possible that quantum-like correlations sometimes happen without the knowledge

of the experimenters. A control/blinding of the experiments in conditions that Benveniste himself defined (even

though for other purposes) could allow detecting such quantum-like correlations.

8. CONCLUSION

This observer-centered quantum-like modeling offers a new framework for Benveniste’s experiments, which

remained paradoxical to date. There are lessons to be drawn from this episode of the history of science and we

propose theoretical tools for apprehending similar experimental situations.

9. APPENDIX

The cognitive state A is described as a superposition of the eigenvectors of the first observable (cognitive states A

indexed with labels IN and AC):

2

ACIN

A

AA

ψ

(Eq. 1)

We then develop the eigenvectors of the first observable (AIN/AAC) on the eigenvectors of the second observable

(ACP/ADP):

DPCPIN AAA 1211

(Eq. 2)

DPCPAC AAA 2221

(Eq. 3)

Therefore, we can express

A

as a superposed state of

CP

A

and

DP

A

:

DPCPAA

μμ

A

μμ

ψ2

)(

2

)( 22122111

(Eq. 4)

The probability of each state is the square of the corresponding probability amplitude:

2

)(

)(Prob 2

2111 μμ

ACPquant

(Eq. 5)

2

)(

)(Prob 2

2212 μμ

ADPquant

(Eq. 6)

As

1

2

12

2

11

,

1

2

22

2

21

, and Probquant (ACP) + Probquant (ADP) = 1, it can be calculated that

2

22

2

11

,

2

21

2

12

, and

12222111

. Therefore, the solutions for the different probability amplitudes µij correspond to

two rotation matrixes M1 and M2:

M1 =

1121

2111

2221

1211

μμ

μμ

μμ

μμ

=

θθ

θθ

cossin

sincos

or

M2 =

1121

2111

2221

1211

μμ

μμ

μμ

μμ

=

θθ

θθ

cossin

sincos

We choose the counterclockwise rotation matrix (M1); note that these two solutions differ only for the sign of θ. In

Figure 2, the state ΨA can be described with one or other basis (AIN/AAC or ACP/ADP) in the vector space. The passage

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from one basis to the other is obtained by a rotation with an angle equal to θ. When θ is different from zero, the two

observables described by these two bases are said to be noncommuting.

We can now write Eq. 2 and Eq. 3 using trigonometric notation:

DPCPIN AθAθAsincos

(Eq. 7)

DPCPAC AθAθAcossin

(Eq. 8)

It follows that:

DPCPAA

θθ

A

θθ

ψ2

)sin(cos

2

)sin(cos

(Eq. 9)

2

)sin(cos

)(Prob 2

θθ

ACPquant

(Eq. 10)

2

)sin(cos

)(Prob 2

θθ

ADPquant

(Eq. 11)

Probquant (ACP) = 1 (concordance of pairs is maximal) if cos θ = sin θ (θ = +π/4).

10. REFERENCES

[1]. Davenas E, Beauvais F, Amara J, et al. Human basophil degranulation triggered by very dilute antiserum against IgE.

Nature 1988;333:816-8.

[2]. Beauvais F. L’Âme des Molécules – Une histoire de la "mémoire de l’eau" (2007). Collection Mille Mondes (ISBN:

978-1-4116-6875-1); available at http://www.mille-mondes.fr

[3]. Benveniste J, Arnoux B, Hadji L. Highly dilute antigen increases coronary flow of isolated heart from immunized

guinea-pigs. Faseb J 1992;6:A1610.

[4]. Aïssa J, Litime MH, Attias E, Allal A, Benveniste J. Transfer of molecular signals via electronic circuitry. Faseb J

1993;7:A602.

[5]. Benveniste J, Aïssa J, Litime MH, Tsangaris G, Thomas Y. Transfer of the molecular signal by electronic

amplification. Faseb J 1994;8:A398.

[6]. Aïssa J, Jurgens P, Litime MH, Béhar I, Benveniste J. Electronic transmission of the cholinergic signal. Faseb J

1995;9:A683.

[7]. Benveniste J, Aïssa J, Guillonnet D. Digital biology: specificity of the digitized molecular signal. Faseb J

1998;12:A412.

[8]. Benveniste J, Jurgens P, Aïssa J. Digital recording/transmission of the cholinergic signal. Faseb J 1996;10:A1479.

[9]. Benveniste J, Jurgens P, Hsueh W, Aïssa J. Transatlantic transfer of digitized antigen signal by telephone link. J

Allergy Clin Immunol 1997;99:S175.

[10]. Hadji L, Arnoux B, Benveniste J. Effect of dilute histamine on coronary flow of guinea-pig isolated heart. Inhibition by

a magnetic field. Faseb J 1991;5:A1583.

[11]. Benveniste J, Aïssa J, Guillonnet D. The molecular signal is not functional in the absence of "informed" water. Faseb J

1999;13:A163.

[12]. Jonas WB, Ives JA, Rollwagen F, et al. Can specific biological signals be digitized? FASEB J 2006;20:23-8.

[13]. Beauvais F. Emergence of a signal from background noise in the "memory of water" experiments: how to explain it?

Explore (NY) 2012;8:185-96.

[14]. Beauvais F. “Memory of water” without water: the logic of disputed experiments. Axiomathes 2014;24:275-90.

[15]. Beauvais F. Quantum-like interferences of experimenter's mental states: application to “paradoxical” results in

physiology. NeuroQuantology 2013;11:197-208.

[16]. Beauvais F. Memory of water and blinding. Homeopathy 2008;97:41-2.

[17]. Thomas Y. The history of the Memory of Water. Homeopathy 2007;96:151-7.

[18]. Benveniste J. Ma vérité sur la mémoire de l'eau; Albin Michel, Paris (2005).

[19]. Busemeyer JR, Bruza PD. Quantum models of cognition and decision: Cambridge University Press; 2012.

[20]. Rovelli C. Relational quantum mechanics. Int J Theor Phys 1996;35:1637-78.

[21]. Fuchs CA. QBism, the perimeter of quantum Bayesianism. 2010:arXiv preprint arXiv:1003.5209.

[22]. Fuchs CA, Mermin ND, Schack R. An introduction to QBism with an application to the locality of quantum mechanics.

2013:arXiv preprint arXiv:1311.5253.

[23]. Beauvais F. Description of Benveniste’s experiments using quantum-like probabilities. J Sci Explor 2013;27:43-71.

[24]. Fuchs CA, Peres A. Quantum theory needs no ‘interpretation’. Physics Today 2000;53:70-1.