“Memory of Water” Without Water: Modeling of Benveniste’s Experiments with a Personalist Interpretation of Probability

Abstract

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.

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ORIGINAL PAPER
‘‘Memory of Water’’ Without Water: Modeling
of Benveniste’s Experiments with a Personalist
Interpretation of Probability
Francis Beauvais
1
Received: 3 June 2015 / Accepted: 21 August 2015
Ó Springer Science+Business Media Dordrecht 2015
Abstract 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 consider ed 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 perc eption by
an agent. By taking into account both the personalist view of probability and
measurement fluctuations, all characterist ics 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 necessar y. 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 contro-
versial and paradoxical till date.
& Francis Beauvais
beauvais@netcourrier.com
1
91, Grande Rue, 92310 Se
`
vres, France
123
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DOI 10.1007/s10516-015-9279-6
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Keywords Personalist probability theory  Quantum Bayesianism  Experimenter
effect  Scientific controversy
To be is to be perceived (or to perceive)
Berkeley
1 Benveniste’s Experiments and ‘‘Memory of Water’’
In 1988, an article published in Nature suggested that molecules were not always
necessary to convey ‘‘biological information’’ (Davenas et al. 1988). It was as if
specific information associated with molecules—including huge macromolecules—
could be stored or imprinted in water samples. However, the proofs of storage of
information in water—quickly called ‘‘memory in water’’ in lay press—remained
indirect and the main weakness of the article was the absence of physical
measurements or clear theory to support these claims. The published data mainly
consisted of results from a single experimental model with biologically-active
solutions (immunoglobulins) that had been highly diluted using a well-defined
protocol (including shaking between each dilution step). The mechanisms of this
phenomenon, as recognized by the authors themselves, however, remained unknown.
A vague hypothesis was proposed—at the insistence of the Editor—on a possible
‘‘hydrogen-bond network or electromagnetic fields that could act as a template for the
biological molecules’’. This suggestion was however more a direction for future
research than an appropriate explanation. Actually, the evidence for ‘‘ghost
molecules’’ in high dilutions was only supported by circular reasoning: (1)
modifications of water structure induced biological changes; (2) biological changes
were a result of modifications in water structure. Nevertheless, the fact that the
outcomes were different for ‘‘inactive’’ and ‘‘active’’ samples in blind experiments
remained puzzling and was the strong point of the article.
Details on the investigation by Nature’s team and the subsequent controversy,
which are not the subject of this article, can be found elsewhere (Benveniste 2005;
de Pracontal 1990; Schiff 1998; Maddox 1988 ; Maddox et al. 1988; Beauvais 2007,
2012). During the following years, new data with the basoph il model were
published by other teams or by Benveniste’s team itself with various concl usions
(Benveniste et al. 1991; Ovelgonne et al. 1992; Hirst et al. 1993; Belon et al. 1999;
Brown and Ennis 2001; Ennis 2010).
The episode with Nature in 1988 was not the end of the ‘‘memory-of-water’’ story.
Indeed, Benveniste developed other biological models and proposed new concepts
such as ‘‘electronic transmission’’ and ‘‘digital biology’’. The isolated rodent heart is a
classical model in physiology (Langendorff apparatus) that was routinely used in
Benveniste’s laboratory. Early attempts in 1991 showed that changes in coronary flow
were recorded after injection of high dilutions of histamine or other molecules in the
circuitry of the Langendorff apparatus (Hadji et al. 1991;Benvenisteetal.1992). One
of the advantages of this biological model was that the changes in the flow through the
coronary arteries were obvious in the series of tubes that covered the coronary flow.
Therefore, it was easy to show ‘‘in live’’ an experiment to a public.
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A series of experiments with the isolated rodent heart showed that high dilutions
of histamine became ineffective after treatment with a magnetic field (Hadji et al.
1991). These results prompted Benveniste to use an electronic amplifier to transmit
the ‘‘biological information’’ supposed to be emitted from a sample containing a
solution of biological molecules. A tube containing the solution of a molecule to be
‘‘transmitted’’ was placed into an electric wire plugged at the input of the electronic
amplifier and a tube containing a sample of ‘‘naive’’ water (i.e. water that did not
contain ‘‘information’’) was placed in a wire plugged at the output. Again the
experiment was a success and coronary flow changes were observed as expected
(Aı
¨
ssa et al. 1993).
For the next step, Benveniste used the sound card of a personal computer as an
electronic amplifier and he reported that the ‘‘electromagnetic information’’ emitted
by a solution containing biological molecules in a wire plugged at input could be
digitized and stored on the hard disk of a computer. In a second time, this file could be
‘‘played’’ and information could be imprinted into a sample of water placed in a wire
plugged at output (Aı
¨
ssa et al. 1993;Benvenisteetal.1994;Aı
¨
ssa et al. 1995;
Benveniste et al. 1996, 1997, 1998). To describe these methods, Benveniste coined
the term ‘‘digital biology’’. In a further refinement, the wire plugged at the output was
placed around the column of the physiological liquid that infused the heart. This
means that the ‘‘digitized information’’ could be directly sent from the computer to
the apparatus without an intermediary water sample. Therefore, the contamination
argument, which was frequently used to dismiss these experiments, became worthless.
2 ‘‘Jumping’’ of Biological Activity from Sample to Sample
The questio n now is—if these results were so obvious—why could Benveniste not
convince the scientific community of the importance of his ‘‘discoveries’’? Indeed,
Benveniste often invited colleagues to witness these experiments. ‘‘Public
demonstrations’’ with the isolated rodent heart model were regularly organized
from 1992 to 1997 for colleagues and other scientists interested in Benveniste’s
experiments. The protocol of these experimental demonstrations was designed as
‘‘proof of concept’’ to hopefully give a definitive confirmation on the reality of
‘‘electronic transmission’’ or ‘‘digital biology’’. Details on these demonstrations
have been given elsewhere (Beauvais 2007, 2012, 2013a); the results of one public
demonstration has been thoroughly analyzed in a recent article (Beauvais 2013b).
During the public demonstrations, inactive samples (controls) and active samples
(supposed to have received specific ‘‘biological information’’) were prepared; in
some experiments, the ‘‘samples’’ were computer files (Beauvais 2007, 2012).
Usually, this preparation was organized in a laboratory other than Benveniste’s
laboratory. The preparation of samples was tightly controlled and their initial labels
were replace d with code numbers by participants not belonging to Benveniste’s
team (Eve in Fig. 1). Open-label samples were also prepared, but they nevertheless
received a blind code in Benveniste’s laboratory by a team member (Bob in Fig. 1)
before testing. During the next days, all samples were tested in Benveniste’s
laboratory. The results associated with each sample (change or no change of the
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biological parameter) were sent to Eve (usually by fax). Eve compared the two lists
(initial labels, i.e. expected effects, and observed effects) and assessed the rate of
concordant pairs, that is, ‘‘inactive’’ label associated with resting state of the
biological device and ‘‘active’’ labels associated with ‘‘activated’’ state of the
biological device.
Thus, suppose that the ‘‘expected’’ results were ;;;;:::: (i.e. four ‘‘inactive’’
and four ‘‘active’’ samples in that order). The observed results showed a statist ically
significant concordance with Bob: ;;;;::::. In contrast, the concordance was lost
with Eve: for example, ;:;:;;::. In other words, blind experiments with Eve
(external assessment) who remotely checked the results disturbed them; the
concordance of the biological outcomes with the labels was not best than random.
Note that ‘‘activated’’ state (:) was nevertheless observed, but not at the correct (i.e.
‘‘expected’’) places. This was in contrast with open-label experiments or blind
experiments with Bob who locally checked the results; in this case, ‘‘expected’’
results were observed. Such a series of experiments with both Bob and Eve who
assessed the results has been described in detail in a previous article (Beauvais
2013b). Description of Benveniste’s experiments in different experim ental condi-
tions (with or without Eve’s assessment) have been reported elsewhere (Beauvais
2012, 2013a).
Various explanations were proposed to explain these apparent disturbances in
experiments: water contamination, electromagnetic pollution, or spontaneous
‘‘jumps’’ of the alleged electromagnetic molecular memor y from sample to sample.
The hypothesis that ‘‘active’’ samples had been ‘‘erased’’ by external influence was
reasonable; but how an ‘‘inactive’’ sample could become ‘‘active’’ was more
challenging. No satisfying explanation was proposed for these results that were
Fig. 1 Definitions of the roles of the different agents in an experimental situation. Eve is outside the
laboratory and she remotely assesses (or not) the rate of success of the blind experiments made by Alice.
For this purpose, Eve replaces the initial label of each experimental sample by a code number. When all
samples have been tested, the observed states of the experimental device are sent to Eve. Then, Eve
assesses the rate of ‘‘success’’ by comparing the two lists: ‘‘expected’’ effects (‘‘inactive’’ (IN) and
‘‘active’’ (AC) samples under code numbers) and observed effects (resting state or ‘‘activated’’ state). Bob
who is inside the laboratory observes Alice making an experiment and can also locally assess the results
in blind experiments
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different according to a simple change of blinding conditions (local asse ssment with
Bob vs. remote assessment with Eve). Note that the formal distinction between these
two types of assessment was not done by Benveniste’s team at this time.
For Benveniste, these weird phenomena did not call into question the validity of
his claims, but indicated that further technical improvements were necessary to
protect the samples from possible external influences, including potential unknow n
influences from the experimenters/observers. Indeed, even if one dismissed
‘‘memory of water’’, the fact that consistent changes of a biological parameter
were observed was difficult to explain (Beauvais 2012). Despite technical
improvements, the mismatches persisted in blind experiments when Eve assessed
the results (Beauvais 2007).
3 A Need for a Theoretical Framework
After the isolated rodent heart, Benveniste’s team developed another promising
biological model, which could help for a clear demonstration of the ‘‘digital
biology’’ concepts. Indeed, one of the advantages of this biological model, based on
plasma coagulation, was the possibility to automate it. It was hoped that the
interaction of the experimenter with an automated device would be minimal, thus
possibly avoiding mismatches between various samples.
At this juncture, the United States Defense Advanced Research Projects Agency
(DARPA) became interested in the concept of ‘‘digital biology’’ proposed by
Benveniste and decided to commission a team of experts to assess the robot analyzer
set up by Benveniste’s team. The results of this expertise have been described in an
article in 2006 (Jonas et al. 2006). The authors concluded that resu lts supporting
‘‘digital biology’’ were obtained when members of Benveniste’s team were present,
but they were unable to reproduce these results in their absence. The possibility of
explaining these results as an experimenter’s effect was put forward by the authors,
but they concluded that a framework was necessary before continuing such a
research (Jonas et al. 2006).
If simple differences in assessment of experiments have such negative effects on
experimental results, it is difficult to continue to talk about water properties, high
dilutions, ‘‘digital biology’’ or biological activity without molecules. The sugges tion
that the experimenter played a nontrivial role in these experiments was repeatedly
suggested, including by Benveniste himself (Jonas et al. 2006). This role was
however generally considered as an external noise that disturbed the ‘‘biological
information without molecules’’.
I proposed in recent articles to describe Benveniste’s experiments in a
probabilistic quantum-like modeling (Beauvais 2012, 2013a, b, 2014). The price
to pay was to abandon the notions of ‘‘memory of water’’, ‘‘digital biology’’, and so
on. Note, however, that there is today no convincing direct proof of a modification
of water structure capable of storing specific information about complex biological
molecules.
In the present paper, using ideas from quantum Bayesianism or QBism, which is
a recent interpretation of quantum physics (and also of classical physics), we pres ent
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a description of Benveniste’s experiments without the explicit use of mathem atical
tools of quantum logic, such as Hilbert’s space, state vectors, Born’s rule,
probability amplitudes, non commuti ng observables, etc. Moreover, we show that
this formalism explains the origin of the relationship between ‘‘expected’’ results
and observed results if the fluctu ations of measurements are taken into account.
4 Violation of the Law of Total Probability in Benveniste’s Experiments
The law of total probability is a basic law of classical probability theory. If we
consider two disjoint events, B
1
and B
2
, such as Prob (B
1
UB
2
) = 1 (the
probability of realization of either B
1
or B
2
is equal to 1), for any event A, we
can express the formula of total probability as:
Prob (A) = Prob (B
1
) 9 Prob (A|B
1
) ? Prob (B
2
) 9 Prob (A|B
2
)
In this formula, the conditional probability of one event with respect to another is
given by the Bayes formula: Prob (A|B
1
) = Prob (A \ B
1
)/Prob (B
1
).
In previous articles, we described Benveniste’s experiments and we colligated
large series of experiments using the Langendorff device (Beauvais 2007, 2012,
2013a). These experiments are summarized in Table 1 according to three
experimental conditions: (1) Alice assessed success rate (open-label) or Bob
assessed success rate (Alice blind); (2) Eve assessed success rate (Alice blind). The
respective probabilities of success (SUCC) should be identical with or without Ev e’s
assessment.
Without Eve’s assessment, Prob
A
(SUCC) = 0.92 (Alice’s assessment) and
Prob
B
(SUCC) = 0.88 (Bob’s assessment). Then Eve tried to confirm these results
by assessing blind experiments with the participation of Alice (Fig. 1). After
receiving the results corresponding to each label, she assessed the success rates for
Table 1 Violation of total probability law in Benveniste’s experiments
Experimental situations Number of
experimental
points
‘‘Expected’’
outcomes
Observed outcomes (Success rate, %)
Outcome ‘‘;’’
(resting state)
Outcome ‘‘ :’’
(‘‘activated’’ state)
(1) Eve did not assess success rate
a
Alice assessed success rate
(Open-label)
N = 372 ‘‘Inactive’’ 93 % 7%
N = 202 ‘‘Active’’ 11 % 89 %
Bob assessed success rate
(Alice blind)
N = 118 ‘‘Inactive’’ 91 % 9%
N = 86 ‘‘Active’’ 15 % 85 %
(2) Eve assessed success
rate
a
(Alice blind)
N = 54 ‘‘Inactive’’ 57 % 43 %
N = 54 ‘‘Active’’ 44 % 56 %
Summary of results presented in (Beauvais 2012)
Rates of ‘‘success’’ (‘‘Inactive’’ label associated with resting state and ‘‘active’’ label associated with
‘‘activated’’ state) are in bold type
a
See Fig. 1 and text
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each label (IN for ‘‘inactive’’ label and AC for ‘‘active’’ label) and she calculated the
overall rate of success:
Prob
E
ðSUCCÞ¼Prob ðINÞProb ðSUCC j INÞþProb ðACÞ
 Prob ðSUCC j ACÞ
¼ 0:5  0:57 þ 0:5  0:56 ¼ 0:57
Therefore the probability of success was different according to the experi-
mental conditions (assessment of success rates firstly by Alice/Bob or firstly by
Eve):
Prob
A
ðSUCCÞProb
B
ðSUCCÞ [ Prob
E
ðSUCCÞ
Remote assessment of success rate led to a decrease of the rate of success
(concordance between ‘‘expected’’ results and observed results). The law of total
probability was thus violated in Benveniste’s experiments.
The law of total probability can be violated in quantum logic. Thus, in the
two-slit Young’s experiment, the probability to observe a screen impact of the
photon at a given place is different if the path of the photon (though slit 1 or slit
2) is identified or not. The decoherence process is however an obstacle to use
quantum logic in macroscopic exper imental situations. In this article we show
how a personalist view of physics gives tools to describe Benveniste’s
experiments.
5 Summary of a Personalist Interpretation of Probability
In a recent article, Mermin commented quantum Bayesianism (or QBism), which
is a personalist interpretation of quantum physics (Mermin 2014). The main
feature of this interpretation is that the scientist (the observer) is central in the
description, not only of quantum phenomena, but of the entire physical world.
The propon ents of this interpretation (Fuchs, Caves and Schack) proposed to
consider the perceptios of the observer as central in any physical description of
the world: ‘‘The outcome of an experiment is the experience it elicits in an
agent’’ (Fuchs 2010; Fuchs et al. 2013). The outcome is thus displaced from the
object to its perception by the obser ver. In other words, the experience is the
outcome. As a consequence, experiments that have not been experienced by one
agent have no result for this agent (there are as many descriptions of the reality
as observers). Moreover, a measurement does not reveal a preexisting outc ome,
but results in the creation of something new . Nevertheless all the observers agree
when they compare their observations and measurements; each observer enters
then the own experience of the other observer. Another interesting and important
feature of QBism is that there is no split between micro scopic and macroscopic,
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but between the world where an agent lives and his internal experience of that
world.
6 Modeling of Benveniste’s Experiments
6.1 Definitions and ‘‘Rules of the Game’’
A ‘‘success’’ is defined as the experience by Alice of either ‘‘inactive’’ (IN)
sample with resting state (;) or ‘‘active’’ (AC) sample with ‘‘activated’’ state (:).
Success is thus defined as A
IN
associated with A
;
or A
AC
associated with A
:
. The
probability that an experimenter/observe r experiences the event X is symbolized
by Prob (A
X
).
A label is like a pointer of a meter device that is moved by Alice (or Bob) toward
the words IN (‘‘inactive’’) or AC (‘‘active’’) (Fig. 2). Which samples are ‘‘inactive’’
or ‘‘active’’ is decided by the experimental protocol. Although these samples are not
physically changed during this process, the formalism requires that the experiences
Fig. 2 Perception by Alice of the different ‘‘pointers’’. A ‘‘label’’ is like a pointer that is moved by Alice
toward IN (‘‘inactive’’) or AC (‘‘active’’). Despite the apparent subjective characteristics of ‘‘labels’’, their
perception is not of a different nature compared to the perception of the states of the experimental device
(resting state or ‘‘activated’’ state). The comparison is also like a pointer moved by the experimenter
(toward ‘‘success’’ or ‘‘failure’’) according to defined rules; the results of comparison that leave traces in
the macroscopic world (pointer) are in turn perceived by the experimenter
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elicited by ‘‘inactive’’ versus ‘‘active’’ labels must be different. The ‘‘aim of the
game’’ is thus to compare for each sample the perception of the position of ‘‘Pointer
1’’ (IN or AC labels) with the perception of the position of ‘‘Pointer 2’’, namely the
biological device (resting state ; or ‘‘activated’’ state :).
The comparison of the position of these two pointers is also like another
pointer which is moved toward ‘‘success’’ or ‘‘failure’’ by the experimenter (or
any automatic device) according to defined rules; the position of this third pointer
in turn is perceived by the experimenter. Therefore, despite the apparent
subjective characteristics of labels and assessment of success, their perception is
not of a different nature compared to the perception of the states of the
experimental device.
6.2 Construction of a relationship betw een ‘‘expected’’ results and observ ed
results
In the context of a pers onalist view of probability, Alice experiences an outcome of
an experiment not only after ‘‘direct’’ observation, but also from other ‘‘channels’’
such as Bob or other observers. Although measurements through these different
channels are independent, the resulting experience by Alice must be both unique
and consistent. For example, Alice and Bob must agree on the unique result of the
experiment—namely, success or failure—and an experimental situation such as
success for Alice and failure for Bob is not allowed.
For simplification, we first consider only two channels that we name Channel #1
and Channel #2. Each measurement through each canal is independent. We suppose
that the probability of success (SUCC)isp and probability of failure is q for
measurement through Channel #1 or Channel #2 (p ? q = 1). Therefore, the
probability for success experienced by Alice via the two channels is the joint
probability (Fig. 3):
ProbðA
SUCC#1
\ A
SUCC#2
Þ¼
p  p
p  p þ q  q
¼
p
2
p
2
þ q
2
‘‘Classically’’ (i.e. if one consider s that the outcome belongs to the object and not to
the observer), the joint probability for success (and the joint probability for failure)
is equal to the probability through each channel:
p ¼
p
2
p
2
þ q
2
and q ¼
q
2
p
2
þ q
2
One can easily calculate that ProbðA
SUCC#1
\ A
SUCC#2
Þ¼1=2.
1
However, measurements are not performed ‘‘in the sky’’, but in the macroscopic
world. As a consequence, any measurement is submitted to random microscopic
fluctuations. In a QBist point of view, the random probability fluctuations e
1
and e
2
,
1
In other words, if samples are all physically identical, then the respective probabilities Prob (A
:
| A
AC
)
and Prob (A
:
| A
IN
) are equal. Measurements of different samples with the same label are equivalent to
repeated measurements of the same sample.
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respectively associated with Channel #1 and Channel #2 are independent (e
1
and e
2
are positive or negative tiny random real numbers).
After one fluctuation, the probability that Alice experiences ‘‘success’’ through
Channel #1 is 1/2 ? e
1
; for both channels the joint probability is given by the
following equation:
ProbðA
SUCC#1
\ A
SUCC#2
Þ¼
ð1=2 þ e
1
Þð1=2 þ e
2
Þ
D
with D = (1/2 ? e
1
) 9 (1/2 ? e
2
) ? (1/2 - e
1
) 9 (1/2 - e
2
)
The initial proba bility of success (equal to 1/2 before the measur ement) is thus
updated with a new value, which in turn is updated after another random
fluctuation and so on. A computer simulation with very small probability
fluctuations easily shows that, after several calculation steps, two stable positions
are obtained (Fig. 4). With a greater number of channels, the transition towards
one of the two stable positions occurs after a lower number of calculation steps
(not shown).
These results show that the initial state with probability of ‘‘success’’ equal to 1/2
is metastable if we take into consideration measurement fluctuations. Indeed, two
stable positions emerge: probability of ‘‘success’’ equal to 1 (A
IN
/A
AC
associated
Agreement (gray areas) = p² + q²
Success through
Channel #1 (p)
Success through
Channel #2 (p)
Failure through both channels (q²)
22
2
2#1#
)(Prob
qp
p
qqpp
pp
AA
SUCCSUCC
+
=
×+×
×
=∩
Fig. 3 Consequences of a personalist view of probability on joint probabilities of the outcome from
different channels. Alice perceives the outcome of an experiment through different channels (e.g.
‘‘direct’’ observation or other observers such as Bob). These different channels must be consistent (same
outcome for all channels) because Alice experiences a unique outcome. For simplification we show only
two channels. White areas correspond to experimental situations where outcomes from the two channels
are not consistent (e.g. success via Channel #1 and failure via Channel #2). These white areas correspond
thus to impossible experimental situations and are excluded for probability calculations. The probability
of each white area is pq (probability of ‘‘cross-terms’’). The probability to observe success from both
channels is thus the ratio of the central gray area (Alice perceives success through both channels) which
has probability p
2
divided by the probability to observe consistent outcomes for either success or failure
via both channels (p
2
? q
2
)
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with A
;
/A
:
for stable position 1) or probability of ‘‘success’’ equal to 0 (A
IN
/A
AC
associated with A
:
/A
;
for stable position 2, respectively).
6.3 Selection of the ‘‘expected’’ stable position and local assessment
of success in blind experiments
Nothing in the modeling allows selecting one of the two stable positions 1 and 2.
However, we must note that, by construction, the biological device is asymmetrical:
A
;
is implicitly associated with A
IN
. One could thus consider that a sample with
‘‘inactive’’ label associated with resting state (;) is systematically intercalated
Prob(A
SUCCESS#1
∩ A
SUCCESS#
2
)
ΔProb at each step: ε = random [-0.5 ; +0.5] × 10
-6
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 5 10 15 20 25 30 35 40 45 50 55 60
Calculation steps
Stable position 2: ↑↑↑↑↓↓↓↓
Stable position 1: ↓↓↓↓↑↑↑↑
Initial state:
↓↓↓↓↓↓↓↓
"Expected" results
↓↓↓↓↑↑↑↑
Fig. 4 Evolution of the probability of success after a series of random microscopic fluctuations.
Microscopic random fluctuations of measurement are the source of tiny variations of the probability of
success perceived by Alice. As in Fig. 1, we consider that Alice gains information from two channels
(from ‘‘direct’’ observation and from Bob for example). The probability of success is initially equal to 1/2.
The equation ProbðA
SUCCESS#1
\ A
SUCCESS#2
Þ¼
ð1=2 þ e
1
Þð1=2 þ e
2
Þ
D
(see text) allows calculating the
next probability of success after one random fluctuation. This new value replaces then the initial 1/2
probability and probability obtained after each random step is reinjected for the next calculation of
probability of success. A small elementary change of probability of ‘‘success’’ is defined at each
calculation step of this computer simulation: from -0.5 to ?0.5 9 10
-6
. In this computer simulation, the
probability of ‘‘success’’ becomes unstable after a few calculation steps toward one of the two stable
positions: either ‘‘success’’ or ‘‘failure’’. With a smaller change of probability of ‘‘success’’, the
bifurcation occurs after a greater number of calculation steps (40–50 calculation steps with e = random
[-0.5 to ?0.5] 9 10
-15
); with a number of channels [2, the bifurcation towards stable positions occurs
with fewer calculation steps (not shown). The results of eight computer simulations are shown in this
figure
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between each test sample. As a consequence, only the possible ‘‘universes’’ where
A
;
is associated with A
IN
are allowed. Therefore, only stable position 1 is possible.
In this case, ‘‘expected’’ results fit observed results (Table 2).
Bob can locally assess the results of Alice by making blind experiments. In this
experimental situation, both Alice and Bob are in the same stable position (Bob is a
channel for Alice) with probability of success equal to one. ‘‘Success’’ with blind
experiments locally assessed by Bob is thus easily explained.
6.4 Transition of the biological device from resting state to ‘‘activated’’
state
It is important to underscore an import ant consequence of the formalism that is the
transition of the biological device from resting state to ‘‘activated’’ state. Indeed, in
stable position 1, A
:
is associated with certainty (probability of success equal to 1)
with A
AC
. Introducing the fluctuation e for probability of success (Sect. 6.2)
implicitly means that the perception of the spontaneous transition from A
;
to A
:
is
possible, even though with a low probability. Indeed, the ‘‘expe cted’’ probability of
success is initially equal to 1/2: the initial probabilities of success associated with
A
IN
and A
AC
are equal since only resting state is observed (A
IN
with A
;
is a success
and A
AC
with A
;
is a failure) (Fig. 4). If the probability of success is slightly
modified (1/2 ? e), it means that the probability of A
:
is different of zero (with
Table 2 Comparison of classical and personalist views of probability to describe Benveniste’s
experiments
Calculation of probability
of success
‘‘Bifurcation’’ and observation
of ‘‘activated’’ state
Classical view of probability
a
Without measurement fluctuations 1/2 No
With measurement fluctuations 1/2 ? e No
Personalist view of probability
b
Without measurement fluctuations 1/2 No
With measurement fluctuations
c
ð1=2 þ e
1
Þð1=2 þ e
2
Þ
D
Yes
e
,
e
1
and e
2
are random numbers (positive and negative) for modeling of microscopic fluctuations inherent
to any measurement; e
1
and e
2
are for two independent channels
a
In the classical view of probability, the experimental device is described independently of any observer
b
In the personalist view of probability, the outcome is displaced from the object to its perception by the
observer. As a consequence, the outcome can be perceived through different independent channels; the
outcome perceived from these different sources must be consistent (either success for both channels or
failure for both channels)
c
With D = (1/2 ? e
1
) 9 (1/2 ? e
2
) ? (1/2 - e
1
) 9 (1/2 - e
2
); only two channels are considered (as in
Figs. 3, 4), but the formula can be easily generalized to any number of channels
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some ‘‘inactive’’ samples associated with ‘‘failure’’ or ‘‘active’’ samples associated
with ‘‘success’’).
6.5 Description of the Apparent ‘‘Jumping’’ of the Biological Activity
from Sample to Sample
As described in Sect. 2, Eve remotely asse sses the experiment by comparing two
lists that summarize the results: for each sample, Eve compares the state of the
biological device (resting state or ‘‘activated’’ state) observed in blind tests by Alice
under code label and the corresponding initial label (‘‘inactive’’ or ‘‘active’’ label).
2
Eve calculates then the rate of success of the experiment (Fig. 1).
The probability of success (SUCC) in this experimental situation can be calculated
using conditional probabilities to take into account information on inactive (IN) and
active (AC) labels (in contrast with Bob, Eve is not a channel for Alice):
Prob A
SUCC
ðÞ¼Prob A
IN
ðÞProb A
SUCC
jA
IN
ðÞþProb A
AC
ðÞ
 Prob A
SUCC
jA
AC
ðÞ
¼ 1=2  1=2 þ 1=2  1=2 ¼ 1= 2
Consequently, in blind experiments with Eve, the proportion of samples with an
‘‘active’’ label observed in association with an ‘‘activated’’ state decreases from 100
to 50 % and the proportion of samples with an ‘‘inactive’’ label observed in
association with an ‘‘activated’’ state increases from 0 to 50 %. Thus, in a series of
samples, it is as if the ‘‘biological activity’’ jumped from some samples with an
‘‘active’’ label to other samples with ‘‘inactive’’ label; success is observed not better
than random. Failure with blind experiments remotely assessed by Eve is thus easily
explained.
6.6 Limits Imposed by the Macroscopic States of the Experimental Device
and of the Experimenter
One could argue that, according to this modeling, a relationship between
‘‘expected’’ results and observed results should be frequently observed in any
experimental context as soon as two parameters—supposed to be connected—are
assessed. However, in real experimental situations, the application of this formalism
could be limited for physical reasons. The fact that Benveniste’s experiments were
performed in the context of a laboratory dedicated to biological sciences is perhaps
not without significance. Indeed, biological models have many degrees of freedom
and Brownian motion of molecules in solution confers a large plasticity to these
systems. The mean values of a biological parameter may vary (under some range),
thus allowing the perception of ‘‘activated’’ state as described in Fig. 4. Such a
2
One could argue that the transition from 1/2 to 1 for the probability of success as described in Fig. 4 is
not possible in blind experiments with Eve since Alice cannot assess the rate of success. This transition
occurs nevertheless with available information (real or supposed) on ‘‘expected’’ results, for example the
number of ‘‘active’’ samples, but without knowledge of their exact place among all samples.
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transition from initial position to stable position is possible only with experimental
systems that are sufficiently ‘‘flexible’’.
Thus, suppose that we replace the Langendorff’s apparatus in Benveniste’s
experiments with a Schro
¨
dinger’s cat. We assume that the radioactive decay of the
device gives a probability 1/100 for dead cat (‘‘activated’’ state) and 99/100 for
living cat (resting state). A stable posi tion (Fig. 4) is achieved only if the
‘‘activated’’ state (dead cat) is observed in 50 % of measurements (supposing that
half of labels should be associated with ‘‘dead cat’’). This is an example of a ‘‘rigid’’
system due to the physical impossibility to change radioactive decay. Another
example is a beam splitter reflecting individual photons with a probability 1/100
(‘‘activated’’ state) or transmitting them with a probability 99/100 (resting state).
Despite random microscopic fluctuations of measurement, there is no possibility to
achieve a stable position. Indeed, the beam splitter does not allow observing 50 %
of transmitted photons and 50 % of reflected photons without changing its ‘‘rigid’’
internal structure. In contrast, in all biological models used in Benveniste’s
experiments, an ‘‘activated’’ state could be easily obtained by adding pharmaco-
logical or biological molecules at ‘‘classical’’ concentrations. In other words, the
formalism allows connecting perceptions of two parameters only if laws of physics
are respected.
Another limitation, which could explain why Benveniste’s exper iments were not
easily reproduced by other teams, is related to the cognitive aspect present in this
formalism. Indeed, the successive calculation steps that allow building Fig. 4
suppose that Alice permanently adjusts her a priori probability for success after each
experiment (or series of experiments) according to the defined rules. If there are
defects in these cognitive processes, stable position with probability equal to unity
(i.e. certainty to experience ‘‘success’’) could not be achieved and maintained.
7 Discussion
For most scientists, Benveniste’s experiments remain an example of poor science —
whatever the alleged reasons (artifact, wishful thinking, unseen error)—aimed to
support an alternative and controversial medicine, namely homeopathy. Among the
arguments against ‘‘memory of water’’ were the incompatibility of this hypothesis
with our knowledge of physics of water, the poor reproducibility of the experiments
by other teams and the failures of blind experiments (with controllers such as Eve).
Other arguments supported however the idea that something was at work in these
experiments and was of scientific interest. More particularly, there were
unexplained variations of biological parameters and numerous consistent results
including blind experiments (with cont rollers such as Bob). For these latter reasons,
Benveniste’s team considered that these results were not due to trivial errors or
artifacts and persisted in this direction.
Even though the ‘‘activated’’ state was not always at the ‘‘expected’’ place, its
appearance remained unexplained and puzzling (Beauvais 2007, 2008, 2013a, b,
2014). In a first step, we analyzed large series of exper iments obtained by
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Benveniste’s team in the 1990s with the Langendorff device (Beauvais 2007, 2012,
2013a). In particular, we studied the correlations of outcomes with two Langendorff
devices that worked in parallel in Benveniste’s laboratory from 1992 to 1996
(double measurements allowed Benveniste’s team to be confident on results for
public demonstrations). The relationship between ‘‘expected’’ effects and observed
effects was quantified and we defined the experimental conditions to observe
significant relationships. The outcomes of the trials strong ly depended on the
location of people who assessed success rates of blind experiments (success with
Bob vs. not better than random with Eve). We analyzed also in detail a ‘‘public
demonstration’’ with four series of blind experiments controlled by Eve and Bob
(Beauvais 2013b).
It appeared thus that the scientific fact in these data was not elusive water
properties, but the difference for ‘‘success’’ according to the experimental
conditions (blind experiments with Bob vs. Eve). Note that the early experiments
with basophils were also not devoid of ‘‘experimenter-dependent’’ outcomes and
effects of blinding (Beauvais 2007). A similar unusual conclusion on a possible role
of the experimenter was also reported by the multidisciplinary team that was
mandated by the DARPA to expertise the ‘‘digital biology’’ of Benveniste (Jonas
et al. 2006).
In mathematical terms, the difference in outcomes according to the experimental
conditions was translated by the violation of the total probability law. In other
words, there was no possible explanation based on classical probability. In these
conditions, finding a ‘‘structural’’ and ‘‘local’’ explanation into water samples
(similar to a classical pharmacological effect) would be a chimera. According to the
present formalism, the experimenters describe outcomes that they contribute to
construct.
Therefore, the violation of the total probability law suggested that these
experiments could have been misinterpreted and that the causal relationship
between samples and outcomes was only apparent. If we accept to abandon the
hypothesis of ‘‘memory of water’’, we have to reinterpret these experiments in a
new framework. In a series of articles, we showed that the logic of Benveniste’s
experiments reminded quantum logic as observed in self-interference of single
photon in two-slit Young’s experiment or in Mach–Zehnder apparatus (Beauvais
2013a, b, 2014).
Decoherence is generally thought to be an obstacle for the description of
macroscopic events with quantum logic. Nevertheless, Fuchs et al. proposed in their
personalist interpretation of quantum physics (QBism) to displace the outcome of an
experiment from the object to its perception by an agent. In QBism approach, there
is no split between microscopic and macroscopic, but between the world where an
agent lives and his internal experience of that world. In the present artic le, we
propose a new framework for Benveniste’s experiments that is inspired from the
personalist principles of QBism. Note that we do not use the typical tools of
quantum logic such as Hilbert space, probability amplitud es, Born rule, etc. Even
though the mathematical tools used in the present modeling are classical, the initial
hypotheses inspired from QBism are nevertheless not classical. The main hypothesis
is the displacement of the outcome from the observed object to its perception by the
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observer. As an example, if one describes a player who flips a coin, one would
classically say that heads came up; in a personalist view, one says that the player
experienced that heads came up (‘‘The experience is the outcome’’).
All characteristics of Benveniste’s experiments, including their paradoxical
aspects, are taken into account in the modeling. Thus, the transition from resting
state to ‘‘activated’’ state of the biological system, the apparent causal relationship
between observables (interpreted as ‘‘success’’) and the ‘‘jumps’’ of the biological
activity from ‘‘active’’ to ‘‘inactive’’ samples (interpreted as ‘‘failure’’) are easily
described. Overall, this modeling fits the corpus of the experimental data gained by
Benveniste’s team over the years (Beauvais 2007, 2012, 2013a, b).
If establishing relationships between observables was so easy as suggested by the
proposed modeling, why ‘‘expected’’ results are not more frequently observed in
daily scientific measurements? We can suggest that some physical const raints
related to the ‘‘rigidity’’ of the macroscopic states corresponding to the experimental
device could limit the evolution toward a ‘‘successful’’ stable position as described
in Fig. 4. Experimental models sufficiently ‘‘flexible’’ are necessary and biological
models—at least some of them—appear to be appropriate for this purpose.
Cognitive processes are also at work in this formalism (with permanent adjustment
of a priori probability according to defined rules) and deficiency of these processes
could be an obstacle for ‘‘successful’’ experiments.
Conversely, we cannot exclude that some ‘‘classical’’ exper iments are ‘‘polluted’’
with phenomena similar to those reported by Benveniste in some ‘‘favorable’’
experimental conditions; this could lead to describe experimental outcomes that
have been in fact ‘‘constructed’’ by the experimenters without their knowledge.
In conclusion, a personalist interpretation of Benveniste’s experiments offers for
the first time a logical framework for these experiments that have remained
controversial and paradoxical till date.
Compliance with Ethical Standards
Conflict of interest The author declares that he has no conflict of interest.
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