“Memory of Water” Without Water: The Logic of Disputed Experiments

Abstract

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.

Full text

ORIGINAL PAPER
‘‘Memory of Water’’ Without Water: The Logic
of Disputed Experiments
Francis Beauvais
Received: 18 February 2013 / Accepted: 16 July 2013 / Published online: 30 July 2013
ÓSpringer Science+Business Media Dordrecht 2013
Abstract The ‘‘memory of water’’ was a major international controversy that
remains unresolved. Taken seriously or not, this hypothesis leads to logical con-
tradictions 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 Ben-
veniste’s experiments are taken into account (emergence of a signal from the
background, difficulties faced by other teams in terms of reproducibility, distur-
bances during blind experiments, and apparent ‘‘jumps of activity’’ between sam-
ples). In conclusion, it is proposed that the cognitive states of the experimenter
exhibited quantum-like properties during Benveniste’s experiments.
Keywords Memory of water Scientific controversy Quantum-like
probabilities Quantum cognition
Where would elementary principles such as the law
of mass action be if Benveniste is proved correct?
(Maddox 1988b)
F. Beauvais (&)
91, Grande Rue, 92310 Se
`vres, France
e-mail: beauvais@netcourrier.com
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DOI 10.1007/s10516-013-9220-9
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1 Introduction
Scientific controversies often reveal the functioning of science and sometimes lead
to paradigm changes (Kuhn 1962). Thus, the ‘‘memory-of-water’’ controversy
exposed the role of leading scientific journals and the peer-review system in the
filtering of ideas from emergent research fields (Schiff 1998). This specific topic has
been widely commented upon and details could be found elsewhere (Maddox
1988a; Maddox et al. 1988; Schiff 1998; Benveniste 2005; Beauvais 2007). For
many scientists, the affair with the journal Nature marked the end of the ‘‘memory-
of-water’’ controversy. Indeed, the hypothesis that a fluid such as water could retain,
even if temporarily, information from large molecules after serial dilutions beyond
the limit of Avogadro was judged highly implausible (Teixeira 2007). Moreover,
other teams encountered difficulties to reproduce the effects with high dilutions with
either the same experimental protocol or other biological systems; these reasons led
to a disinterest in an idea that was considered at one time as a ‘‘new area for
biology’’ if it could be confirmed (Benveniste 2005).
After 1988, Benveniste and his team continued to explore the new research
domain that they thought to have discovered. After the disputed basophils, two
biological models with promising results were successively developed: the isolated
rodent heart (Langendorff model) and the coagulation model. In parallel, after high
dilutions, Benveniste proposed other methods to ‘‘imprint’’ biological information
into water. Thus, in 1992, he reported that a specific electromagnetic radiation
emitted from a solution containing a biologically-active molecule could be
transmitted to water via an electronic amplifier (Benveniste et al. 1992;Aı
¨ssa
et al. 1993; Benveniste et al. 1994;Aı
¨ssa et al. 1995). Finally, in 1996, he described
the storage of this ‘‘biological information’’ on a hard disk via the sound card of a
computer; the stored information could then be ‘‘played’’ to water to transmit this
specific ‘‘information’’ (Benveniste et al. 1996; Benveniste et al. 1997; Benveniste
et al. 1998).
Close examination of the whole ‘‘memory-of-water’’ saga supports the idea that
the controversy has not been closed satisfactorily (Beauvais 2007). Indeed,
substantiated arguments were made from both sides. On one side, the a priori
impossibility for writing ‘‘bits’’ in water was far from absurd and the proponents of
‘‘memory of water,’’ despite promising results, have not been able to offer
convincing proofs to the contrary. On the other side, the effects that were related to
the ‘‘memory of water’’ were reported by a laboratory with an excellent reputation.
Benveniste himself was a reputed senior director of INSERM, the French medical
research organization, and he was a member of the scientific establishment. He was
one of the discoverers of the platelet-activating factor, a new inflammatory molecule
discovered in the 1970s, and he had everything to lose with such extraordinary
claims. This research extended on for approximately 20 years and involved
successive experimenters who were experts in the management of different
biological models. Therefore, suggesting trivial explanations, such as artifact, fake,
or incompetence cannot explain the whole story.
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2 Why Did Benveniste’s Experiments Fail to Convince?
The initial program of Benveniste’s team was to assess a causal relationship
between water samples, which were supposed to have been ‘‘informed’’ by different
processes and the corresponding biological outcomes. Although the initial program
was a failure, significant correlations were observed in these experiments.
The hypothesis of the ‘‘memory of water’’ was supported by experiments that were,
at first sight, similar to classical pharmacological experiments. However, odd results
were repeatedly observed during the ‘‘public demonstrations’’ that Benveniste
organized to convince other scientists about the importance of his research (Table 1).
The aim of these public demonstrations was to establish a definitive proof of concept
for ‘‘electronic transmission’’ and ‘‘digital biology’’ with other scientists as witnesses.
During these demonstrations, scientists who were interested in these experiments
participated in the production of the experimental samples by using the electronic
tools devised by Benveniste’s team for the ‘‘transmission of biological activity.’’ The
samples received a code number from the participants and the samples were assessed
in Benveniste’s laboratory. The protocols and results of these public blinded
demonstrations have been previously described in detail (Beauvais 2007).
An unexpected phenomenon that was an obstacle for the establishment of a
‘‘definitive’’ proof repeatedly occurred. Indeed, after the unblinding of the masked
experiments, an effect on the biological system was frequently found associated with
the ‘‘control’’ tubes, whereas some of the samples supposed to be ‘‘active’’ were
without effect. Benveniste generally interpreted these mismatches as ‘‘jumps of
activity’’ between the samples owing to the electromagnetic nature of the specific
Table 1 The antagonistic pro and con arguments of the ‘‘memory-of-water’’ controversy and their
peaceful coexistence in a quantum-like model
Classical view Quantum-like view
Yes, ‘‘memory of
water’’ exists
a
No, ‘‘memory of water’’
does not exist
Arguments Arguments Description of the experiments with a quantum-
like probabilistic model taking into account
the experimental context
‘‘Success’’ and ‘‘failure’’ of the experiments are
described as the two facets of the same
phenomenon
No need of ‘‘memory-of-water’’ hypothesis
Emergence of signal
from the background
Numerous coherent
results
Success with blind
experiments (type-2
observer
b
)
Not compatible with our
knowledge of physics of
water
Reproductions of
experiments by other
teams generally failed
Blind experiments (type-1
observer
b
) failed
Paradox No paradox
a
‘‘Memory of water’’ is the hypothesis that specific biological information could be ‘‘imprinted’’ in water
samples in the absence of the original biological molecule. Highly diluted solutions of biologically active
compounds or other methods (‘‘electronic transmission’’ and ‘‘digital biology’’) were used
b
Blind experiments with type-1 and type-2 observers: see text
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‘‘molecular signal.’’ The logical consequence of this interpretation was trying to
protect the ‘‘informed’’ water samples and their controls from external influences, such
as electromagnetic waves. Despite additional precautions and further improvements
of the devices, this weirdness nevertheless persisted and ‘‘jumps’’ could not be
prevented (Benveniste 2005; Beauvais 2007,2008,2012; Thomas 2007).
At this stage, one could conclude that the initial hypotheses were ‘‘falsified’’ and that
the concepts of ‘‘memory of water,’’ ‘‘electronic molecular transmission,’’ and ‘‘digital
biology’’ were illusions. Benveniste, however, clung to the idea that a variation of the
biological parameters was nevertheless observed during these experiments, a phenom-
enon that was not explained by current scientific knowledge. For example, the
experimental outcomes were correlated after two successive measurements on the same
biological system or after measurements on two experimental devices (Beauvais 2007).
Therefore, Benveniste’s team constructed an automatic robot analyzer to perform
coagulation experiments with minimal intervention of the experimenter, which was
suspected to interfere, by unknown reasons, with the device.
In 2001, the United States Defense Advanced Research Projects Agency
(DARPA) that was amazed by Benveniste’s theories decided to investigate the
automatic robot analyzer and assess if the digital signals recorded on a hard disk
could be the source of specific biological effects. In the article that summarized their
study, the experts reported that some effects supporting the concepts of ‘‘digital
biology’’ were observed. However, they did not admit that the concepts of ‘‘digital
biology’’ were valid, but that an unknown ‘‘experimenter effect’’ could explain the
results. The experts concluded that a theoretical framework was necessary before
trying to apprehend these phenomena (Jonas et al. 2006).
In a previous article, we analyzed a large set of experiments obtained by
Benveniste’s team in the 1990s with the Langendorff model including ‘‘public
demonstrations’’ (Beauvais 2012). Comparing the results obtained in different
blinding conditions, we concluded that the results of these experiments were related to
experimenter-dependent correlations. Although these results did not support the initial
‘‘memory of water’’ hypothesis, the signal that emerged from the background noise
remained puzzling. We proposed a model in which the emergence of a signal (i.e., a
change of biological parameter) from the background noise could be described by the
entanglement of the experimenter with the observed system. However, entanglement
is a notion that is borrowed to quantum physics and decoherence of any macroscopic
system was an obstacle to the general acceptance of such an interpretation. In a second
article, we showed that Benveniste’s experiments and quantum interference exper-
iments of single particles had the same logical structure. This parallel allowed
elaborating a more complete formalism of Benveniste’s experiments and we proposed
to see Benveniste’s experiments as the result of quantum-like probability interferences
of cognitive states (Beauvais 2013).
The purpose of this article is to present an original framework based on a quantum-
like description of Benveniste’s experiments. Biological systems will not be detailed
and will be considered as black boxes with inputs (sample labels) and outputs
(biological outcomes); only the logical aspects and the underlying mathematical
structures of these experiments will be taken into account. Some of the ideas presented
here have been previously published, but the present article offers a synthesis and takes
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a closer look at specific issues raised by the quantum-like formalism that were not
addressed before (Beauvais 2012,2013).
3 The Logic of Benveniste’s Experiments and Single-Particle Interference
Experiments
In Benveniste’s experiments and single-particle interference experiments, a
quantum object (photon) or quantum-like object (cognitive state of the experi-
menter) interact with macroscopic devices for measurement/observation. Therefore,
we drew a parallel between Benveniste’s experiments and single-particle interfer-
ence experiments in a Mach–Zehnder interferometer (Table 2; Fig. 1).
A Mach–Zehnder interferometer has the advantage of possessing only two
detectors and not a screen as the two-slit Young’s experiment. As seen in Fig. 1
(upper drawing), 50 % of light emitted from a source is transmitted by a beam
splitter (BS1) in path T and 50 % is reflected in path R (Scarani and Suarez 1998).
In BS2, the two beams are recombined and 50 % of light is transmitted to detector
D1 and 50 % to detector D2. If light is considered a wave, it can be demonstrated
that waves from the two paths are constructive when they arrive in D1 and are
destructive in D2. This is indeed what experiments show: only detector D1 clicks
after light detection. This result is in favor of the wave nature of light. Indeed, if
light is considered as a collection of particles, then they should be recorded
randomly into D1 or D2 (with a probability of 1/2 either D1 or D2). However, if
light intensity is decreased in order that particles are emitted one by one, the
interference pattern persists (only detector D1 clicks). Each particle behaves as if it
Table 2 Parallel between the single-particle interference experiment with the Mach–Zehnder interfer-
ometer and Benveniste’s experiments
Interferometer experiment Benveniste’s experiments
a
First ‘‘path’’ Path T A
IN
Second ‘‘path’’ Path R A
AC
k2
1Prob (path T) Prob (A
IN
)
k2
2Prob (path R) Prob (A
AC
)
Superposition (quantum probabilities) Path T and path R A
IN
and A
AC
Outcome 1 100 % detector D1 100 % ‘‘concordant’’ pairs
b
Outcome 2 0 % detector D2 0 % ‘‘discordant’’ pairs
c
No superposition (classical probabilities) Path T or path R A
IN
or A
AC
Outcome 1 50 % detector D1 50 % ‘‘concordant’’ pairs
b
Outcome 2 50 % detector D2 50 % ‘‘discordant’’ pairs
c
Acognitive state of the experimenter, IN ‘‘inactive’’ labels, AC ‘‘active’’ labels, ;background, :signal,
Ttransmission, Rreflection
a
For an experiment with optimal correlations between labels and biological outcomes (and with k2
1¼k2
2)
b
A
IN
with A
;
or A
AC
with A
:
c
A
IN
with A
:
or A
AC
with A
;
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would interfere with itself. This counterintuitive (i.e., nonclassical) behavior
disappears if the information on the initial path (T or R) is obtained by
measurement: then D1 or D2 click randomly with a probability of 1/2 for each
detector (classical probabilities apply in this case) (Fig. 1; lower drawing).
Fig. 1 Experiments of single-particle interference have the same logical structure as Benveniste’s
experiments. When a unique particle interferes with itself, interferences are constructive in the detector
D1 and destructive in the detector D2. Therefore, only detector D1 clicks (upper drawing). If one
evidences by measurement the path of the particle (R or T), then both detectors click with a probability of
0.5 for each (classical probability apply because information on the path must be taken into account)
(lower drawing). In Benveniste’s experiments, significant correlations of the labels and outcomes (IN with
‘‘;’’ and AC with ‘‘:’’; concordant pairs) were observed in the open-label experiments (or after blinding
by a type-2 observer) (upper drawing). In case of blinding by a type-1 observer, correlations vanished and
the association between labels and outcomes were broken and were randomly distributed in concordant
and discordant pairs (lower drawing)
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Therefore, the logic of the two experimental situations (Benveniste’s experiments
and one-particle interference experiment) is comparable. In Benveniste’s experiments,
‘‘active’’ samples were expected to be associated with a change in the experimental
biological system (we name it a ‘‘signal’’) whereas ‘‘inactive’’ samples were expected to
be associated with background. According to the context of the experiment (detection or
not of the ‘‘initial path,’’ i.e., sample labels), either only concordant pairs (equivalent to
only detection in D1) or both concordant/discordant pairs (i.e., equivalent to random
detection by D1 and D2) were obtained (Fig. 2;Table 2).
4 The Quantum Probabilities in Brief
In the classical world, the probabilities P1 and P2 of two incompatible events E1
and E1 add (for example, head or tail after coin toss):
Prob
class
(E1 or E2) =P1 ?P2
This is not the case for quantum probabilities where probability amplitudes add;
probability is obtained by the squaring of the sum of probability amplitudes. If we
define the complex numbers aand b(probability amplitudes), such as P1 =a
2
and
P2 =b
2
, then:
Prob
quant
(E1 or E2) =(a?b)
2
=P1 ?P2 ?‘‘interference term.’’
Therefore, in quantum probabilities, the probability amplitudes of two events can
interfere constructively or destructively (as, for example, in the interference pattern
on the screen of the two-slit Young’s experiment).
Fig. 2 Roles of type-1 and type-2 observers. The role of the type-1 and type-2 observers was to check the
results of Benveniste’s experiments in the blind experiments. These observers replaced the initial label of
all the experimental samples by a code number. The type-2 observer was inside the laboratory where he/
she could interact with the experimenter and the experimental system. The type-1 observer was outside
the laboratory, and he did not interact with the experimenter or experimental device and had no
information on the on-going measurements. When all the samples had been tested, the results of the
biological effects were sent to the type-1 observer and the two observers could assess the rate of
concordant pairs by comparing the two lists: biological effects (background or signal) and corresponding
labels under code number (‘‘inactive’’ and ‘‘active’’ samples)
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In quantum logic, the term ‘‘observable’’ is used to designate a ‘‘physical
variable.’’ To each observable (for example, the outcome of Schro
¨dinger’s cat
experiment) corresponds a set of possible pure states obtained after measurement
(dead cat; alive cat). Before measurement, the quantum system is said to be in a
superposed state of all possible pure states. Vectors in a vector space called
Hilbert’s space represent the states. Thus, before measurement, the state of the
Schro
¨dinger’s cat in this vector space is:
Cat
ji
¼1
ffiffiffi
2
pdead
ji
þ1
ffiffiffi
2
palive
ji
In this equation, each pure state is associated to a probability amplitude 1
ffiffi2
p;1
ffiffi2
p

and the probability to obtain a pure state after measurement is calculated by
squaring the probability amplitude (1/2; 1/2). The quantum formalism involves
that, before measurement, the quantum object is in an undetermined state
(superposed state), which is not a mixture of the different possible pure states.
Moreover, there are no ‘‘hidden variables’’ that predetermine the future outcome
after measurement.
5 The Quantum-Like Formalism of Benveniste’s Experiments
5.1 Open-Label Experiments
In open-label experiments, the experiments are performed without blinding; the
experimenter assesses the rate of concordant pairs by associating the changes of a
biological parameter with the ‘‘labels’’ of the samples to be assessed. Samples are
said to be ‘‘active’’ (AC) if a change of biological parameter (‘‘signal’’ or ‘‘:’’ ) i s
expected and ‘‘inactive’’ if a change of the biological parameter that is not different
from the background (‘‘;’’) is expected.
The cognitive state Ais described in a superposed state for the first observable:
wA
ji
¼k1AIN
ji
þk2AAC
ji
for each sample ð1Þ
In Eq. 1, that describes the cognitive state Awith regard to the label of a given
sample, A
AC
is the cognitive state Aassociated with the ‘‘active’’ label (and A
IN
is
associated with the ‘‘inactive’’ sample). This equation means that the probabilities
for Ato be associated with an ‘‘inactive’’ or ‘‘active’’ label for this sample are k2
1and
k2
2, respectively.
The second observable is the concordance of pairs with A
CP
for concordant pairs
and A
DP
for discordant pairs. The observable is said to be concordant if A
IN
is
associated with A
;
(Ais associated with background, i.e., no change of biological
parameter) or if A
AC
is observed with A
:
(Ais associated with the signal, i.e., change
of biological parameter). Otherwise, the observable is said to be discordant (A
IN
is
associated with A
:
and A
AC
is associated with A
;
).
We introduce the possibility for the observables to be noncommuting.
Technically speaking, this means that two bases to describe any vector in the
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vector subspace where Ais described exist. When the two bases are confounded, the
observables commute (classical probabilities are therefore only a special case of
quantum probabilities).
The four vectors AIN
ji
,AAC
ji
,ACP
ji
and ADP
ji
are four unitary vectors; the two
pairs AIN
ji
=AAC
ji
and ACP
ji
=ADP
ji
form two bases of the vector subspace. We can
express one basis as a function of the other basis with four coefficients named l
11
,
l
12
,l
21
, and l
21
:
AIN
ji¼l11 ACP
jiþl12 ADP
ji ð2Þ
AAC
ji
¼l21 ACP
ji
þl22 ADP
ji ð3Þ
Therefore, wA
ji
can be expressed as a superposed state of ACP
ji
and ADP
ji
:
wA
ji
¼ðk1l11 þk2l21 ÞACP
ji
þðk1l12 þk2l22ÞADP
ji ð4Þ
The quantum probability (Prob
quant
)ofA
CP
is the square of the probability
amplitude of this state:
ProbquantðACPÞ¼ k1l11 þk2l21
jj
2ð5Þ
Similarly, ProbquantðADPÞis calculated:
ProbquantðADPÞ¼ k1l12 þk2l22
jj
2ð6Þ
Since l2
11 þl2
12 ¼1;l2
21 þl2
22 ¼1;and Prob
quant
(A
CP
)?Prob
quant
(A
DP
)=1,
it means that the matrix for change of basis is a rotation matrix. Two rotations
matrixes with opposite directions are solutions. We choose the matrix that allows
the correct association of A
IN
with A
;
and A
AC
with A
:
:
l11 l12
l21 l22

¼l11 l21
l21 l11

¼cos hsin h
sin hcos h

Therefore, we can replace the probability amplitudes in the equations calculated
above:
AIN
ji
¼cos hACP
ji
sin hADP
ji ð7Þ
AAC
ji
¼sin hACP
ji
þcos hADP
ji ð8Þ
wA
ji
¼ðk1cos hþk2sin hÞACP
ji
þðk2cos hk1sin hÞADP
ji ð9Þ
ProbquantðACPÞ¼ k1cos hþk2sin h
jj
2ð10Þ
ProbquantðADPÞ¼ k2cos hk1sin h
jj
2ð11Þ
We can easily see that the rate of concordant pairs is maximal for k
1
=sin h(and
consequently k
2
=cos h):
ProbquantðACPÞ¼ k1cos hþk2sin h
jj
2¼k2
1þk2
2



2¼1ð12Þ
ProbquantðADPÞ¼ k2cos hk1sin h
jj
2¼k2k1k1k2
jj
¼0ð13Þ
In this case, all pairs (samples labels and biological outcomes) associated with
the cognitive state Aare concordant.
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5.2 Angle hand Emergence of Signal from the Background
The quantum-like formalism allows describing the results of Benveniste’s
experiments without the notion of the ‘‘memory of water’’ or its avatars, such as
‘‘digital biology.’’ In the present model, changing the value of the angle hallows the
passage from the logic of classic physics to quantum logic. The logic of classic
physics appears as a particular case (h=0) of a generalized probability theory
(with any hvalue). If his equal to zero, then the observables commute:
AIN
ji
¼1ACP
ji
0ADP
ji
¼ACP
ji ð2Þ
AAC
ji
¼0ACP
ji
þ1ADP
ji
¼ADP
ji ð3Þ
Therefore, with h=0, A
IN
is always associated with A
CP
and A
AC
is always
associated with A
DP
. In other words, concordant pair for the IN label is the back-
ground, and the discordant pair for the AC label is also the background: only the
background is associated with the cognitive state Aif h=0.
These results mean that h=0 is necessary not only for the concordant pairs, but
also for the emergence of the signal. The state A
:
must exist in the background of all
the possible states of A, even with a low probability. The superposition of the states
and the noncommuting observables allow the emergence of A
:
.
Some questions however remain. Thus, the origin of the noncommuting
observables remains unknown. Moreover, we chose one direction for the rotation
matrix to associate the ‘‘inactive’’ label with the background on one hand and the
‘‘active’’ label and the background on the other hand. However, the other rotation
matrix with the angle hin the opposite direction was also allowed by the formalism
(‘‘inactive’’ label with signal and ‘‘active’’ signal with background). How
asymmetry could be introduced in this formalism remains undefined. These
questions will be explored in a future article.
In the next sections, we discuss how the other characteristics of Benveniste’s
experiments (such as ‘‘jumps of activity’’) are also described by the quantum-like
formalism.
5.3 Definition of Type-1 and Type-2 Observers
As explained above, some observers checked the results of Benveniste by using a
blind procedure. After samples had received a code number, the experimenter did
not know which sample (inactive or active) was tested and the outcome of the
experiment could not be unconsciously influenced. Since it appeared that the
outcomes (rate of concordant pairs) varied according to the circumstances of the
blinding in Benveniste’s experiments, we will first precisely describe the roles and
characteristics of the different observers.
The definitions of the observers are based on the ‘‘Wigner’s friend,’’ a thought
experiment proposed by Wigner (1983). In this thought experiment, Wigner
imagines that a quantum experiment with two possible outcomes is performed in his
laboratory by his friend; Wigner is outside the laboratory for the duration of the
experiment (Fig. 2). At the end of the experiment, from the point of view of Wigner
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who has no information on the experiment’s outcome, his friend and the complete
chain of measurements are in an undetermined state (superposed state). When
Wigner enters the laboratory, he learns the outcome of the experiment. Therefore,
from his point of view, the quantum wave ‘‘collapses’’ at this moment. However,
from the point of view of Wigner’s friend, the ‘‘collapse’’ occurred when he looked
at the measurement apparatus at the end of the experiment and he never felt himself
in a superposed state. On the contrary, he felt that one and only one of the two
possible outcomes occurred with certainty. Therefore, according to this thought
experiment, two valid but different descriptions of the reality coexist: there is a
‘‘collapse’’ of the quantum wave at different times according to the information that
the observers get on the quantum system.
This interpretation of a quantum measurement, however, is now generally
considered out-of-date. Wigner himself subsequently adopted the theory of
decoherence when this theory was proposed in the 1970s. Decoherence occurs
when a quantum system interacts with its environment in a way that is
thermodynamically irreversible. Consequently, the different elements of the wave
function in the quantum superposition cannot interfere and the interferences become
negligible. Therefore, quantum decoherence has the appearance of a wave collapse.
However, in contrast with the Wigner’s thought experiment, no conscious observer
is necessary in the decoherence theory.
It is important to note that we do not endorse Wigner’s interpretation for the
quantum measurement (in fact, we are agnostic on this issue). This well-known
thought experiment simply allows a precise and immediately understandable
definition of the different observers/participants in Benveniste’s experiments.
Indeed, the type-1 observer and type-2 observer are respectively at the same
positions as Wigner and Wigner’s friend in the thought experiment (Fig. 2).
5.4 Blinding by Type-1 or Type-2 Observers into Practice
In blind experiments, the type-1 and type-2 observers replaced the initial labels of
the samples to be tested by a code number. The type-1 and type-2 observers were at
their respective places as defined before (Fig. 2). When Benveniste’s team
completed all the measurements with samples, the results were sent to the type-1
observer (generally by fax or e-mail). The type-1/type-2 observers compared the
two lists: biological effects (background or signal) and labels (‘‘inactive’’ and
‘‘active’’ samples); then, she/he could assess the rate of concordant pairs (i.e.,
‘‘inactive’’ with the background and ‘‘active’’ with the signal).
5.5 Quantum Formalism with Blinding by a Type-2 Observer
In case of blind experiments by a type-2 observer with cognitive state O, Eq. 1is
modified:
wO
ji
¼k1OIN
ji
þk2OAC
ji
wAO
ji
¼k1AIN
ji
OIN
ji
þk2AAC
ji
OAC
ji
ð1bisÞ
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Finally, we obtain:
wAO
ji
¼ðk1cos hþk2sin hÞACP
ji
OCP
ji
þðk2cos hk1sin hÞADP
ji
OCP
ji
ð4bisÞ
Therefore, this experimental situation is formally not different from open-label
experiments described above since the cognitive states of both the experimenter
(A) and type-2 observer (O) are on the same ‘‘branch’’ of the state vector (Eq. 1bis;
Fig. 2). The type-2 observer can be considered as an integral part of the experiment
as the biological system or any automatic device for blinding.
5.6 Quantum Formalism with Blinding by a Type-1 Observer
When a blind experiment is performed by a type-1 observer, he/she assesses the rate
of concordant pairs by comparing labels and biological outcomes. This experimen-
tal situation is then formally comparable to a ‘‘which-path’’ measurement in the
Mach–Zehnder interferometer experiment and therefore, classical probabilities
apply. Indeed, the information gained by the type-1 observer on the label has to be
taken into account for the calculation of the probability for Ato be associated with
the concordant pairs:
ProbclassðACP Þ¼ProbðAIN ÞProbðACP jAIN Þþ ProbðAAC ÞProbðACP jAAC Þ
ð14Þ
with ProbðACPjAIN Þ¼cos2hand ProbðACP jAAC Þ¼sin2h, then:
ProbclassðACP Þ¼k2
1cos2hþk2
2sin2hð15Þ
Prob
class
(A
DP
) is calculated similarly:
ProbclassðADP Þ¼k2
2cos2hþk2
1sin2hð16Þ
The important point is that Prob
quant
(A
CP
)=Prob
class
(A
CP
) in the general case
(compare Eqs. 10 and 16). In the squaring of the sum of probability amplitudes,
there is an additional term 2 k
1
k
2
cos hsin h, which is typical of all the quantum
mechanical interference effects.
The calculations for the different classical and quantum probabilities are
summarized in Fig. 3. Quantum probabilities are calculated as the square of the sum
of probability amplitudes and classical probabilities (in case of measurement/
observation of the first observable by the type-1 observer) are obtained as the sum of
the squares of all probability amplitudes.
5.7 Consequence of the Formalism: ‘‘Jumps’’ of Activity
As we have seen, the apparent ‘‘jumps of activity’’ between the samples was a
strange phenomenon that poisoned Benveniste’s experiments, particularly, during
public demonstrations (Table 3). The design of these experiments involved blinding
by a type-1 observer, and in our quantum-like probabilistic model, this phenomenon
is simply explained.
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If we suppose that the number of ‘‘inactive’’ samples (labels IN) and ‘‘active’’
samples (labels AC) are equal (i.e., k2
1¼k2
2¼0:5) and that the concordance is
optimal (i.e., cos h=k
1
and sin h=k
2
), we can calculate the respective
probabilities according to Eqs. 10,11,15, and 16.
For open-label experiments (or with blinding by a type-2 observer),
ProbquantðACPÞ¼ k1coshþk2sinh
jj
2¼1
ProbquantðADPÞ¼ k2coshk1sinh
jj
2¼0
For experiments with blinding by a type-1 observer,
ProbclassðACPjAIN Þ¼cos2h¼0:5
ProbclassðACPjAAC Þ¼sin2h¼0:5
These calculations indicate that in the open-label experiments (or with blinding by
a type-2 observer), A
IN
is always associated with A
;
and A
AC
is always associated
with A
:
. In contrast, after blinding with a type-1 observer, Prob
class
(A
CP
)=0.5 and
Prob
class
(A
DP
)=0.5.
Therefore, for a participant in these blind experiments with a type-1 observer, the
proportion of samples with the AC labels associated with the signal decreases from
Fig. 3 Design of a quantum-like experiment (application to Benveniste’s experiments). The quantum-
like object (cognitive state Aof the experimenter) is ‘‘measured’’ through two successive noncommuting
observables (h=0), which are mathematical operators. The first observable (‘‘labels’’) splits the state of
the cognitive state Ainto two orthogonal (independent) states (‘‘inactive’’ and ‘‘active’’ labels). Each of
these two states is split by the second observable (‘‘concordance of pairs’’) into two new orthogonal
states, concordant pairs and discordant pairs. If the events inside the box are not measured or observed,
the system is in a superposition of states. If the events inside the box are measured, then, classical
probabilities apply because we have to take into account the information obtained on the path
(consequently, there is no superposition of the initial ‘‘path’’). The probabilities for the concordance of
pairs are different according to the quantum or classic probabilities. Indeed, quantum probabilities are
calculated as the square of sum of the probability amplitudes of paths. Classical probabilities are
calculated as the sum of squares of the probability amplitudes of paths. Interferences of the two initial
paths (in area with dashed line) are possible with the probability amplitudes (quantum probabilities) but
not with probabilities (classical probabilities)
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100 to 50 % and the proportion of samples with the IN labels associated with the
signal increases from 0 to 50 %. It is as if the ‘‘biological activity’’ (signal)
‘‘jumped’’ from some samples with the AC label to samples with the IN label
(Table 3).
This is a chief consequence of the quantum-like formalism that easily describes
this phenomenon without supposing ad hoc hypotheses involving uncontrolled
‘‘external’’ causes or artifacts.
5.8 ‘‘Success’’ and ‘‘Failure’’ in Benveniste’s Experiments
Quite different results are obtained in the Mach–Zehnder interferometer experiment
(or in the two-slit Young’s experiments) based on the decision to measure the initial
path or not. In one case (interference pattern), light behaves as a wave and in the
other case (no interference pattern), it behaves as a collection of particles. In
Benveniste’s results, the experimental context also appeared to play an important
role (blinding by a type-1 observer vs. a type-2 observer) (Beauvais 2007,2008,
2012,2013). According to the blinding conditions, different results were obtained
that were considered as ‘‘successes’’ or ‘‘failures’’ (Table 3). In the two-slit
experiment, observing interferences on the screen or not, according to the
experimental context, is not considered as a success or a failure: both results are
Table 3 Summary of the quantum-like probabilistic model describing Benveniste’s experiments in
different experimental contexts
Patterns of results
Expected results
a
;;;;:::: ;;;;:::: ;;;;::::
Observed results ;;;;:::: ;;::;:;: ;;;;;;;;
Description Signal present at expected
places
Signal present but at
random places
No signal
Conclusion
according to
classic logic
Success Failure (‘‘jumps of
activity’’ between
samples)
Failure
Conclusion
according to
quantum logic
h=0 with interferences of
quantum states
h=0 without
interferences of quantum
states
h=0
Probability of
concordant
pairs
a
1
ffiffi2
pcos hþ1
ffiffi2
psin h





2¼11
2cos2hþ1
2sin2h¼1
2
1
2
Corresponding
experimental
situations
Benveniste’s experiment
without blinding by a type-
1 observer
b
Benveniste’s experiment
with blinding by a type-1
observer
Results as predicted
by classical
probabilities
c
;Background, :signal
a
Experiments with k2
1¼k2
2¼0:5 (i.e., numbers of ‘‘inactive’’ and ‘‘active’’ labels are equal); we sup-
pose that sin h=k
2
for the first two columns (quantum interferences are maximal in the first column)
b
Open-label experiment or experiment blinded by a type-2 observer
c
Such results (i.e., no signal with all samples) were generally obtained by other scientific teams that tried
to reproduce Benveniste’s experiments
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necessary to describe the physics of light. In Benveniste’s experiments also, the
‘‘successes’’ and ‘‘failures’’ were the two faces of the same coin. Results of the
blinding with the type-1 observer played the same role as the measurement of the
path entered by the particle in the single-particle interference experiments.
6 Quantum-Like Formalism and Decoherence
Decoherence is an obstacle to the general acceptance of any quantum or quantum-like
model that deals with macroscopic phenomena. In our quantum-like model, it is
important to note that we borrow only some notions from the quantum logic, such as
Hilbert’s space, vector superposition, and noncommuting observables. However,
there is no term equivalent to the Planck constant and no Schro
¨dinger equation. The
cognitive state itself is an abstract ‘‘object,’’ which is involved in measurement/
observation processes involving nonphysical observables. Thus, labels take the
meaning that the experimenter decides (samples are considered as physically the same
in the formalism). Definition of a concordant pair is also arbitrary and assessing pair
concordance requires information processing for ‘‘interpretation.’’ Therefore, the
formalism deals not with the events themselves, but with the relationships between
these events. For all these reasons, the superposition of the different possible states of
the cognitive state is supposed to be not exposed to a decoherence process (except in
the case of a blind experiment with a type-1 observer).
Such an approach has never been proposed for these experiments but there are
comparable uses of notions from the quantum physics in other domains. Thus,
Walach proposed to use a ‘‘generalized’’ version of the quantum theory by
weakening some constraints of the original quantum formalism. Therefore, the
theory is applicable in more general contexts than in the original quantum physics
(Walach and von Stillfried 2011). In quantum cognition, which is an emerging
research field, the cognitive mechanisms and information processing in the human
brain are modeled by using some notions from the formalism of quantum physics.
This approach allowed addressing problems, that were until now considered
paradoxical, and has been applied to human memory, decision making, personality
psychology, etc. (see, for example (Bruza et al. 2009) for the special issue of
Journal of Mathematical Psychology in 2009).
7 Conclusions
Our description of Benveniste’s experiments can be summarized with only two
equations, whose general form is a
2
?b
2
and |a?b|
2
. Only one parameter (the
angle h) is necessary for the passage from classical (h=0) to quantum-like
(h=0) probabilities.
We understand now why Benveniste’s experiments were the ideal ground for a
controversy. Indeed, as soon as one tried to ‘‘measure/observe’’ the initial ‘‘path’’
(namely, the cognitive state Aassociated with sample labels), correlations between
the effects and supposed causes vanished. Nevertheless, a signal persisted and that
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was the reason why Benveniste’s team pursued its technical quest for the best
experimental device and the crucial experiment. Moreover, other teams (for
which—in our interpretation—observables were commuting) could not confirm
these experiments and their results were as expected according to the logic of
classical physics.
In conclusion, the use of a quantum-like probabilistic model allows describing all
the characteristics of Benveniste’s experiments and brings a new light on this major
controversy. We propose that the outcomes of these experiments were related to
quantum-like interferences of the cognitive states of the experimenter.
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