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Psychophysical interactions with a double-slit interference
pattern: Exploratory evidence of a causal influence
Dean Radin,1 Helané Wahbeh,1 Leena Michel,1 and Arnaud Delorme1,2
1Institute of Noetic Sciences,101 San Antonio Road, Petaluma, California 94952, USA
2University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0559, USA
Abstract: An experiment we conducted from 2012 to 2013, which had not been previously
reported, was designed to explore possible psychophysical effects resulting from the interaction of
a human mind with a quantum system. Participants focused their attention toward or away from
the slits in a double-slit optical system to see if the interference pattern would be affected. Data
were collected from 25 people in individual half-hour sessions; each person repeated the test 10
times for a total of 250 planned sessions. “Sham” sessions designed to mimic the experimental
sessions without observers present were run immediately before and after as controls. Based on
the planned analysis, no evidence for a psychophysical effect was found.
Because this experiment differed in two essential ways from similar, previously reported double-
slit experiments, two exploratory analyses were developed, one based on a simple spectral analysis
of the interference pattern and the other based on fringe visibility. For the experimental data, the
outcome supported a pattern of results predicted by a causal psychophysical effect, with the
spectral metric resulting in a 3.4 sigma effect (p = 0.0003), and the fringe visibility metric
resulting in 7 of 22 fringes tested above 2.3 sigma after adjustment for Type I error inflation, with
one of those fringes at 4.3 sigma above chance (p = 0.00001). The same analyses applied to the
sham data showed uniformly null outcomes. Other analyses exploring the potential that these
results were due to mundane artifacts, such as fluctuations in temperature or vibration, showed no
evidence of such influences. Future studies using the same protocols and analytical methods will
be required to determine if these exploratory results are idiosyncratic or reflect a genuine
Résumé: Une expérience, menée entre 2012 à 2013, a été conçue pour explorer les effets
psychophysiques résultant de l'interaction d’un participant humain avec un système quantique. Les
participants ont concentré leurs attentions sur un système optique à double fente et nous avons
déterminé si le motif d'interférence était affecté par rapport à des périodes où ils ne concentrait par
leur attention sur le système. Les données ont été recueillies auprès de 25 personnes lors de
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séances individuelles d'une demi-heure; chaque personne a répété le test 10 fois pour un total de
250 séances. Des séances «fictives» conçues pour imiter les séances expérimentales sans la
présence d'observateurs ont également été enregistrées immédiatement avant et après les seances
expérimentales. Sur la base des analyses planifiées avant le début de l’expérience, aucune preuve
d'un effet psychophysique n'a été observée.
Comme cette expérience différait de manières essentielles par rapport à d'autres expériences
similaires à double fente, deux analyses exploratoires ont été développées, l'une basée sur une
analyse spectrale du diagramme d'interférence et l'autre basée sur la visibilité des franges
d’interférence. On observe dans ce cas, un effet psychophysique causal, la mesure spectrale ayant
un effet de 3,4 sigma (p = 0,0003) et la mesure de la visibilité des franges 7 à 22 ayant un effet de
2,3 sigma après correction pour comparaisons multiples, avec l’une de ces franges à 4,3 sigma (p
= 0,00001). Les mêmes analyses appliquées aux sessions «fictives» ne produisent aucun effet
significatif. Des analyses supplémentaires pour tester si ces résultats sont dus à des artefacts, tels
que des fluctuations de température ou des effets vibratoires, ne montrent aucune preuve de telles
influences. Des études futures utilisant les mêmes protocoles et méthodes analytiques seront
nécessaires pour déterminer si ces résultats exploratoires sont idiosyncratiques ou reflètent une
véritable influence psychophysique de sujets humain sur un système quantique.
Key words: Quantum Measurement Problem; Psychophysical Interactions; Double-Slit
In the latest survey on foundational issues in quantum theory (in 2016), questionnaires
were sent to 1,234 physicists at eight universities; 149 people responded.1 The results echoed the
findings of previous surveys,2,3 which indicated that a century after the formation of quantum
theory there is still no firm consensus on how to best interpret it. One of the survey questions
was about the role of the observer, a topic discussed at length by prominent contributors to
quantum theory, including Planck, Pauli, Eddington, Jordan, von Neumann, Jeans, Gödel,
London, Stapp, and others.4 Interest in these questions has not diminished over the years, as
demonstrated by 22% of the respondents in the 2016 survey who believed that the observer
“plays a distinguished physical role” in nature. Despite the profound metaphysical implications
of this interpretation,5 very few physicists have attempted to investigate this question
empirically. This apparent disinterest is not a matter of experimental intractability, because there
is a directly relevant empirical literature.6 Perhaps the deficit is due to what the traditional
discipline of physics considers to be proper topics of study, which includes all aspects of the
physical world but not postulated realms that reside somewhere in between physics and the
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In any case, our approach to this topic has been to take seriously Planck’s (and others)
position, based on the philosophy of idealism, that consciousness is more fundamental than
matter.8 From that perspective, consciousness (i.e., awareness) transcends the constraints of the
physical world, in which case conscious entities may be able to become aware of anything,
anywhere in spacetime, by merely narrowing their focus of attention to a particular location. If
that were possible, then one could, in principle, gain which-path knowledge about photons
passing through a double-slit interferometer, in which case the interference pattern would shift
into a diffraction pattern in proportion to the degree of certainty of the information gained. The
ability of humans to precisely control awareness in this way would presumably be relatively
weak and variable, which in turn would require considerable experimental data to detect changes
in the interference pattern.
To conduct such a test in practical terms, individuals would be invited to focus their
attention toward or away from a double-slit system with intent to gain information about the
photons’ path. To date, starting in 1998, some 28 experiments based on this idea have been
reported by four labs using different protocols, optical apparatus, gas and diode lasers, single-
photon designs, and analytical approaches.9–14 Of these tests, 11 were reportedly statistically
significant at p < 0.05 (two-tail), where just one would be expected by chance. The binomial
cumulative probability of the published results so far is p < 10-7. This suggests the existence of a
genuine psychophysical effect, however, as a new line of research these experiments have not yet
matured into designs that are easily replicated, so caution in interpreting these results is
A. Professional reactions
Several responses to previously reported studies have been published. Sassoli de
Bianchi15 and Pradhan16 did not question our empirical results, but they offered different
theoretical interpretations. Baer reanalyzed data from one of our published online double-slit
studies using a simpler method he devised,10 and after a statistical adjustment his analysis
confirmed our results.17,27 In another reanalysis, Tremblay examined data from our two-year
online double-slit experiment.12,18 He confirmed that our reported results were correct, but then
decided to analyze each of the two years of data separately. Considering those datasets as
independent experiments resulted in reduced statistical power to detect an effect, and thus the
results of his two analyses were not significant. Later, in a personal correspondence, Tremblay
brought to our attention that a data trimming procedure we used to reject outliers in that study
had inflated the statistical results. His comment was correct, but fortunately we had also reported
results with no trimming, and that showed a 4 sigma effect in the predicted direction, so the
trimming error did not nullify our reported results.
In another article, Walleczek and von Stillfried claimed that a control condition in an
double-slit study we conducted from 2012 to 2013, which we had not previously reported, was a
false positive.19 We responded that their critique was flawed because they failed to adjust the
results for the 8 tests performed in that study. Such an adjustment was necessary because the
probability of obtaining at least one false-positive in 8 tests performed on partitions of a single
dataset is p =1 – (0.95)8 = 0.336, or 33.6%. That is, by not adjusting for the inflation of Type I
error, one or more false-positives are six times more likely to occur purely by chance than the
conventional threshold for declaring statistical significance (p = 0.05).20 Because a full
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description of the procedures used in that unpublished study has not yet been published, here we
describe that experiment along with the originally planned analysis and two exploratory
As previously described,9 the light source was a 5 mW linearly polarized HeNe laser
(Model 25 LHP 151-249, 632.8 nm wavelength, TEM00, Melles-Griot, Albuquerque, NM, USA).
The beam passed through two 10% transmission neutral density filters (Rolyn Optics, Covina,
CA), and then through two slits etched through a metal slide with slit widths of 10 microns and
separated by 200 microns (Lenox Laser, Glen Arm, MD, USA). The interference pattern was
recorded by a 3,000 pixel CCD line camera with a pixel size of 7 x 200 microns and 12-bit A-D
resolution (Thorlabs Model LC1-USB, Newton, NJ, USA). The camera was located 14.0 cm
from the slits, and it was programmed to record the interference pattern by integrating light for
50 ms, allowing for the collection of 20 camera frames per second. The actual mean integration
time (± standard deviation) in the experiment discussed here was 50.14 ms ± 0.12 ms.
The optical system was housed inside an eighth-inch thick aluminum housing painted
matte black inside and out. The laser and camera were powered on an hour before each
experimental session, and the experiment was controlled by a Microsoft Windows 7 computer
running a program written in Matlab (version 2009b, MathWorks, Natick, MA, USA); the
camera was interfaced to the computer via Thorlabs software libraries.
All test sessions were conducted inside an 8 × 8 × 7.5 foot, double steel walled, ceiling
and floor, electromagnetically shielded chamber (Series 81 Solid Cell chamber, ETS-Lindgren
Cedar Park, TX, USA) located at the Institute of Noetic Sciences (IONS) in Petaluma,
California, USA. This space was not specifically designed as an anechoic chamber, but when the
door was closed the double steel walls noticeably reduced external sounds, which enhanced the
participants’ ability to concentrate without distractions. Electrical line power inside the chamber
was conditioned by an electromagnetic interference filter (ETS-Lindgren filter LRW-1050-S1).
The chamber’s interior walls and ceiling were covered with fabric, and the floor was covered
with anti-static carpeting.
Individuals recruited for the test were selected based on their performance in previous
experiments of this type,15,16 or because they maintained an active meditation practice or other
form of mental discipline that required focused attention, such as musician, healer, or artist.
Before participating in the experiment, candidates signed an informed consent form approved by
the IONS Institutional Review Board (dated January 25, 2012).
An hour before a participant (P) was scheduled to arrive at the lab, a research assistant
(RA) turned the laser power on and prepared the computer used to control the experiment. When
P arrived, the RA closed the shielded room and started a “sham” session. At the start of that
session, a computer generated a pseudorandom sequence of 20 attention assignments (e.g., direct
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one’s attention toward the apparatus, or away). While that session was running and P was
waiting outside the shielded room, P was asked to fill out a standard mood-reporting
When the sham session finished collecting data from the double-slit apparatus, RA
invited P into the shielded chamber to run the first experimental session, which used the same
sequence of attention assignments used for the sham session. The RA showed the optical
apparatus to P, including the approximate location inside the device where the double-slit was
located (i.e., the housing itself was sealed and light-tight). P was then invited to sit in a chair
about 2 meters from the apparatus, to remain quietly seated, and to not leave the chair or
otherwise approach the optical system at any time during the test session. In a few of the initial
experimental sessions a GoPro video camera was used to record the interior of the chamber to
provide a way to check if P had left the chair. This was later deemed unnecessary because any
gross movements within the chamber were visibly apparent as artifacts in the interference pattern
data (no such artifacts were subsequently observed). Photos of P at the beginning of each session
were taken to provide a record confirming P’s participation.
The RA explained that the task was to focus attention on the two slits inside the optical
system when P heard a recorded voice instructing them to “now please concentrate.” Then, when
the recorded voice announced, “now please relax,” they were asked to withdraw their attention
from the apparatus. The RA further clarified that the task was performed through their “mind’s
eye,” and not their physical eyes. Ps were advised that if they wished they could mentally try to
block one of the two slits, to “become one with” the optical system in a contemplative way, or to
mentally “push” the photons so as to cause them to pass through one slit rather than both. The
precise form of interaction, and combination of attention and intention, were left to P’s discretion
and could be modified at will.
When P indicated that they understood the task, they put on Bose noise-canceling
headphones and the RA left the shielded chamber. Shortly thereafter, P heard a recorded voice
over the headphones that welcomed them, followed by instructions to relax for a minute while a
pre-session baseline was recorded. Then a recording announced each attention condition. For
expository simplicity, the concentrate condition is now referred to as X and the relax condition as
Use of headphones, as well as the sound-blocking nature of the steel chamber, helped to
ensure that the RA, who sat at a desk about 3 meters from the chamber, could not accidentally
overhear the condition assignments and possibly influence the experimental results or the
participants, by say, fidgeting more during X periods than O periods. In addition, the same RA
ran all experimental and sham sessions to help maintain uniform interactions with participants
across all sessions. When the experimental test session was completed, P took a rest break for
about 10 minutes. Then P ran a second experimental session using a newly randomized sequence
of epoch-pair instructions. When that session finished, the RA ran a second sham session using
the epoch-pair sequence that was just used in the second experimental session.
Each test session lasted about 25 minutes, resulting in about 28,000 recorded camera
frames. During a session, P was presented with a series of 20 pairs of attention instruction
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epochs, where each epoch lasted 30 seconds. Thus, each epoch consisted of about 20
frames/second x 30 seconds ≈ 600 frames, and each epoch-pair consisted of about 1200 samples.
Four epoch-pair conditions were employed: OO, XX, OX, and XO (see Figure 1). E.g.,
OX was a 30-second epoch with the instruction to relax (O) followed by a 30-second epoch with
the instruction to concentrate (X). Epoch-pairs were separated from one another by a randomized
latency between 3 and 5 seconds. The protocol was based on designs commonly used in
biological experiments to test whether an ingredient, like a drug, introduced into, say, an in vitro
cell culture, causally influences that system.22 In the present case, the hypothesized “ingredient”
was focused attention.
Figure 1. The epoch-pair condition OO is a systematic negative control, negative because
attention is focused away from the optical system. XX is a systematic positive control because the
“ingredient” of attention is focused toward the optical system. OX and XO are standard
differential comparisons as used in previous experiments of this type. The label “Differences”
indicates the expected differential comparisons within each pair when the results of the first epoch
is compared to the second. The label “Means” indicates the raw mean results of each epoch above
or below the grand mean. The label “Signal” indicates how a metric associated with the wave-like
component of the interference pattern would be hypothetically influenced by a causal
The experimental design called for 25 Ps to each contribute 10 sessions in the form of
two experimental sessions per appointment along with two matched sham sessions. Thus, the
final database was planned to consist of 250 experimental and 250 sham sessions. During sham
sessions, the RA placed a lamp with a 60-watt bulb in the chair where P sat; this was intended to
simulate an approximately equal source of heat as P’s body, and the headphones used by P were
placed on that same chair. Four thermocouples in the chamber, one located on the laser tube, a
second on the apparatus housing, a third between the apparatus and participant, and the fourth
about six inches behind P’s head, continuously monitored temperature during all sessions.
Unlike previous experiments of this type conducted in our lab, real-time feedback was
not provided. In earlier studies, the real-time spectral amplitude of the double-slit portion of the
interference pattern was associated with the volume of an audio tone. This was used to assist P in
focusing their attention during the concentration periods. Feedback was not provided in the
present experiment because Ps in the early testing phase complained that they felt the audio tone
was distracting. While the lack of feedback differed from the design of previous studies, this
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study offered a useful advantage because it provided a way to directly test the role of focused
attention on the optical apparatus, i.e., without an intermediary link in the form of a feedback
To ensure data and analytical integrity, the attention assignments that were randomly
generated in all sessions were encrypted in real-time, ensuring that the recorded data could not be
analyzed until after all planned sessions were completed. Data collection began in February 2012
and was completed in February 2013. The encryption code was broken in March 2013 by the
study’s funder (J. Walleczek), who held the decryption key, and the results were analyzed in his
presence at that time. The 8-year hiatus in our reporting this study was due to the funder’s
request to withhold public disclosure of this experiment until after his analysis of the results was
published (in 2019).19
Hypothesis I (planned) predicted that for the experimental data, the differential
comparisons for conditions XX and OO would each result in a null effect, XO would result in a
negative effect, and OX would result in a positive effect. In the sham sessions, the same
comparisons were predicted to result in uniformly null outcomes. The original analytical plan did
not specifically call for an adjustment of Type I error inflation for these eight comparisons, but
as mentioned above such an adjustment is necessary for this experimental design. To accomplish
this, we used the False Discovery Rate (FDR) procedure,23 which is a more powerful method
than the Bonferroni-type adjustment.24
Hypothesis II (exploratory) predicted that comparison of all samples in the X versus O
conditions would be negative, i.e., that attention focused toward the optical apparatus would
cause a decrease in interference. This is the standard differential comparison used in our previous
Hypothesis III (exploratory) predicted that the differential comparisons among epoch-
pairs, as well as the sample means of the epochs used within the epoch-pairs, would show a
predictable pattern of results consistent with a causal interpretation of a psychophysical
influence. That pattern, and its interpretation, are described below in the analysis section.
Hypothesis IV (exploratory) predicted that some participants were more talented, in terms
of their performance on the task, than others and that this talent would persist across their 10
repeated sessions. To test this idea, participants were ranked by their performance in their first 5
sessions, then based on that rank, the top 5 performers were predicted to continue to do well on
their last 5 sessions. By contrast, the 5 least talented participants were not predicted to perform
well on their last 5 sessions.
Psychological experiments involving tasks that repeatedly switch attention from one
condition to another have shown that it takes a few seconds to achieve these mental shifts.25
Previous double-slit studies found that it took about 3 seconds to optimally switch between the X
and O conditions. Thus, the data in all of the following analyses were lagged by 3 seconds.
1. Planned spectrum analysis
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Each recorded camera image in each session was transformed by a Fast Fourier
Transform (Matlab function fft) to determine the interference pattern’s spectrum (Figure 2A and
2B). The spectral portion of interest was the log of the real component, which we refer to as
“power” (p). In the apparatus we used, the double-slit component of the power spectrum peaked
at wavenumber 45; call this p45. Examination of p45 showed that the HeNe laser power randomly
hopped between two power regimes (Figure 2C).26 This unavoidable “mode-hopping” variance
was ameliorated by a series of transforms that involved linearly detrending the spectrum between
wavenumbers 14 and 39 in each camera frame (Figure 2D), then detrending the values at
wavenumber 45 in successive camera frames across the entire session (Figure 2E).10 This
“double-detrended” variable, pdd, was the metric used to test the hypothesis.
This approach eliminated the variance due to mode-hopping (Figure 2E), but it also
introduced a disadvantage because the distorted spectrum was no longer directly associated with
the interference pattern. That, in turn, introduced uncertainty about whether pdd was measuring
what we intended it to measure. This same concern was raised by Baer in an earlier study that
had used this same method.27 Nevertheless, pdd was the planned metric, and the method of
comparing the means across each of the four types of epoch-pairs was based on a nonparametric
randomized circular shift technique. This entailed calculating the mean differences in each
epoch-pair based on the observed data, then randomly circular-shifting the data in the whole
session, recalculating the mean differences, repeating this procedure many times, and then
comparing the original differences against the means and standard deviations of the randomized
data. The output of that method was a standard normal deviate (i.e. z score) for each epoch-pair
type per session, and then the resulting 250 z scores were accumulated across sessions as
Stouffer Z scores.28 The same procedure was used to analyze the data from the sham sessions.
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Figure 2. (A) Interference pattern. (B) Log of real portion of the spectrum. (C) Spectral power
mode-hopping at wavenumber 45. (D) Log spectrum linearly detrended from wavenumbers 14 to
39. (E) Detrended samples at wavenumber 45 from detrended spectrum in graph D. (F) Detrended
mean of wavenumbers 25 to 50 from original log spectrum in graph B.
2. Exploratory spectrum analysis
After the above method was used to analyze the results, the funder asked us about the
magnitude of the effect in terms of percentage change. That measure was not part of the original
plan, so in the process of developing the new, post-hoc metric, we investigated other exploratory
methods. Our aim was to develop an approach that would achieve two goals: It would eliminate
the bimodal distribution produced by the laser’s mode-hopping behavior, and it would provide a
metric that was directly associated with the interference pattern to avoid the power spectrum
distortion introduced by the double-detrending technique.
We began by observing that the spectral peak associated with the interference pattern was
not merely a spike at wavenumber 45, but rather a range of wavenumbers. Thus, for our new
metric we simply took the mean of the right-hand side of the spectrum, i.e., wavenumbers from
25 to 50 (call this
). Then we removed possible drift of this value within sessions by linearly
across samples within each session (see Figure 2F). Evaluation of the resulting
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showed that the samples were normally distributed (Matlab function ztest) and
independent (Matlab function runstest). As a result, a standard t-test was used to perform the
epoch-pair comparisons in each session (Hypothesis I), and then those results were combined
across sessions as a Stouffer Z. This approach also provided an easy way to evaluate Hypothesis
II: comparing all data in the X versus the O conditions per session, then combining those results
across sessions as a Stouffer Z.
Hypothesis III predicted that the differential comparisons among epoch-pairs, as well as
the means of the epochs within epoch-pairs, would show a predictable pattern of results. The
tested variables can be expressed by a 12-element array:
The first four values in this model are the differential comparisons in the four types of epoch-
pairs, and the last eight values are the means used to form those 4 epoch-pair comparisons. This
analysis was useful because the pairs XX and OO were each predicted to result in a null
difference, but that difference tells us nothing about the values within each pair. It is possible, for
example, for the means in the OO condition to both be significantly below the grand mean of the
session and for their difference to be null. The latter outcome would be consistent with the
psychophysical hypothesis, but the former would not. Thus, to match the hypothesis’s prediction
we would expect each mean within the XX pair to be below the grand mean of the entire session,
and each mean within OO to be above the grand mean (because the samples in each session were
detrended, and thus the grand mean per session was, by definition, zero).
If focused attention causally influenced the interference pattern, then the expected values
of the 12-element array should conform with the model: [0 0 1 -1 1 1 -1 -1 1 -1 -1 1]. In this
array, the first four values represent the predicted differential results, with 0 indicating null
expectation, 1 indicating a positive result, and -1 indicating a negative result. The next 8 items
represent values predicted to rise above (1) or fall below (-1) the grand mean. To evaluate this
model against the data, (a) the 8 mean values were first z-score normalized and then
concatenated with the array of 4 differential z scores, (b) a Spearman correlation was calculated
between the 12-element model and the 12 z scores per session, (c) the p-value resulting from the
Spearman correlation per session was converted into a z score, and (d) those z scores were
combined across the 250 sessions via a Stouffer Z, which was predicted to be positive.
To evaluate Hypothesis IV (talent), performance per participant per session was
where the z subscript refers to the combined (via Stouffer Z) differential comparisons in
the 5 OX and 5 XO epoch-pairs per session. Then was combined for each participant’s first 5
sessions, and those results were ranked best to worse. The talent hypothesis predicted thatfor
the top 5 individuals would remain positive for their last 5 sessions. By contrast, the participants
with the 5 lowest ranks were predicted to result in a null result for their last 5 sessions.
3. Exploratory fringe visibility analysis
To provide a double-check on the results of the exploratory spectral analysis, we
determined fringe visibility for the central portion of each interference pattern. To reduce pixel
jitter, each interference pattern was first smoothed using a Savitzky–Golay second-order
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polynomial (Matlab function smooth, with window size 30 pixels and optional parameter
sgolay). A small number of frame images were distorted in the process of being recorded, so to
reject those outliers the summed difference was determined between each interference pattern in
a session and the overall mean interference pattern in that session. If that sum exceeded an
empirically determined threshold, the frame was rejected. The threshold was selected to retain
99.5% of the data, rejecting only frames that were obvious outliers.
Then, the interference pattern's peaks and troughs were identified for the middle 22
values (Matlab function extrema). From those measures, fringe visibility was calculated as
, for fringes i = 1 to 22 (Figure 3, left). Each of the fringe
visibility measures was then detrended over the session (Matlab function detrend, Figure 3,
right) and analyzed separately.
Figure 3. (Left) Interference pattern with peaks and troughs identified. (Right) Fringe visibility
measures at fringe # 13 over one session, ranging from about 93% to 95%.
These fringe visibility values did not pass a Wald-Wolfowitz runs test (Matlab function
runstest) for sample independence in many of the sessions, so to compare X vs. O across the
entire array, a nonparametric randomized circular shift method was employed (as previously
described). For shorter arrays, the runs test did indicate adequate sample independence, so a t-
test was used to compare the epochs’ means within each epoch-pair. The same hypothesis tests
described for the exploratory spectrum analysis were conducted separately for each of the 22
fringes, and then the results of those analyses were adjusted for 22 comparisons using the FDR
A. Planned Analysis
Data were collected from 25 participants from February 2012 to February 2013, during
which 249 experimental and 250 sham sessions were recorded. One experimental session failed
to record properly, so an additional session was performed to complete the planned number. A
total of 7,211,411 camera frames were collected in the experimental sessions and 7,228,214
frames in the matched sham sessions. Table 1 shows the results. After adjustment for multiple
testing, none of these comparisons were statistically significant.
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Table 1. Results of planned analysis.
Prior to conducting this experiment, which had been proposed by the funder, we
documented our concern that the protocol might exacerbate known difficulties in sustaining
focused attention. That is, the protocol made it possible for a participant to receive attention
assignments containing the sequences …OX XX XO… or …XX XX XX…. In such cases,
participants would be required to sustain focused attention for 2 or 3 minutes at a time.
Inspection of the actual condition sequences later used in the experiment found 27 instances
where attention was required to be held for 3 minutes, and 325 instances where it had to be held
for 2 minutes. It is challenging even for experienced meditators to sustain unwavering attention
for much more than a minute without mind-wandering, so we were uncertain about the effect this
protocol might have on the results.
Based on those doubts, we conjectured that the hypothesized effect might become
unstable due to Ps’ accumulated fatigue and frustration within and across sessions. Our concern
was later supported by their mood questionnaire entries, which showed that Ps’ mood
significantly declined over the course of the 10 sessions each had contributed (Spearman ρ = -
0.295, p = 2 x 10-6), as did the mood subscales labeled “attentiveness” (r = -0.235, p = 0.0002)
and “self-assuredness” (p = -0.241, p = 0.0001).
Based on this suspected and later confirmed decline in mood and attention, we
anticipated that the planned tests might not detect a hypothesized directional effect, which would
have required a stable and uniformly applied focus of attention. However, a bi-directional test
might detect the effects of fluctuating attention. This led us to guess (while the experiment was
still underway) that (a) the variance in the OX and XO comparisons, determined by the sum of
the z scores squared in each case, might be above chance expectation, (b) the variance of the OO
and XX conditions would be null, and (c) those same comparisons in the sham data would be
null. Ultimately, the data did support our expectation about the variance in the experimental XO
condition (p = 0.008), but the OX condition and all of the other comparisons were null, including
the comparisons in the sham data. This partial confirmation was intriguing, but its interpretation
falls into a gray area because it was not part of the planned hypothesis, but nor was it discovered
post-hoc because, as mentioned above, the attention conditions were encrypted so the data could
not be analyzed until the experiment had ended. We mention this observation because it suggests
that protocols in future studies that require extended periods of attention might be better analyzed
with variance-shift rather than mean-shift statistics.
B. Exploratory Analyses: New Spectrum Metric
Hypothesis II predicted that the comparison of all experimental samples in X versus O
conditions would be negative. This prediction was confirmed with the simplified spectrum
metric, at z = -2.829, p = 0.002. For the sham data, the same test was nonsignificant, z = -0.580,
p = 0.281.
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Hypothesis III predicted that the 12-element relationship model would match the results
of the 4 epoch-pair comparisons and the 8 normalized epoch means. This was confirmed with a
Spearman ρ = 0.873, p = 0.0001 for the experimental data, and ρ = 0.106, p = 0.37 for the
matched sham data (Figure 4).
Figure 4. (Upper left) For the experimental data, the 12-element model is on the left and the 12 test
results on the right. The first two bars in the model are actually at zero but are shown slightly
above the x-axis to allow those values to be visible. (Upper right). Same for sham data. (Lower
left). Experimental results plotted against the model, resulting in Spearman ρ = 0.873, p = 0.0001.
(Lower right) Same analysis for the sham data, with Spearman ρ = 0.106, p = 0.37.
Hypothesis IV predicted that talented participants would continue to do well across their
sessions, whereas less talented participants would not. For the experimental data, the combined
spectral metric for the first 5 sessions of the top 5 participants was = 6.05. This large value was
expected because these individuals were selected based on their performance in the first 5
sessions. The question of interest was whether they continued to perform well in their last 5
sessions. They did, with = 3.22, p = 0.0006. By contrast, for the worst-performing 5
participants, their last 5 sessions were nonsignificant = 0.35. The same analysis applied to the
matched sham data resulted in the top 5 “performers” achieving = -0.83 for their last 5
sessions, whereas the worst 5 performers achieved = -0.34.
C. Exploratory Analyses: Fringe Visibility Metric
Hypothesis II predicted that comparison of all samples in X versus O conditions would
be negative. For the experimental data, this was observed in 20 of the 22 fringes (Figure 5, left),
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with fringe #2 surviving adjustment for FDR adjustment with alpha set at p = 0.05. There are
dependencies among these fringe tests, of course, but the FDR algorithm takes those
dependencies into account. Of the 22 sham fringes, 13 were in the predicted direction but none
were significant (Figure 5, right).
Figure 5. X vs. O results. (Left) Experimental data, showing 20 of 22 fringes in the predicted
direction, and fringe #2 passing FDR adjustment at alpha = 0.01. (Right). None of the fringes in
the sham data were significant.
Hypothesis III predicted that the 12-element model would result in a positive Spearman
correlation. This was confirmed in 20 of 22 fringes, with 7 of those fringes surviving FDR
adjustment at p = 0.01 (Figure 6, left). One might argue that dependencies among the elements of
this correlation might have inflated the overall significance, but a randomized permutation test
that compared the observed results against randomly scrambled data confirmed that these results
were valid. The same analysis applied to the sham data showed that 9 fringes were in the
predicted direction, but none were individually significant (Figure 6, right).
Figure 6. Twelve-element model test. The ordinate of these graphs shows the probability of the
Spearman ρ outcomes in terms of z scores. (Left) Results applied to the experimental data,
showing 20 of 22 fringes in the predicted direction and 7 fringes surviving FDR adjustment at
alpha = 0.01 (the dotted line is the threshold for significance at that level). (Right) None of the
correlations with sham data were significant.
To evaluate Hypothesis IV (talent) with the experimental data from the one fringe that
survived FDR adjustment (fringe #2), the last 5 sessions from the best 5 performers resulted in a
nonsignificant = 0.82. For the worst 5 participants, their last 5 sessions resulted in a
nonsignificant = 0.30. The same analysis applied to the sham data resulted in the “talented”
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performers achieving = 0.09 for their last 5 sessions, whereas the worst 5 performers achieved
= 0.78. Thus, no fringes confirmed the talent hypothesis.
The planned directional analysis did not provide evidence for a psychophysical effect.
However, because we were later asked to perform a post-hoc analysis, we took that opportunity
to address our concerns that the planned metric was not directly associated with the interference
pattern. In the process, we developed two new metrics: One based on a simplified measure of
spectral changes in the interference pattern, and the second on interference fringe visibility.
Both exploratory metrics resulted in significant support for the hypothesis that a double-
slit interference pattern would shift toward a diffraction pattern during X as compared to O
conditions. By contrast, the same analyses applied to the sham data were uniformly null. Of
greater importance, the predicted relationship between the epoch-pair conditions (e.g. OO XX
OX XO) and the means that composed these pairs was significantly correlated with a model of
the psychophysical effect, suggesting a causal influence. This same analysis applied to the sham
data resulted in a null outcome. This supports von Neumann’s proposal that consciousness may
play an active role in the transition from quantum potentials into classical actuals. Of course, this
does not mean that consciousness is the only factor involved in such transitions. Other factors,
like decoherence arising from variations in ambient temperature or vibrations, as well as
dephasing between the two Gaussian wavepackets generated in a double-slit system, may also
play a role.29,30
The principal limitation of this study is that the two exploratory metrics were not part of
the planned analysis, and as such the only way to know if these results are valid will be through
future replications. In conducting those replications, it will be useful to first run a series of pilot
tests to identify individuals who seem to have talent and only use those participants in
subsequent formal replications.
There are two potential mundane sources for these observed results. Optical
interferometers are exquisitely sensitive to fluctuations in ambient temperature and vibration. It
is conceivable, for example, that during X epochs, participants leaned toward the optical system.
If that behavior were systematically performed by many participants, it could have raised the
temperature of the apparatus a bit, caused some vibrations, and added noise to the interference
pattern. Such an effect would introduce a confound because a noisy interference pattern would
result in reduced fringe visibility and a decline in double-slit portion of the spectrum, which is
exactly what the X instruction was hypothesized to achieve. Likewise, during the O periods,
participants might have leaned backwards, in which case noise would decline and the
interference fringes would become sharper.
A. Effects of temperature
To test the effects of temperature, recall that data from four thermocouples were collected
in each session. The value of primary interest was the temperature recorded on the housing of the
optical system because that was closest to the double-slits and the camera. Inspection of that
variable showed that it steadily increased over the course of each session, likely due to the
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participant’s body in the experimental sessions and the 60W bulb in the sham sessions. To adjust
for this rise, for each session a third-order polynomial was fit to the housing temperature data,
then that curve was subtracted from the original data to form nonlinear residuals.
For the experimental sessions, these residuals showed that the temperature compared
between the X versus O conditions was z = 1.812. For sham sessions, the same comparison was
slightly larger, z = 2.136. These positive z scores indicate that, on average, the optical housing
was somewhat warmer during X conditions, but the difference between the experimental and
sham sessions was not significant (z = -0.229). This argues against temperature fluctuations as a
plausible cause of the observed results.
B. Effects of vibration
As a proxy for an accelerometer (which was not included in this study’s design), we
assessed the possible effects of vibration by comparing the variance of the simplified spectral
metric in experimental sessions versus the same measure in the matched sham sessions. To
perform this comparison, spectral data in each experimental and matched sham session were
linearly detrended, then potential outliers were rejected using the Matlab function rmoutliers,
which identifies outliers more than three scaled median absolute deviations. Then, the variance
across each of those two sessions was compared using a nonparametric randomized circular shift
technique (similar to the method described above), which returned one z score per comparison.
Those scores were then combined across the 250 comparisons to form a single Stouffer Z.
The result was z = 4.058, p = 0.00002, indicating that the variance of data in the
experimental sessions was substantially larger than the data in the matched sham sessions. This
could be interpreted as more participant movement during the experimental sessions, but this is
also what is expected by the psychophysical hypothesis. That is, it predicted that the interference
pattern would be modulated by variations of attention in the experimental X and O conditions,
whereas in the sham sessions there would be no such influences. To help clarify between these
two possibilities, the same variance comparisons were determined separately for experimental
versus sham samples only in the X condition (zX = 2.423, p = 0.008), and then the same
comparison for the O conditions (zO = 1.812; p = 0.035). No significant difference was found
between these two conditions (z = 0.424), thus there was no evidence that participants influenced
the optical apparatus by systematically varying vibration.
For the fringe visibility metric, the same variance comparisons showed results similar to
the spectral metric for most of the 22 fringes when considering all data across sessions and also
when comparing just X and just O conditions (Figure 7). However, none of the differences
between measures in the X and O conditions were statistically significant. This again argues
against participants’ movements being the cause of the observed results. It also demonstrates that
the experimental and sham environments, despite the aspirations of the original design, were
actually quite different in this regard.
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Figure 7. (Left) For fringes 1 to 22, variance comparison across all experimental vs. matched sham
sessions. (Middle) Same analysis but between X condition samples in experimental and matched
sham sessions. (Right) Same but between O condition samples.
In designing future studies exploring the psychophysical hypothesis, it would be useful to
(a) pre-test candidate participants and only use those who displayed some talent, (b) revise the
protocol to prevent mood and attention fatigue, (c) design a sham condition that includes
participants who are present but engaged in other tasks to better match the sham to the
experimental environment, (d) include one or more accelerometers to measure ambient
vibrations on or near the double-slit apparatus, (e) employ metrics that are as close to the
hypothesized effect as possible, such as fringe visibility, and (f) use as the source of light power-
and temperature-stabilized lasers that do not display mode-hopping behavior.
This line of research was supported by the Federico and Elvia Faggin Foundation, Inc.,
the Bial Foundation, Richard and Connie Adams, and an institute that prefers to remain
anonymous. We also thank the members and staff of the Institute of Noetic Sciences for their
support, and the individuals who participated in this experiment.
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