Psychophysical Effects on an Interference Pattern in a Double-Slit Optical System: An Exploratory Analysis of Variance 1,2

: Objective: A two-year online experiment tested the hypothesis that focused human attention alternatively directed toward or away from a double-slit optical system would affect the interference pattern in a predictable, unidirectional fashion. A control condition was employed by having a web server periodically simulate a human observer. Method : Based on the results of an independent reanalysis of these data and the outcome of an independent conceptual replication, we revisited the original directional hypothesis to explore the possibility that mind-wandering and other distractions might have caused attention or intention to unpredictably fluctuate. That in turn might have caused the hypothesized psychophysical influence to be more readily detected as a bidirectional effect (i. e., a shift in variance) rather than as unidirectional effect (a shift in mean). To test this idea, we developed a vari-ance-based analysis using data collected during the first year of the experiment and applied it to data from the second year. Results : The first year’s data showed that experimental sessions conducted by humans resulted in significant variance differences as compared to control sessions conducted by a computer, z = 4.16, p = .00002. The same analysis applied to the second year’s data resulted in z = 3.14 , p = .0008. Examination of environmental and apparatus variables indicated that those factors were not responsible for the observed changes in variance. Conclusion: The results suggest that a variance analysis may be more sensitive to psychophysical effects in this type of experiment. Effekt (eine Verschiebung des Mittelwerts) nachgewiesen werden kann. Methode: Um diese Idee zu testen, entwickelten wir eine varianzbasierte Analyse anhand der Daten, die im ersten Jahr des Experiments erhoben wurden, und wandten sie dann auf die Daten des zweiten Jahres an. Ergebnisse: Die Daten aus dem ersten Jahr zeigten, dass von Menschen durchgeführte Experimentalsitzungen zu signifikanten Varianzunterschieden im Vergleich zu den von einem Computer durchgeführten Kontrollsitzungen führten, z = 4,16, p = ,00002. Die gleiche Analyse für die Daten des zweiten Jahres ergab ein z = 3,14, p = ,0008. Die Untersuchung der Umgebungs- und Gerätevariablen ergab, dass diese Faktoren nicht für die beobachteten Varianzveränderungen verantwortlich waren. Schlussfolgerung: Die Ergebnisse deuten darauf hin, dass eine Varianzanalyse bei Experimenten dieser Art empfindlicher auf psychophysische Effekte reagieren könnte.

. To do this, we compared differences in variance between the two attentional conditions in sessions conducted by humans, as compared to the same differences in control sessions conducted by a computer.

Method
Details about the apparatus, methods, and procedures used in this experiment are described in a previous publication (Radin et al., 2016). For convenience, they are briefly repeated here. The new analytical approach is described in more detail later in this section.
Apparatus entation of the beam, the camera electronics, the path of individual photons, and so on.
Another is that if one could gain knowledge about which of the two slits the photons passed through (i.e., so-called "which-path" information), then the wave-like nature of the interference would shift into a particle-like diffraction pattern in proportion to the accuracy of the knowledge gained. In either case, attention-or intention-associated effects might alter the interference pattern in detectable ways.
The present reanalysis of the previously published experiment was motivated by four factors. The first was an independent double-slit replication reported by Guerrer (2019). In a series of pilot tests, he reported confirmation of the directional hypothesis that consciousness would "collapse" the interference pattern. However, in follow-up formal studies, there was no evidence for a directional effect using the planned analysis, but post-hoc he found a significant bidirectional effect.
The second motivation was a reanalysis of the data gathered in this online study by Tremblay (2019). In his first published analysis, he confirmed that a significant effect was observed in one year of a two-year dataset. In a later correction, he found that a data trimming method we had used to remove outliers inadvertently inflated the p-values (Tremblay, 2021), which had been previously noted by Walleczek & von Stillfried (2019). We should note that we had also reported results with data that were not trimmed, and that outcome remained statistically significant, so the shortcoming in our outlier rejection procedure did not change the interpretation of the results (Radin et al., 2016, p. 20). Based on his analysis, Tremblay concluded in his latter paper that, "We observe, as in [the 2019 article] shifts in fringe visibility in the direction expected by the mind-matter interaction hypothesis. However, these shifts are not deemed significant (p > 0.05). Our re-analysis concludes that this particular dataset does not contain evidence of mind-matter interaction" (Tremblay, 2021, p.1). from 2014. After those two analyses was performed, all data were combined to further investigate the hypothesized effect.

Analysis
Figure 1 (top) shows the interference pattern observed by the line camera, averaged over 2,400 images collected in one session. Figure 1 (bottom) shows the log of the real portion of the Fourier transform associated with that pattern, from wavenumbers 1 through 60.
The peak at wavenumber 42 is associated with the double-slit (DS) component of the interference pattern, and it is the metric of interest (henceforth referred to as "DS power").    To achieve this transformation, for each frame collected in each session we: 1) Determined the log power spectrum of the interference pattern wavenumbers 1 through 60 (as in Figure 1, bottom).
2) Normalized the spectrum associated with each camera frame using a z-score transform to retain the spectrum's shape without regard to its absolute baseline amplitude.
Then, across all camera frames within each session, we: 3) Calculated the difference between wavenumbers 1 and 42 in each frame. The former is associated with the baseline illumination level, and the latter with the peak DS power. The difference between these two values provides a way to measure changes in DS power with respect to the baseline (call this difference Δ).

4)
Linearly detrended Δ to remove potential drifts over the course of each session.

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Journal of Anomalous Experience and Cognition (JAEX) lag in the results because the mind cannot "switch gears" instantaneously.

Sessions
Over the calendar year 2013, a total of 4,008 sessions were recorded. Of those, 1,256 were completed by humans and 2,312 by robots, where "completed" means that the data in a session were collected during a full run of 21 alternating attentional epochs. Those sessions were readily identified because the web server marked such sessions as "finished." For the remaining 440 sessions, the server marked the session as "crashed" and were not analyzed. Crashed sessions could happen because the participant quit the web browser before the session ended, or because transmission of data from the optical system to the server was interrupted for unknown reasons.
During 2014, a total of 5,798 sessions were recorded, of which 1,569 were completed human sessions, 3,157 were completed robot sessions, and 1,072 were crashed sessions. 10) Combined the z |Δ|H scores as a Stouffer Z to form a single score associated with human observers, and the same for the z |Δ|R scores (Stouffer et al., 1949). This step requires the |Δ| scores to be independent, which was confirmed as shown in Figure 3. 11) Used a Wilcoxon rank sum test to compare the medians of the distribution of z |Δ|H versus z |Δ|R (a t-test could have been used, but the nonparametric test is more conservative).
12) Finally, lagged the original attentional condition assignments from 0 to 5 seconds to account for the time it takes to switch attention between two conditions. The optimal time shift was determined empirically for the 2013 dataset, and then the same parameter was used in analyzing the 2014 dataset. The reason that a lag analysis is important is that if the observed effect is really due to shifts in attention, then there should be a

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Journal of Anomalous Experience and Cognition (JAEX) We may note here that in our original study the maximum lag was observed at +9 seconds (Radin et al., 2016). Why the maximum lag in this analysis occurred at 1.25 seconds is unknown but it may be related to differences between the original and the present methods of analysis. In addition, previous experiments of this sort conducted in our laboratory found lags of 3 or 4 seconds (e.g., Radin et al., 2012). Establishing why these lag lengths differ with alternative analytical methods requires further study, although notice that even at zero lag the results in the present analysis remain significant (assuming FDR adjustment is not required if one considers only that one comparison).  The 2014 value at the 2013 peak of 1.25 seconds was associated with z = 3.14, p = .0008, replicating the 2013 results.

Time of Day Comparison
Considering all data across both years, Figure 8 compares effect sizes and 95% confidence intervals during the day (6 AM to 6 PM, Pacific Time), when laboratory staff were generally within a few meters of the optical apparatus, versus in the evening (before 6 AM or after 6 PM), when no one was present. The results show similar peak effect sizes at the same lags in both time periods. This argues against the possibility that the results were due to the presence of people in the lab, which may have introduced environmental artifacts like vibration or changes in ambient temperature.

Figure 8
Effect Size ± 95% Confidence Intervals Based on a Wilcoxon

Other Environmental Factors
We assumed that the robot sessions were ideal controls to compare against human sessions, and that the use of a detrended, differential metric reduced the possibility that variations in laser power or environmental influences might have given rise to spurious differences between the human and robot sessions. Neither the optical system nor the computer collecting camera data from that system "knew" if data were being served 2022, Vol. 2, No. 2, pp. 362-388

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Journal of Anomalous Experience and Cognition (JAEX) Figure 6 shows the Stouffer Z scores for all human and robot sessions combined across both years. After FDR adjustment at alpha = 10 -6 , the combined data showed two significant deviations for human sessions (red circles) and no deviations for robot sessions (with the latter more liberally tested with FDR, p = .05). The peak value for the human sessions at a lag of 1.5 seconds was z = 5.57 (p = 1.3 x 10 -8 ). Figure 7 shows the Wilcoxon rank sum comparison between the human and robot data, indicating three significant deviations with FDR, p = .002 . The peak value at 1.5 seconds in that case was z = 3.79 (p = .00008). robot trials, the correlation between z|Δ| (lagged 1.5 seconds) and the illumination level was not significant (r = .015, p = .18).

Relation Between Mean Illumination Level and z|Δ|
Although no relation was found between the illumination level or distribution of the type of session, a Kolmogorov-Smirnov comparison of the distributions of human versus robot z|Δ| values resulted in p = 3 × 10 -6 (Matlab function kstest2; see Figure 12), and a Wilcoxon rank sum comparison of the medians of those distributions resulted in p = 3 × 10 -5 . This again showed that the double-slit interference pattern differed when humans were observing the system as compared to when robots were observing. to a distant human or a robot, and there were no indications on the apparatus or computer that might have revealed if it was idling or currently serving data. This "silent operation" was by design to prevent laboratory staff from being aware of, and thus inadvertently influencing, the on-going status of the experiment.
To check if these assumptions were correct, we explored if the results might have been due to a correlation between laser power and the z|Δ| metric, or to a non-unform distribution of human and robot sessions. To do this we first examined the mean illumination level recorded by the line camera in each session in chronological order. Figure 9 shows that illumination declined over the course of the two-year experiment. This decline occurred for two reasons: Progressive reduction in laser power output (the laser was powered on continuously for two years), and accumulated misalignments of the laser beam in the apparatus due to ambient vibrations and/or variations in ambient temperature, the latter associated mostly with heating and cooling the lab as the seasons changed.

Figure 9
Mean Line Camera Illumination Level (in Arbitrary Units Returned by the Camera Software), Across all Sessions in Chronological Order Figure 10 shows z|Δ| values obtained in all sessions in chronological order, with human sessions as black circles and robot sessions as red circles. This shows that there were periods when human trials were run with few or no interspersed robot trials. Figure 11 shows that despite the drop in illumination and the nonuniform distribution of human and ticipants who are not selected for potential talent, or meditation experience, or other skills that require expertise in maintaining focused attention. It is also possible that even in those who can maintain tightly focused attention than their intentions may unavoidably wax and wane, akin perhaps to punctuated moments or "quanta" of consciousness.
The possibility that assumptions of the statistical tests used in this analysis were violated was avoided by using nonparametric methods, and also by demonstrating that the |Δ| values used to characterize the results in each session were independent of each other. Potential biases due to data selection were avoided by evaluating all completed sessions, and possible biases that might have arisen by adjusting analytical parameters to fit the data were addressed by first developing a method that was applied to the 2013 data, and then applying the same method to the 2014 data.
The primary limitation in this reanalysis is that it is unknown if the same analytical approach could successfully detect results in a similarly designed experiment. Only future replications can answer that question. However, the results so far suggest that revising the original hypothesis from directional to bidirectional reverses Tremblay's conclusion, suggesting instead the presence of a psychophysical interaction effect in an online double-slit experiment.

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Journal of Anomalous Experience and Cognition (JAEX)

Figure 12
Histogram of z|Δ| for all Human (Black Bars) vs. Robot Sessions (White

Discussion
Tremblay's (2021) conclusion after reanalyzing the data from this experiment was: "this particular dataset does not contain evidence of mind-matter interaction…." That conclusion was justified based on the original hypothesis that focused attention would unidirectionally collapse the wavefunction in accordance with the observer's attention and/or intention. Incidentally, it is noteworthy that his conclusion was also extremely conservative because Tremblay's analytical method required Holm-Bonferroni adjustment for hundreds of statistical tests. By contrast, the present analysis only required a few adjustments.
If the original hypothesis were correct then such an effect would be best detected as a shift in the mean of a suitable metric. However, given the results observed in the present analysis, in Guerrer's replication attempt (Guerrer, 2019), and similar variance effects observed in another laboratory experiment we conducted (Radin et al., 2021), we suspected that a unidirectional hypothesis may not be the most sensitive way to detect the hypothesized effect. Instead, because of internal and external distractions (i.e., mindwandering, phone calls, multitasking, etc.), a more suitable hypothesis may be bidirectional. This may be an especially important consideration when dealing with online par-