Independent Replication of an “Excess Correlation” Effect in pH between Isolated Beakers of Water ()
1. Introduction
The term “excess correlation” refers to anomalous entanglement-like correlations that reportedly arise between properties of physically isolated systems when both are exposed to a common sequence of magnetic field pulses at the same time, which in practical terms means within a fraction of a second. Published articles describing such effects include pH shifts in water, seed germination, cell culture growth, photochemical reactions, human brain activity, and human behavior [1]-[18]. Two types of electromagnetic systems have been used to evoke such correlations: one with eight solenoids arranged in a circle to create a rotating magnetic field, and a simpler plastic-core toroidal system dubbed the “halo” [3] [19].
These reported effects are considered controversial for two reasons. First, while there have been many published reports of excess correlation effects, to date they have only been reported by researchers from Michael Persinger’s laboratory at Laurentian University in Sudbury, Canada. Second, the underlying physical mechanisms remain highly speculative. For example, one proposed explanation was that the correlations appeared to be analogous to quantum entanglement [20]. As an analogy that suggestion is acceptable, but the actual mechanism is unlikely to be quantum because decoherence effects in water and biological systems would preclude the presence of long-range or long-lasting entanglement [21].
Another proposal was based on the notion of nonlocal “informational fields,” which might mediate the observed correlations [22]. While interesting from a philosophical perspective, e.g., dual-aspect monism offers an expanded view of mind and matter that might be compatible with the existence of nonlocal correlations [23], these proposed explanations do not offer falsifiable physical mechanisms. Other hypotheses involved subtle electromagnetic field interactions or resonances that are said to arise between spatially separated systems, including shared environmental variables like geomagnetic fluctuations, Schumann resonances, or atmospheric noise [24]. Again, such ideas are plausible in principle, but the strength and range of the extremely low frequency and miniscule magnitude of the magnetic fields used in these experiments would not appear to be sufficient to account for correlations reportedly observed across tens to thousands of meters. Still other hypotheses were based on mathematical analyses of entanglement velocities for elementary particles in Minkowski space [15], and other arcane speculations.
From a conventional perspective, it seems more likely that the reported correlations were due to methodological artifacts or statistical errors. However, a notable lack of interest in empirical effects that resist conventional theoretical explanations appears to be the default in science [25], so no independent replication attempts have been reported. Sometimes anomalies turn out to be understandable in conventional terms, but if the anomalies resist mundane explanations, they might provoke a revolution. The only way to advance beyond the impasse is through replications, thus motivating the present study.
2. Methods
2.1. Hypothesis
When acetic acid from white vinegar is added to a “local” beaker of water placed in one halo, the pH of a “remote” beaker of water in a distant halo will shift toward alkaline during a magnetic stimulation sequence known as the effector and not during a preliminary sequence called the primer.
2.2. Data Analysis
Samples of pH in each 30-minute test session were sampled at 1 Hz. To accommodate baseline variability and focus on temporal dynamics, each pH series was first normalized by subtracting the initial pH in each phase of interest (i.e., primer vs. effector) from subsequent values to form ΔpH. A linear mixed-effects (LME) model, defined as ΔpH ~ Time × Phase × Condition + (1 + Time | Trial), was used to analyze these data [26] [27], with fixed effects of Time, Phase (primer vs. effector), and Condition (experimental vs. control), plus random effects for intercepts and slopes to account for between-run variability and potential drift.
Based on this method, the analysis of interest focused on two outcomes: the main effect of Condition and the Phase × Condition interaction. In the first case, the Condition factor compared the experimental (magnetic stimulation) vs. control (no stimulation) conditions to test the hypothesis that this difference would result in a positive ΔpH effect. In the second case, the Phase × Condition interaction tested if the experimental and control conditions differed between the two temporal phases, with the primer vs. effector difference predicted to result in a negative ΔpH. Other factors, like Time, Time × Condition, Time × Phase, as well as the three-way interaction, would be of interest in future studies, but this replication attempt was specifically focused on evidence supporting the excess correlation claim.
Applying Akaike Information Criterion comparisons to alternative LME models indicated that including both Time and its interaction terms would improve the model’s fit over simpler approaches [28]. Residual autocorrelations were planned to be checked with the Durbin-Watson method to assess if residual autocorrelations were acceptably low [29]. If autocorrelations were deemed high, which was not unexpected given the pH measures, then a BCa (bias-corrected and accelerated) nonparametric bootstrap method would be used to form 95% confidence intervals and adjust for possible autocorrelation biases, non-normal residuals, heteroscedasticity, and inflation of p-values [30].
2.3. Equipment
Each halo consisted of a 25.4 cm diameter plastic hoop wound with 225 loops of a 16-gauge copper wire. The wire ends were connected to an Arduino-driven microcontroller circuit (Figure 1). Although that circuit lacked a classic current return path through the toroid, the diode’s junction capacitance allowed a weak displacement current to flow during each pulse, generating a small magnetic field (~20 nT) in the halo’s center. When the halo was energized, the presence of the magnetic field was confirmed using a magnetometer (TriField Model TF2, lower AC range rated at 10 nT sensitivity, AlphaLab, Salt Lake City, UT). An amplified telephone pickup coil also produced an audible signal that matched the pulse sequences.
Figure 1. Arduino and electrical circuit used to energize the toroid. Short electrical pulses created a potential difference across the diode that allowed current to pulse through the toroid, in turn creating a weak magnetic field.
2.4. Protocol
Each Arduino microcontroller used to energize its halo ran a 30-minute program consisting of a 6-minute baseline period during which the electrical stimulation circuit was idle, then for 6 minutes it repeatedly generated the primer sequence, followed by 12 minutes running the effector sequence, and then ended with a 6-minute post-baseline idling period. At the middle of the primer sequence or start of the effector sequence several drops of acetic acid (~0.25 mL of white vinegar) were added to the local beaker. In some test runs acid was dropped once, and in other runs it was repeatedly dropped once a minute.
pH samples were time-stamped based on manually resynchronizing the Windows Network Time Protocol. The pH sensor was sampled at 1 Hz by a separate Arduino connected via USB to a Windows 11 PC (Atlas Scientific, Long Island City, NY, Model Gen3, resolution 0.001 pH).
Fifty experimental runs were conducted. Figure 2 illustrates the experimental set up for the first 25 sessions, in which two 40 mL beakers were placed 1 meter apart and each was filled with 20mL of Fiji brand spring water (
152, SiO2 93, Ca2+ 18, Na+ 17, Mg²⁺ 15, K+ 5, Cl− 11,
2,
0.27, F− 0.24; total dissolved solids (TDS) 222 mg·L−1 and pH 7.7) or tap water (chemical analysis unavailable). Each beaker was placed in the center of a halo, and both beakers and halos were placed on top of a 6 cm stack of plastic foam sheets on a plastic-topped table (to avoid magnetic distortions from proximal metallic sources). Each halo was energized separately, and the magnetic stimulation periods were manually started within a second of each other. In each beaker, a pH sensor (Atlas Scientific, Long Island City, NY, Gen3 pH sensor, resolution 0.001 pH) was placed and sampled at 1 Hz by an Arduino connected via USB to a Windows 11 PC.
For the next 15 tests, the beakers were placed in rooms 6 meters apart. For the following 10 tests, the beakers were again located 1 meter apart, but a single Arduino circuit was used to energize both halos simultaneously. In these runs, a third non-stimulated control beaker of water was placed between the local and remote beakers. The final 5 tests placed the local beaker and halo 10 meters away from the control and remote beakers. The magnetic stimulation sequences in those runs were synchronized via a 901 MHz radio transceiver (Adafruit RFM69HCW, https://www.adafruit.com/product/3070). Figure 3 shows photos of the various components used in these tests.
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Figure 2. Illustration of experimental set up with two beakers subjected to the same type and timing of magnetic stimulation controlled by separate microcontrollers powered via USB (MCU, Arduino UNO r3). Separate laptops also recorded data from the MCUs that ran the pH sensors. For simultaneous control runs, a third beaker and sensor may be placed between the two stimulated beakers.
Figure 3. Left. Magnetic stimulation circuit combined with the radio transceiver used in the last 5 test sessions. Middle. pH sensor circuit and three pH sensors soaking in a conditioning solution. Right: Local and remote halos and beakers one meter apart, plus a central beaker used for control sessions, each with a pH sensor.
3. Results
3.1. Asynchronous Experimental vs. Control Tests
For illustrative purposes, Figure 4 shows the results of two of 17 experimental runs. Notice that the remote beaker’s pH displayed interesting inflection points near the moment when acid was added to the local beaker, with accelerated alkalinity shifts during the effector phase. Figure 5 shows the results averaged across 17 experimental and 7 separate control runs.
LME analysis of these 24 half-hour sessions (17 experimental and 7 control) revealed a significant Phase × Condition interaction (p
0.001, see Table 1), indicating that ΔpH during the effector phase was significantly different from the primer phase. But the lack of a Condition main effect indicated no significant difference between experimental and control runs in the effector phase.
Figure 4. Examples of experimental runs where the local and remote beakers were 1 meter apart and the magnetic stimulation in each halo was controlled separately. The sharp drop in local ΔpH (blue line, left y-axis) indicates when acid was dropped into the local beaker. Error bars for the remote beaker curve are ±6 standard errors calculated and displayed in 30-second segments (because 95% error bars would be too small to visualize).
Figure 5. Mean pH across 17 experimental runs (acid added to the local beaker, black squares) and 7 control runs (no acid added to the local beaker, white dots) during the primer (left graph) and the effector (right graph) phases. Error bars are one standard error).
Table 1. LME results for independent experimental and control trials, with the statistical factors of interest highlighted in bold.
Term |
Effect size estimate |
SE |
95% CI Lower |
95% CI Upper |
p-value |
Intercept |
−0.004 |
0.002464 |
−0.008984 |
0.000674 |
0.09 |
Time |
0.000051 |
0.000022 |
0.000008 |
0.000095 |
*0.02 |
Phase |
0.004 |
0.000384 |
0.003276 |
0.004781 |
*
0.001 |
Condition |
0.003 |
0.002927 |
−0.002746 |
0.008729 |
0.31 |
Time × Phase |
−0.000014 |
0.000022 |
−0.000017 |
−0.000010 |
*
0.001 |
Time × Condition |
−0.000010 |
0.000026 |
−0.000053 |
0.000050 |
0.96 |
Phase × Condition |
−0.004 |
0.000456 |
−0.004485 |
−0.002697 |
*
0.001 |
Time × Phase × Condition |
0.000008 |
0.000002 |
0.000003 |
0.000012 |
*0.0006 |
*indicates statistically significant effects.
The mean Durbin-Watson statistic was 0.354, indicating strong autocorrelation in the ΔpH measures, as expected. Thus, the bias-corrected and accelerated (BCa) nonparametric bootstrap method was used to provide a more robust estimate for the confidence intervals and the actual p-values. That procedure produced the results shown in Table 2, which reduced the Phase × Condition interaction to a nonsignificant p = 0.111. Thus, neither of the two main comparisons of interest showed significant results, but the effect size estimates were in the predicted directions, i.e., a positive effect size of 0.003 for Condition and a negative effect size of −0.004 for the Phase × Condition interaction. This outcome was promising but prompted a different approach for the second set of experimental tests.
Table 2. BCa bootstrap results and adjusted p-values.
Term |
Effect size estimate |
95% CI Lower |
95% CI Upper |
Estimated SE |
Estimated
p-value |
Intercept |
−0.004 |
−0. 008157 |
−0.010233 |
0.001820 |
*0.023 |
Time |
0.000051 |
0. 000021 |
0. 000090 |
0.000017 |
*0.003 |
Phase |
0.004 |
0. 000761 |
0. 006861 |
0.001556 |
*0.010 |
Condition |
0.003 |
−0. 001671 |
0. 007799 |
0.002416 |
0.213 |
Time × Phase |
−0.000014 |
−0. 000061 |
−0. 000029 |
0.000023 |
0.558 |
Time × Condition |
−0.000010 |
−0. 000044 |
0. 000036 |
0.000021 |
0.949 |
Phase × Condition |
−0.004 |
−0. 007994 |
0. 000852 |
0.002257 |
0.111 |
Time × Phase × Condition |
0.000008 |
−0. 000037 |
0. 000057 |
0.000024 |
0.744 |
3.2. Simultaneous Experimental and Control Tests
To more rigorously control for possible environmental effects and to improve statistical power, 26 additional sessions were run wherein a remote and a control beaker were each measured simultaneously. Figure 6 shows two representative runs and Figure 7 shows the average of all combined results, respectively.
Figure 6. Examples of two experimental results with the local and remote beakers 6 meters apart, and with a third control beaker in between. The graphs show the remote ΔpH as black squares and simultaneously recorded control ΔpH in white dots. Error bars are ±6 standard errors.
Figure 7. Combined results for mean ΔpH across 26 sessions with experimental results as black squares and control results as white dots. Error bars are one standard error.
LME analysis of these runs revealed a significant main effect for Condition (p = 0.006) and a significant Phase × Condition interaction (p
0.001) (see Table 3). However, the Durbin-Watson statistic again indicated excess autocorrelation in the ΔpH measures (D-W = 0.296), so the BCa bootstrap method was used to create a more robust estimate, as shown in Table 4. The BCa analysis indicated that the Condition and the Phase × Condition effects remained significant and in the predicted directions, and the effect sizes were close to those observed in the first set of asynchronous tests.
Table 3. LME results for simultaneous experimental and control beakers.
Term |
Effect size estimate |
SE |
95% CI Lower |
95% CI Upper |
p-value |
Intercept |
−0.001935 |
0.001037 |
−0.003967 |
0.000097 |
0.062 |
Time |
0.000019 |
0.000007 |
0.000005 |
0.000034 |
0.009 |
Phase |
0.002011 |
0.000153 |
0.001712 |
0.002310 |
0.001 |
Condition |
0.004 |
0.001466 |
0.001133 |
0.006881 |
0.006 |
Time × Phase |
0.000009 |
0.000001 |
0.000008 |
0.000010 |
0.001 |
Time × Condition |
0.000003 |
0.000011 |
−0.000017 |
0.000024 |
0.745 |
Phase × Condition |
−0.004 |
0.000216 |
−0.004903 |
−0.004057 |
0.001 |
Time ×Phase × Condition |
−0.000008 |
0.000001 |
−0.000009 |
−0.000006 |
0.001 |
Table 4. BCa bootstrap results and adjusted p-values.
Term |
Effect size
estimate |
Estimated SE |
95% CI Lower |
95% CI Upper |
Estimated
p-value |
Intercept |
−0.001944 |
0.001167 |
−0.004220 |
0.000356 |
0.096 |
Time |
0.000019 |
0.000005 |
0.000010 |
0.000029 |
*
0.001 |
Phase |
0.002023 |
0.001289 |
−0.000585 |
0.004470 |
0.117 |
Condition |
0.004 |
0.001426 |
0.001199 |
0.006789 |
*0.005 |
Time × Phase |
0.000009 |
0.000008 |
−0.000006 |
0.000024 |
0.241 |
Time × Condition |
0.000003 |
0.000008 |
−0.000012 |
0.000019 |
0.665 |
Phase × Condition |
−0.005 |
0.001682 |
−0.007749 |
−0.001154 |
*0.007 |
Time × Phase × Condition |
0.000008 |
0.000024 |
−0.000037 |
0. 000057 |
0.744 |
4. Discussion
To assess the combined results of all 50 runs across the two experiments, Fisher’s method was used to combine the BCa adjusted probabilities associated with the Condition effect and Phase × Condition interaction [31]. The result based on the four p-values (and Fisher’s method of calculating df) was: χ2 = 28.09 (df = 8), p = 0.00046. Then, because the p-values derived for Condition and Phase × Condition in each study were not completely independent, Brown’s method, augmented by Kost and McDermott’s refinements, was used to take the within-experiment dependencies into account to calculate a revised combined p-value [32] [33]. That process resulted in a more significant outcome, p = 5.27 × 10−9, which can happen when the underlying tests contain a level of dependency that, when modeled appropriately, reveals stronger evidence against the overall null hypothesis. To be conservative, Fisher’s method of combining p-values is used as the outcome of these experiments.
In sum, based on appropriate statistical techniques (LME, BCa nonparametric bootstrapping, and Fisher’s method), plus consistent effect sizes observed across two experiments, it appears that these studies supported the hypothesis of excess correlation, bolstering the credibility of the previously published reports. It should be noted that those same reports suggest that the effect is sensitive to numerous controllable and uncontrollable factors, including the field strength generated by the halo, the specific magnetic sequences used, the quantity and type of water in pH tests, a claimed “space memory” effect, the orientation of the halos with respect to magnetic North, and the Earth’s geomagnetic field strength [34]. Such factors indicate that the excess correlation effect may not be strong enough to be easily observed under any conditions, but on the other hand, it was apparently robust enough to be discerned in the present studies without attempting to optimize those factors.
4.1. Limitations
While the results were statistically quite strong, the effect size (ΔpH ~0.004) was small. The pH sensors used in this replication had a resolution of 0.001, and each sensor was calibrated several times using a standard three-point calibration procedure (Atlas Scientific calibration solutions, pH 4.00, 7.00, and 10.00, described as standardized against NIST-certified references), so they were in principle capable of measuring an effect of that magnitude. However, caution is advised when measuring an effect that is so close to a sensor’s measurement resolution.
Another caution involves the low Durbin-Watson scores, because they raise valid questions about potential autocorrelated errors. The BCa bootstrap approach significantly mitigates such concerns, but future efforts might explore additional analyses that explicitly model autocorrelation, e.g., ARIMA structures or generalized least squares with autocorrelation corrections.
A further limitation is that on average both the experimental and control results exhibited a drift in pH toward alkaline. The rise in pH in the experimental sessions was predicted by the hypothesis, so that was not surprising. However, pH in control water exposed to air is expected over time to become more acidic, not alkaline [35]. This raises questions about the behavior of the pH sensors, or possibly it revealed an experimental confound called a “space memory” effect in a publication reported by Dotta et al., and described as “…the ‘memory’ or representation of pH (H+) shifts remain in space long after the stimulus has been removed and can be retrieved within that space if the specific electromagnetic field is repeated” ([28], p. 511). If that reported memory effect was a genuine phenomenon, then the drift toward alkaline in the control beaker, which in some experiments was the same beaker but with fresh water, and in others it was a beaker in proximity to the remote beaker, might have been due to that effect.
In any case, despite the many successful replications reported by investigators in Persinger’s laboratory, these claims will likely remain controversial because there are as yet no well accepted theoretical models to explain the effect. Conventional explanations include effects of fluctuations in ambient temperature, sensor drift, and other uncontrolled environmental artifacts. Unconventional explanations, as alluded to in the Introduction, have included quantum entanglement [6] [14] [19], “information fields” possibly mediated by ultra-weak magnetic fields [20] [36] [37], and “active information” as proposed by Bohm [38]. Another possibility involves longitudinal or scalar potentials, drawing analogies from the Aharonov-Bohm effect, wherein magnetic potentials can exert subtle nonlocal influences even without the presence of traditional EM fields [39] [40]. Also, collective coherence effects in water structure might underlie nonlocal coupling under certain conditions [41], and most of the systems tested using the magnetic stimulation technique involved water in some form.
4.2. Recommendations
The experimental setups used in these preliminary replications were straightforward, but a series of methodological enhancements may improve the reliability and credibility of the effect and also address potential confounds. Such improvements, in no particular order, could include:
Automating acid injection into the local beaker via a robot fluid handler.
Using blinding measures to ensure that some automated runs are experiments and others are controls.
Testing water samples at various initial pH levels.
Networking the microcontrollers to provide precise, unified timestamps for each measurement.
Running experiments over many days to account for variation in geophysical factors.
Frequently recalibrating all pH sensors.
Performing all data logging directly on the microcontrollers.
Automating data analyses from start to finish.
Employing randomized delays or offsets in the magnetic stimulation start times.
Testing multiple halos simultaneously to explore multi-site correlations.
Adding ambient air and water temperature sensors.
Changing the locations of the beakers on each experimental run to avoid the potential of a “space memory” influence.
Preregistering study protocols and planned statistical analyses.
Using a magnetometer with resolution of at least 1 nT to confirm the presence and strength of the magnetic fields created by the halo device.
5. Conclusion
This study successfully replicated a small magnitude but statistically significant excess correlation effect in water pH. Further independent replications are crucial to advancing our understanding of this potential nonlocal phenomenon. If it turns out to be a reliable effect, these phenomena may provide new insights into the nature of nonlocal connections.
Acknowledgements
This work was generously funded by the Bial Foundation. The author thanks Don Hill for lending the original halo equipment developed by Ryan Burke and Nicolas Rouleau. The author acknowledges the assistance of OpenAI’s ChatGPT in generating portions of the Matlab scripts for the LME and BCa analyses. All AI-derived content was critically reviewed and revised by the author to ensure scientific accuracy. The Arduino code, Matlab analysis scripts, and data collected in this study are available to qualified researchers from the author upon request.