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.

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] .

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.

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 ( ${\text{HCO}}_3^{-}$ 152, SiO₂ 93, Ca²⁺  18, Na⁺ 17, Mg²⁺ 15, K⁺ 5, Cl⁻ 11, ${\text{SO}}_4^{2-}$ 2, ${\text{NO}}_3^{-}$ 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.

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 $\ll$ 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.

*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.

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.

LME analysis of these runs revealed a significant main effect for Condition (p = 0.006) and a significant Phase × Condition interaction (p $\ll$ 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.

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.

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: