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States of excess correlation have previously been achieved at macroscopic levels by simultaneously exposing two non-local spaces to weak electromagnetic field patterns, generated by toroids, presented in a sequence such that the angular velocity of the field is modulated by changes in frequency over time. Here we systematically investigated effects upon the local space at the center of a single toroid generating the excess correlation sequence. The results indicated that a 1 - 5 nT diminishment in field intensity on the Y- or east-west axis was characteristic of the excess correlation sequence which was not indicated for control conditions. Statistically significant shifts in field intensity approximately 40 to 60 s before the onset of the first field associated with the excess correlation sequence indicated a temporally non-linear effect which converged upon the ratio of g and the rotational velocity of the Earth for the local space where Coriolis-like forces were inferred. Intensity shifts associated with the excess correlation sequence but not controls were quantitatively convergent upon parameters of the hydrogen line (1.42 GHz). Implications for these findings were discussed in relation to Mach’s principle and, in particular, to the electron as a physical unit which was found to relate classical and quantum systems.

The experimental treatment of two non-local spaces such that they behave as if they were the superimposed and had become the “same space” has theoretical and practical applications. Excess correlations, a frequently employed analogue for “entanglement” [

Based upon the conclusions by Tu et al. [^{−}^{11} W・m^{−}^{2}) as measured by photomultiplier tubes from the right hemispheres of the other member of the pair who was sitting in complete darkness in another room. A similar effect was measured for pairs of cell cultures separated by this distance and exposed to the same field parameters simultaneously.

In order to discern if photons, per se, were involved rather than processes associated with living systems, Dotta and Persinger [

This “doubling of the photon duration” [

The circular array of eight-solenoids that produced the discrete bursts of magnetic fields with changing angular velocities was operated by Complex^{©} software and required custom-constructed Digital-to-Analogue Converters (DAC). A more accessible technology was required. After Burke et al. [

However, in the process of measuring the static components of what is primarily the Earth’s magnetic field by a magnetometer in the three axial planes (X, N-S; Y, E-W, and Z, vertical), we noted an interesting anomaly that was consistent with the magnitude and direction of potential variations in G (ΔG), the gravitational constant, and “geomagnetic” static intensity in the Y-axis. Typical daily fluctuations in G are within the range of ~3 × 10^{−}^{3} of the average value. Recently Persinger and St-Pierre [^{−}^{9} T and 10^{−}^{14} m^{3}・kg^{−}^{1}・s^{−}^{2} might share the same source of variance. The energy equivalence for the ΔG and this magnitude of magnetic field intensity within 1 L of space converged to be ~3 × 10^{−}^{14} J [

Each toroid core was a plastic ring with a diameter of 25.4 cm (circumference = 79.8 cm). It was wrapped with 225 turns of 16 gauge wire (stereo speaker copper wire). The coil was wrapped in black, vinyl electrical tape. The elevation from the surface upon which the toroid rested and its top (i.e., the diameter of the ring around which the wire was wrapped) was 3.81 cm. An actual picture of the toroid is shown in

A MEDA FVM-400 Vector Magnetometer sensor was placed at the center of the toroid. Fluctuations in background electromagnetic field intensity (nT) were measured. The probe’s X-axis was oriented to magnetic north, positioning the Y-axis within the perpendicular horizontal plane, and the Z-axis within the vertical plane (

The same laptop provided digital-to-analog output to an Arduino Uno R3 microcontroller which carried a patterned current through the toroidal coil. The 5 V output sequence and its associated electromagnetic field has previously demonstrated a capacity to establish states of “excess correlation” between beakers of spring water separated by 1 m [

A 300 s pre-exposure baseline recording was obtained before the initiation of the first field pattern in the sequence.

Once initiated, the first field―a temporally decelerating pattern―looped continuously for 360 s. A temporally accelerating field was initiated at the 660 s mark, exposing the space within which the sensor was placed for an additional 660 s. The second field pattern was then terminated and 480 s of post-exposure baseline data were collected. This protocol, similar to that employed by Dotta and Persinger [

Two variants of this protocol were performed as comparators in order to control for non-specific artifacts from the generation of magnetic fields. The first protocol variant (Reverse) involved a reversal of the temporal pattern associated with the first and second field exposure such that the accelerating field preceded the decelerating field. The exposure times of the first and second field remained consistent. The second variant (control) was a control protocol wherein 1800 s of baseline data are collected without the initiation of any field.

All protocols were repeated 6 times for a total of 18 trials. No two trials were completed on the same day.

However, all trials were completed between 9 PM-2 AM local time in order to control for diurnal variations in background electromagnetic field intensities. Once collected, raw data were extracted and new variables were computed. First, a 60 s average of field intensity was computed from the center of each exposure phase. For example, the mean and standard deviation for the pre-exposure baseline phase were computed by averaging second-by-second nT values from minute 2.5 of each trial (n = 18) during pre-exposure baseline phase and computing grand averages within each exposure protocol for X-, Y-, and Z-axes. Shifts in intensity (nT) were then computed by subtraction in order to infer net changes in intensity as a function of experimental manipulation. Running 30 s intensity averages were then calculated for all axes and incremental nT shifts were computed in order to infer fine-scale changes.

An ANOVA revealed statistically significant differences in nT shifts from the pre-exposure baseline phase to the first field phase along the Y-axis only as a function of exposure protocol [F(2,15) = 7.20, p < 0.01], explaining 53% of the variance. Post-hoc tests revealed the source of variance to be a subtle negative shift (decrease) in field intensity associated with the Excess protocol (M = −2.77, SEM = 0.37) relative to control protocol (M = −0.34, SEM = 0.60), [t(8) = 3.45, p < 0.01, r^{2} = 0.60]. Similarly negative shifts were observed from pre-expo- sure baseline to the first field exposure in Excess protocol trials relative to Reverse trials (M = 0.35, SEM = 0.72), [t(9) = −3.61, p < 0.01, r^{2} = 0.59]. There were no significant differences in shifts from pre-exposure baseline to the first field exposure between control and reverse protocols along the Y-axis (p > 0.05). These results are presented in

In order to discern the temporal characteristics of this shift as a function of exposure protocol, multiple independent t-tests were generated examining incremental shifts from minute 2.5 to 3.0, 2.5 to 3.5, 2.5 to 4.0, etc. The differences between excess and control protocols were first noted when examining the shift from minute 2.5 to 4.0, t(10) = 3.20, p < 0.05. This incremental shift difference between excess and control protocols persisted for 120 s until the shift from minute 2.5 to 6.5, t(10) = 2.03, p > 0.05. There were no significant differences noted for incremental shifts between control and reverse protocols. Differences between excess and reverse protocols were transient, however, and were comparable to those observed for excess and control comparisons. These results are reported in

Correlational analyses were completed to discern any relationship between the aforementioned 30 s-by-30 s serial nT shifts and time. Serial nT shifts along the Y-axis (n = 58) positively correlated with time (r = 0.68, p < 0.001) for the Excess protocol only. These correlations for the Y-axis were not statistically significant for the control or reverse trials (p > 0.05). No further significant relationships were revealed. These results are presented in

The contribution from the energy from the rotation of the Earth to the east-west magnetic shift measured in our experiments for only the excess correlation procedure should have quantitative consistency. Assuming the mass of the earth to be 5.98 × 10^{24} kg and the velocity to be 4.63 × 10^{2} m・s^{−}^{1}, the total energy of the system would be 1.27 × 10^{30} J distributed over a spatial field equivalent to the surface area of the earth (5.1 × 10^{14} m^{2}), or, about 0.25 × 10^{16} J・m^{−}^{2}. When applied to the area occupied by an electron as a particle (6.15 × 10^{−}^{30} m^{2} per electron), the average energy would be about 1.5 × 10^{−}^{14} J per electron. This energy is remarkably similar (the same order of magnitude) to the mass equivalent of an electron.

The energy of a system from a magnetic field can be estimated by B^{2} divided by 2μ when this quotient is multiplied by the volume involved. In this instance μ_{o} is magnetic permeability (4π × 10^{−}^{7} N・A^{−}^{2}) and B is the strength of the field. From

the value would be 0.96 × 10^{−}^{2} m^{3}, or a linear distance of 21 cm. This value is important because it reflects the approximate width of the toroid (25 cm). It is also the approximate wavelength of the most copious standing wave in the universe, the neutral hydrogen line (1.42 GHz). If a procedure were to be developed to capture this condition of excess correlation over non-traditional distances, the hydrogen line would be expected to be involved.

The phenomena may have occurred because of the circumference of the toroid. We had selected these parameters in order to place the toroid over or around the average human head. According to conventional calculations of inductance (L):

where N is the numbers of turns around the toroid, A is the torus’ cross-sectional area and r is the radius of the toroid. For our equipment these values were 225, 3.7 × 10^{−}^{4} m^{2}, and 1.3 × 10^{−}^{1} m. The inductance of the toroid would have been 2.9 × 10^{−}^{5} H.

Application of dimensional analysis for values potentially relevant for a type of universal entanglement suggests that the product of inductance (kg・m^{2}・A^{−}^{2}・s^{−}^{2}), unit charge (A・s), and the square of frequency (s^{−}^{2}), in this case the neutral hydrogen line, would be relevant. Consequently the product of 2.9 × 10^{−}^{5} H, 1.9 × 10^{−}^{19} A・s, and (1.42 × 10^{9} Hz)^{2} results in 9.4 × 10^{−}^{6} V. In experiments with human brain activity we had considered this an important range because of its congruence with the change of voltage associated with the conduction within a single ion channel in the plasma membrane of a neuron. In the present application the product of this potential difference and the unit charge is associated with a quantity of energy ~ 1.5 × 10^{−}^{24} J. The value is clearly recognizable because its quantum frequency obtained by dividing it by Planck’s constant (6.626 × 10^{−}^{34} J・s) is within error of measurement of the 1.42 GHz hydrogen line.

Because the Earth is rotating in an east-west direction and the current within the toroid was rotating as well there would be the potential for Coriolis-like forces to contribute. In the balance of probabilities if they interacted the interface of the process should be manifested by the relationship between the axial drift velocity of the current in the toroid and intrinsic frequency at this latitude as define by the angular velocity of the system and the latitude. Drift velocity is classically defined as:

where v is velocity, I is the current in the toroid, n is the molar density of the material (in this instance copper), A is the area (of the wire) and q is the unit charge. Both direct measurements of the circuit during the generation of the frequency-modulated magnetic fields during the excess correlation protocol and calculations from the Arduino-toroid circuit indicate that the nominal current was 0.55 mA during the decelerating phase and 0.85 × 10^{−}^{3} A during the accelerating phase.

Assuming 9.0 gm・cm^{−}^{3} density for copper, 6.023 × 10^{23} molecules per mole and 1 electron per atom, this product when divided by copper’s atomic weight (64 gm per mole) shows the numbers of free electrons would be 8.5 × 10^{28} m^{−}^{3}. When multiplied by the cross-sectional area of the 16 gauge copper wire (1.32 × 10^{−}^{6} m^{2}) and the unit charge 1.6 × 10^{−}^{19} A・s for the unit charge, the value is 17.95 × 10^{3} A・(s・m^{−}^{1})^{−}^{1}. When divided into the 0.55 × 10^{−}^{3} A (decelerating phase) to 0.85 × 10^{−}^{3} A (accelerating phase) measured in the circuit, the median drift velocity would between ~3.1 and 4.7 × 10^{−}^{8} m・s^{−}^{1}. This would occur for a steady current. However our current was oscillating. We assumed that this temporal component could facilitate the drift by the factor f × v, where f is the intrinsic frequency of the oscillations. For the 3 ms intervals employed here, the equivalent f is 3.33 × 10^{2} Hz. For a unit second this results in an enhancement to a “dynamic” drift value between 1.0 to 1.6 × 10^{−}^{5} m・s^{−}^{1}.

If the forces of interaction between the angular velocity of the system (the Earth) and the internal rotation of the toroid are similar in relation to Coriolis forces, then the radius of the “circular” rotation generated by the toroid can be estimated by:

where v is the drift velocity and f is the Coriolis parameter at the specific latitude (46.39 N) which is determined by the angular velocity of the system. In this instance we assumed the average of the velocity for the decelerating (205 ms) and accelerating (128 ms) cycle completions around the circumference of the toroid, or, 5.1 m・s^{−}^{1}. The value would be 8.6 × 10^{−}^{5} s^{−}^{1}. When the dynamic drift velocity, v, was divided by the Coriolis parameter, the resulting radius for the “circular motion” or “inertia of the circle” would be between ~11 cm and 18 cm. The diameter for this “circular inertia” would be within the range of the 21 cm hydrogen wavelength. However the nature of the coefficients required for the congruence is not obvious at this time. Higher current intensities and stronger measured magnetic fields within the toroid would solve for different drift velocities and hence different solutions. This may explain the efficacy of the ~30 nT and associated current (mA level) time-varying fields in the excess correlation condition compared to the 300 nT strengths applied in the same manner [

If the adjustment for time-variation had not been made within the original drift velocity the radius of the inertia of the circle would have been between 3.1 and 4.7 × 10^{−}^{4} m or a circumference of 1.9 to 3 mm with a corresponding frequency, if electromagnetic, of 1.6 × 10^{11} Hz to 1 × 10^{11} Hz. When multiplied by Planck’s constant and divided by the Boltzmann constant of 1.38 × 10^{−}^{23} J・K^{−}^{1}, the equivalent temperature approaches within a factor of 2 the cosmic background microwave levels. We cannot exclude the possibility at this time that some static component of the current induction, even though it was time varying by the Arduino circuit, occurred. The diminishment of the E-W component of the “geomagnetic” field within the center of toroid was not phasic but constantly persistent for several minutes and occurred only when the excess correlation protocol was applied.

The Coriolis force involved with our parameters for the latitude at which the experiments were conducted according to classic calculations would be 4.32 × 10^{−}^{4} m・s^{−}^{2}. The energy associated with the mass of an electron (9.11 × 10^{−}^{31} kg) for this acceleration spread along the circumference of the toroid (0.8 m) would be ~3.15 × 10^{−}^{34} J. This is remarkably similar to the energy from a unit frequency for Planck’s constant (6.626 × 10^{−}^{34} J・s), again reiterating the potential significance of the phenomena associated with electrons in this process. It is relevant that the energy equivalence of the mass of an electron multiplied by the square of the fine-structure velocity for a Bohr magneton when multiplied by the time required to complete one orbit is effectively Planck’s constant.

Movement in a circle is uniquely interesting because the process would always be accelerating (m・s^{−}^{2}) and a changing rate of this acceleration (m・s^{−}^{3}) often referenced as a “jerks”, would be a second derivative containing the potential temporal non-continuities that could encourage the conditions we assume may be associated with the observed excess correlations. They could spread over the Minkowski four-dimensional field [

We suspect that these “jerks” or “sputters” could be coupled to the rotation (angular momentum) of the Earth. Minute but measureable changes in angular momentum or the terrestrial spin have been detected over durations of days or months. Eubanks et al. [^{−}^{1} and when divided by 9.8 m・s^{−}^{2} would involve a more or less fixed interval of 43 s. This value is within the range of the “retro-occurrence” of the decrease in the east-west component of the static magnetic field inside of the toroid during the excess correlation protocol. The concept of specious present, if valid, would predict that the functional increment of time (Δt) associated with the observation of phenomenon within a relativistic framework could change such that the “future” of one framework could become the “present” of another. When the perceptual Δt is expanded significantly from that of the reference Δt events that appear serial and causal in the smaller temporal window may appear to be simultaneous and superimposed within the wider temporal frame.

We are pursuing the possibility that the excess correlation between two loci at non-traditional distances for photon emissions from chemical reactions, cells, and brain activity when the technology described in this paper has been employed involves a narrow range of energies where geomagnetic activity and gravitational processes interact. According to dimensional analysis the product of G (m^{3}・kg^{−}^{1}・s^{−}^{2}), magnetic field intensity (kg・A^{−}^{1}・s^{−}^{2}) and unit charge (A・s) would be a cubed velocity term. With actual values for ΔG, that is 3 × 10^{−}^{3} of 6.67 × 10^{−}^{11} m^{3}・kg^{−}^{1}・s^{−}^{2}, 10^{−}^{9} T, and 1.6 × 10^{−}^{19} A・s, the real value is 32 × 10^{−}^{42} m^{3}・s^{−}^{3} or 3.16 × 10^{−}^{14} m・s^{−}^{1}. The frequency associated with the radius of classic electron, 2.82 × 10^{−}^{15} m, would be ~11 Hz. This is precisely within the range of the second harmonic of Schumann resonance [

Researchers in our laboratory have been designing experiments and testing various configurations of magnetic fields within circular arrays in order to discern potentially the parameters by which excess correlation might occur. We have been pursuing the potential validity of Mach’s principle of “prominence of the universe” [^{2}, 4/3πr^{3} and 2πrf, or 21.3π^{4}r^{7}s^{−}^{1}. By applying dimensional analysis to obtain a similar aggregate based upon universal values they found:

where G was the gravitational constant (m^{3}・kg^{−}^{1}・s^{−}^{2}) mass was the estimated mass [^{23} m・s^{−}^{1}. This velocity, if it reflected “entanglement” latency, should be reflected in the dragging of inertial frames such as those noted in satellite orbits. The predicted temporal value for this drag for the orbit of a satellite was within the same order of magnitude and coefficient (10^{−}^{16} s) as that measured directly and derived from more complex mathematical models [

The time required for such entanglement to occur around the circumference of the Earth (4 × 10^{7} m) would be that value divided by the entanglement velocity or 2 × 10^{−}^{16} s. When applied to the diffusion velocity of a charge within the variations of G and 1 nT geomagnetic variation as noted previously, that is 1.7 × 10^{−}^{14} m・s^{−}^{1}, the distance would be 3.4 × 10^{−}^{30} m. This value is about 2.1 × 10^{5} more than Planck’s length (1.6 × 10^{−}^{35} m). The potential significance of this value becomes apparent when the expansion time for an electron is incorporated. Persinger and Koren [^{22} m) or 2.3 × 10^{−}^{18} s^{−}^{1}, the length (twice the radius, 4.86 × 10^{−}^{15} m) of an electron would have a velocity of 11.66 × 10^{−}^{33} m・s^{−}^{1}. When divided into Planck’s length (1.6 × 10^{−}^{35} m), the time required would be 1.1 ms. There is now experimental evidence that the supports this solution for the electron and the proton [

With this assumption the time required to expand 2.1 × 10^{5} of that value would about 4 to 5 min. A range in this duration would be expected given the significant standard deviation for the actual Hubble parameter which is not a fixed value. The 4 to 5 min duration is within the range of the “entanglement time” noted in our excess correlations for shifts in pH of water when employing the equipment reported in this paper and the displacement of the Y-axis of 1 nT of the magnetic field within the toroid but only during the excess correlation protocol. If this explanation is valid then the “time limited” excess correlations and the anomalous diminishment of intensity of the east-west magnetic component within the toroid during the specific sequence of changing angular velocities (interacting with the earth’s angular momentum at the electron level) would reflect the dynamics of this “expansion time”. We suggest there is a moderate probability that the consistency of quantification could relate Planck-level phenomena to the macrolevel we have measured in the laboratory.

The data indicated a temporally non-linear effect within the toroid space which was exclusive to the excess correlation field presentation sequence. Quantitative solutions converged upon the hydrogen line as a standing wave source which might be accessed for practical use in entanglement. Coriolis-like forces present a relativistic approach to excess correlation phenomena, where the local space is affected by planetary rotation. An approximate mechanism is presented which relates physical parameters of the electron to fundamental processes at quantum and universal scales of discourse.

The authors would like to thank Trevor Carniello for his insights.