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Is There a Geomagnetic Component Involved with the Determination of G?

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Michael Persinger at Laurentian University
Michael Persinger
Linda St Pierre at Laurentian University
Linda St Pierre
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Abstract

We compared the small quantitative changes (range) in G over repeated measures (days) with recently improved methods of determinations and those recorded over 20 years ago. The range in the Newtonian constant of gravitation G is usually in the order of 400 ppm as reflected in experimentally-determined values. The moderate strength negative correlation between daily fluctuations in G, in the range of 3 × 10-3 of the average value, and an index of global geomagnetic activity reported by Vladimirsky and Bruns in 1998 was also found for the daily fluctuations in the angular deflection θ (in arcseconds) and geomagnetic activity within 24 hr for the Quinn et al. 2013 data. A temporal coupling between increases of geomagnetic activity in the order of 10-9 T with decreases in G in the order of 10-14 m3·kg-1·s-2 could suggest a recondite shared source of variance. The energy equivalence for this change in G and geomagnetic activity within 1 L of water is ~3 × 10-14 J.
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International Journal of Geosciences, 2014, 5, 450-452
Published Online April 2014 in SciRes. http://www.scirp.org/journal/ijg
http://dx.doi.org/10.4236/ijg.2014.54042
How to cite this paper: Persinger, M.A. and St-Pierre, L.S. (2014) Is There a Geomagnetic Component Involved with the
Determination of G? International Journal of Geosciences, 5, 450-452. http://dx.doi.org/10.4236/ijg.2014.54042
Is There a Geomagnetic Component
Involved with the Determination of G?
Michael A. Persinger, Linda S. St-Pierre
Laurentian University, Sudbury, Canada
Email: mpersinger@laurentian.ca, lx_stpierre@laurentian.ca
Received 27 February 2014; revised 25 March 2014; accepted 21 April 2014
Copyright © 2014 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
We compared the small quantitative changes (range) in G over repeated measures (days) with re-
cently improved methods of determinations and those recorded over 20 years ago. The range in
the Newtonian constant of gravitation G is usually in the order of 400 ppm as reflected in experi-
mentally-determined values. The moderate strength negative correlation between daily fluctua-
tions in G, in the range of 3 × 10−3 of the average value, and an index of global geomagnetic activity
reported by Vladimirsky and Bruns in 1998 was also found for the daily fluctuations in the angular
deflection θ (in arcseconds) and geomagnetic activity within 24 hr for the Quinn et al. 2013 data. A
temporal coupling between increases of geomagnetic activity in the order of 10−9 T with decreases
in G in the order of 10−14 m3·kg−1·s−2 could suggest a recondite shared source of variance. The
energy equivalence for this change in G and geomagnetic activity within 1 L of water is ~3 × 10−14 J.
Keywords
Gravitational Constant Variations, Geomagnetic Activity, Energy Convergence,
Electromagnetic-Gravitational Interactions
1. Introduction
The recent quantitative measurements by Quinn et al. [1] who employed two methods to estimate the Newtonian
gravitational constant G were remarkably congruent. The servo and free-deflection (torsion balance) or Caven-
dish methods yielded values of 6.67520 × 10−11 m3·kg−1·s−2 and 6.67566 × 10−11 m3·kg−1·s−2, respectively. The
difference in G between the two methods was 4.6 × 10−15 m3·kg−1·s−2 or ~70 ppm. The difference is within the
range of 10−4 which was considered by Vladimirskii [2] to be the boundary for accuracy to infer G with torsion
balances. Vladimirskii [2] and later Vladimirsky and Bruns [3] reported a source of variability that could ac-
count for the spread in G of ~400 ppm noted by Quinn et al. [1].
M. A. Persinger, L. S. St-Pierre
451
This source involved heliophysical perturbations as inferred by inferences of geomagnetic activity. Subtle
variations in G which are systematically and quantitatively related to alterations in geomagnetic activity could
be secondary to direct influences upon instrumentation [2] [3]. However if there is a third variable that is shared
by both variation in G and geomagnetic activity, it may have both theoretical and practical significance. Here we
indicate that two series of measurements from different localities, separated by more than two decades revealed
comparable magnitudes of negative correlations between daily subtle changes in G and ambient geomagnetic
activity.
2. Methods and Results
According to Figure 3 from [1] the means of the coefficients for G from 11 different sources range from 6.6725
to 6.6756 or ~3.1 × 10−3 of an average for G. This value is within error measurement variability of 5.2 × 10−3
reported [3] between days when the interplanetary magnetic field shifted from a positive to a negative sign and
geomagnetic Ap values ranged between −8 and +8 nT. In those previous measurements [2] between 29 August
and 23 December 1991, the mean value for the coefficient of G was 6.6728 for the 77 measurements during
which Ap values were <15 nT and 6.6675 during the 48 measurements during which the Ap values were >30 nT.
The difference in G, 5.3 × 10−3, is equivalent to 5.3 × 10−14 m3·kg−1·s−2. The Pearson correlation was calcu-
lated from Vladimirsky and Bruns’ data [3] between the different daily values of G and the Ap indices in their
Figure 1. For those 16 days the Pearson r coefficient was −0.50 (Spearman rho = −0.53, both, p < 0.05). To en-
sure daily specificity, the correlations between the two values with the lag or lead days were completed; they
were not significant statistically (all rs and rhos < |0.20|). Although the dispersion (Standard Error of the Esti-
mate) was substantial with such a weak correlation, the slope indicated that for every 0.01 decrease in G be-
tween 6.6840 and 6.6705, there was a 3.8 nT increase in Ap values.
For the Quinn et al. [1] data shown in Figure 2 from their paper the Pearson correlation between θ a−1·s−1 per
day (range = 31.542 to 31.549) and the Planetary A index (Sec) from http://www.dxlc.com/solar/indices.html
(range 2 to 23) during the previous 24 hr for the 10 days measured from 31 August to 11 September 2007 was
−0.70 (p < 0.05). The Spearman rho (−0.68, p < 0.05) was comparable indicating the effect was not due to out-
liers. Each of the 10 averages was based upon 34 values of angular deflection extracted from successive 30
minute (the limit where white noise dominated) data collections. Because G = τΓ−1 where τ = the measured tor-
que and Γ is (70 Mmr4·R−5) fixed by the method, an increase in θ = τc−1 (c is the stiffness of the suspension)
would imply an increase in G.
Lag/lead correlations for each day before and after the days in which these correlations were obtained were all
<|0.20|, that is not significant statistically, which is similar to the results found for Vladimirsky and Bruns. The
coefficient for the slope for the Quinn effect indicated that for every 0.001 θ a−1·s−1 decrease there was a 1.6 unit
increase in the Planetary A index. The quantitative proportion is similar to that obtained for [3].
3. Discussion
The z-score differences for the correlation coefficients for the negative associations between the inferences of
geomagnetic activity and G were not significant statistically for the Vladimirsky and Burns [3] and Quinn et al.
[1] results. Both were negative indicating a shared source of variance between the two qualities such that as the
intensities of G increase the intensities of geomagnetic background fluctuations decrease. Vladimirski [2] sug-
gested that “magnetoplasticity” from the low to ultra-low electromagnetic fields associated with geomagnetic
activity may have affected the elasticity parameters of the suspending thread of the torsion pendulums. He sug-
gested that such variables could explain the enigma of why the upper limit of accuracy for measurements of G
with torsion balances could not exceed 10−4. However a recondite quantitative equivalence between some quali-
ty of gravity and electromagnetic phenomena [4] could also be revealed.
Even a simplistic comparison of the energies associated with force suggests a shared convergence for 1 L
(10−3 m3) of water, perhaps the most relevant proportion of mass on the earth’s surface. The change of G of 3 ×
10−15 m3·kg−1·s−2 multiplied by (1 kg2/0.1m (10 cm)) is 3 × 10−14 J. On the other hand the energy represented
(B2/2μ) within this volume for a mean variation of ~8 nT from Vladimirsky and Burns’ [3] experiments also re-
sults in a value of ~3 × 10−14 J. Although there are insufficient data to conclude that they share the same source
of variance at this time, the similarity of quantitative values suggests that further examination of this possible
coupling is warranted.
M. A. Persinger, L. S. St-Pierre
452
Acknowledgements
Thanks to Dr. Blake T. Dotta and Viger Persinger for technical contributions.
References
[1] Quinn, T., Parks, H., Speake, C. and Davis, R. (2013) Improved Determination of G Using Two Methods. Physics Re-
view Letters, 111, 101102. http://dx.doi.org/10.1103/PhysRevLett.111.101102
[2] Vladimirskii, B.M. (1996) Measurements of the Gravitational Constant and Heliogeophysical Electromagnetic Pertur-
bations. Biophysics, 40, 915-923.
[3] Vladimirsky, B.M. and Bruns, A.V. (1998) Influence of the Sector Structure of the Interplanetary Magnetic Field on
the Results of Measurements of the Gravitational Constant. Biophysics, 43, 720-725.
[4] Persinger, M.A. (2012) Potential Origins of a Quantitative Equivalence between Gravity and Light. Open Astronomy
Journal, 5, 41-43. http://dx.doi.org/10.2174/1874381101205010041
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