As one knows, strong discrepancies are found between the different precise measurements of the gravitational constant carried out in Earth-based laboratories. While the precision is increasing in different laboratories and with various methods, these measurements are even more and more discordant. We have shown since 2002 that an improved 5D Kaluza-Klein (KK) theory may provide a satisfactory explanation to these discrepancies by referring to the geomagnetic field as a possible cause. Here we take advantage of different precise measurements performed on the same location but at different epoch to address the temporal variation of the gravitational constant measurements. It turns out that taking into account the secular variation of the geomagnetic potential introduces a greater consistency into the apparent lack of concordance amongst the most precise gravitational constant measurements. Indeed, we obtain results that are in good agreement with all laboratory measurements. Moreover, this study yields an independent way to derive the coupling constant of the internal 5D KK scalar field to the electromagnetic field, namely, F⁻¹ = (3.25 ± 0.35) × 10⁻¹⁴ m/J, which matches quite well with the earlier one, F^-1 = (3.40 ± 0.41) × 10⁻¹⁴ m/J.

中文翻译：

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基于地球的引力常数测量值的时间变化

众所周知，在地球实验室进行的引力常数的不同精确测量之间存在很大差异。尽管在不同的实验室中使用各种方法提高精度，但这些测量却越来越不一致。自2002年以来，我们已经证明，改进的5D Kaluza-Klein（KK）理论可以通过将地磁场作为可能的原因来为这些差异提供令人满意的解释。在这里，我们利用在相同位置但在不同历元执行的不同精确测量来解决重力常数测量的时间变化。结果表明，考虑到地磁势的长期变化，在最精确的引力常数测量之间明显缺乏一致性的情况下，引入了更大的一致性。实际上，我们获得的结果与所有实验室测量结果都非常吻合。此外，这项研究提供了一种独立的方法来推导内部5D KK标量场与电磁场的耦合常数，即F ^-1 =（3.25±0.35）×10 ^-14 m / J，与早期的F ^-1 =（3.40±0.41）×10 ^-14 m / J非常匹配。