Abstract

We consider, within the framework of an improved \(5D\) Kaluza-Klein theory (KK\(\psi\)), the set of twenty most precise values ever published of Earth-based gravitational constant measurements. We take into account the possibility of a jump discontinuity into the geomagnetic potential in connection with the spin crossover of the iron (III) complex ions migrating from the Earth’s outer core into the deep Earth mantle as well as the spin crossover of the copper (III) complex ions migrating downwards within either the Earth’s crust or deep in the Earth’s mantle. Moreover, it turns out that the boundary conditions assigned to both internal, \(\phi\), and external, \(\psi\), scalar fields are sensitive to the aforementioned jump discontinuity too. Again, the fits to the experimental data are found in good agreement with the predictions of the linearized KK\(\psi\) theory. An estimate around the vacuum expectation values \(\psi=v\) and \(\phi=1\) of the second derivatives \({\partial^{2}f_{\textrm{EM}}}/{\partial\phi^{2}}(v,1)\), \({\partial^{2}f_{\textrm{EM}}}/{\partial\phi\partial\psi}(v,1)\) and \({\partial^{2}f_{\textrm{EM}}}/{\partial\psi^{2}}(v,1)\) of the coupling function, \(f_{\textrm{EM}}(\psi,\phi)\), of the electromagnetic field (EM) with \(\psi\) and \(\phi\), is provided for the first time, thereby enabling the determination of the product \(v\times f_{\textrm{EM}}(v,\phi)\) and \(v\times f_{\textrm{EM}}(\psi,1)\) in the second-order approximation from the experimental data.

中文翻译：

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实验室测量得出有效引力常数的证据

摘要

我们在改进的\（5D \） Kaluza-Klein理论（KK \（\ psi \））的框架内考虑二十个最精确的基于地球的重力常数测量值的集合。我们考虑到与铁（III）离子从地球外核迁移到深层地幔的自旋交叉以及铜（III）的自旋交叉相关的地磁势跃变不连续的可能性）复杂的离子在地壳内或地幔深处向下迁移。而且，事实证明，边界条件同时分配给内部\（\ phi \）和外部\（\ psi \），标量场也对上述跳跃不连续性敏感。再次，发现对实验数据的拟合与线性化KK \（\ psi \）理论的预测非常吻合。二阶导数\（{\ partial ^ {2} f _ {\ textrm {EM}}} // {\ partial的真空期望值\（\ psi = v \）和\（\ phi = 1 \）附近的估计\ phi ^ {2}}（v，1）\），\（{\ partial ^ {2} f _ {\ textrm {EM}}} // {\ partial \ phi \ partial \ psi}（v，1）\ ）和\（{\局部^ {2} F到_ {\ TEXTRM {EM}}} / {\局部\ PSI ^ {2}}（v，1）\）的偶联功能，\（F _ {\ TEXTRM { EM}}（\ psi，\ phi）\）的电磁场（EM），其中\（\ psi \）和\（\ phi \）首次提供，因此可以确定乘积\ {v \ times f _ {\ textrm {EM}}（v，\ phi）\）和\ {v \ times f _ {\ textrm {EM}} （\ psi，1）\）来自实验数据的二阶近似值。