Evidence for an Effective Gravitational Constant from the Laboratory Measurements

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.