Gravitation of vacuum fluctuations in three regimes: The effect on measurement of the Newtonian gravitational constant
Résumé
There are perhaps four primary observational uncertainties that question the foundations cosmology, known as: the Hubble tension, dark matter, dark energy, and the predictive phenomenology of modified Newtonian dynamics (MOND). While available empirical evidence corroborates general relativity, precise measurement of the Newtonian gravitational constant and a complete theory of quantum gravity remain elusive. We assume firstly that the equivalence principle applies identically to matter and anti-matter vacuum fluctuations. Secondly, that on a sufficiently large scale in vacuum, the mass density of fluctuations is isotropic everywhere. From isotropy it follows at large scale the resultant gravitational field of vacuum fluctuations is zero. On addition of attracting mass matter and anti-matter fluctuations accelerate and are displaced identically. Gravitational displacement of the vacuum induces a small resultant mass and energy density - without assuming gravitational vacuum polarisation. Given conservation of gravitational four-momentum vacuum fluctuations form a virtual fluid at large scale. From a model relativistic Lagrangian density only gravitational displacement orthogonal to the directional of fluid flow are effective. Thus, the resultant vacuum effect is reduced in the Solar System and can possibly explain large discrepancies in measurement of the Newtonian gravitational constant on Earth. The resultant gravitational potential energy density of vacuum fluctuations yield a cosmological constant $\Lambda \gtrsim 10^{-54} \text{m}^{-2}$, two orders of magnitude less than the observed value. The value of $G$ corrected for the gravitational vacuum effect is $6.67\;419 \cdot 10^{-11}\text{m}^3\text{kg}^{-1}\text{s}^{-2}$ with a relative standard deviation of $15.0$ ppm, reduced from $87.9$ ppm as shown in Figure 1.
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