Electrostatics Gravistatics Like charges repel Like planckion masses repel and attract, Unlike charges attract Unlike planckion masses attract and repel, indirectly Fluid forces acting on each species, the positive, and the negative mass planckions $\stackrel{\to }{E}=\stackrel{\to }{{E}^{\left(0\right)}}-\stackrel{\to }{{E}^{\left(1\right)}}$ $\stackrel{\to }{g}=\stackrel{\to }{{g}^{\left(0\right)}}+\stackrel{\to }{{g}^{\left(1\right)}}$ $=\left(K-\chi \right)\stackrel{\to }{E}$ $=\left(K+\chi \right)\stackrel{\to }{g}$ $\stackrel{\to }{E}=\stackrel{\to }{{E}^{\left(0\right)}}/K<\stackrel{\to }{{E}^{\left(0\right)}}$ (screening) $\stackrel{\to }{g}=\stackrel{\to }{{g}^{\left(0\right)}}/K>\stackrel{\to }{{g}^{\left(0\right)}}$ (anti-screening) $\stackrel{\to }{P}={\epsilon }_{0}\chi \stackrel{\to }{E}={\epsilon }_{0}\stackrel{\to }{{E}^{\left(1\right)}}$ $\stackrel{\to }{P}={\epsilon }_{0}\chi \stackrel{\to }{g}={\epsilon }_{0}\stackrel{\to }{{g}^{\left(1\right)}}$ $k=1/\left(4\pi {\epsilon }_{0}\right)=8.99\text{E}9\left(\text{MKS}\right)$ ${G}_{0}=1/\left(4\pi {\epsilon }_{0}\right)=6.67\text{E}-11\left(\text{MKS}\right)$ $\stackrel{\to }{\nabla }\cdot \stackrel{\to }{P}={\rho }_{B}$ $-\stackrel{\to }{\nabla }\cdot \stackrel{\to }{P}={\rho }_{B}$ $\oint \stackrel{\to }{P}\cdot \stackrel{\to }{\text{d}A}={Q}_{B}$ $-\oint \stackrel{\to }{P}\cdot \stackrel{\to }{\text{d}A}={M}_{B}$ $\stackrel{\to }{D}={\epsilon }_{0}K\stackrel{\to }{E}={\epsilon }_{0}\stackrel{\to }{{E}^{\left(0\right)}}$ $\stackrel{\to }{D}={\epsilon }_{0}K\stackrel{\to }{g}={\epsilon }_{0}\stackrel{\to }{{g}^{\left(0\right)}}$ $\stackrel{\to }{\nabla }\cdot \stackrel{\to }{D}={\rho }_{F}$ $-\stackrel{\to }{\nabla }\cdot \stackrel{\to }{D}={\rho }_{F}$ $\oint \stackrel{\to }{D}\cdot \stackrel{\to }{\text{d}A}={Q}_{F}$ $-\oint \stackrel{\to }{D}\cdot \stackrel{\to }{\text{d}A}={M}_{F}$ $\stackrel{\to }{\nabla }\cdot \left({\epsilon }_{0}\stackrel{\to }{E}\right)={\rho }_{F}-{\rho }_{B}$ $-\stackrel{\to }{\nabla }\cdot \left({\epsilon }_{0}\stackrel{\to }{g}\right)={\rho }_{F}+{\rho }_{B}$ $\oint \left({\epsilon }_{0}\stackrel{\to }{E}\right)\cdot \stackrel{\to }{\text{d}A}={Q}_{F}-{Q}_{B}$ $-\oint \left({\epsilon }_{0}\stackrel{\to }{g}\right)\cdot \stackrel{\to }{\text{d}A}={M}_{F}+{M}_{B}$ $\stackrel{\to }{E}=\stackrel{\to }{{E}^{\left(0\right)}}-\stackrel{\to }{{E}^{\left(1\right)}}$ $\stackrel{\to }{g}=\stackrel{\to }{{g}^{\left(0\right)}}+\stackrel{\to }{{g}^{\left(1\right)}}$ can be written as, can be written as, $\left({\epsilon }_{0}\stackrel{\to }{E}\right)=\stackrel{\to }{D}-\stackrel{\to }{P}$ $\left({\epsilon }_{0}\stackrel{\to }{g}\right)=\stackrel{\to }{D}+\stackrel{\to }{P}$ $\stackrel{\to }{D}$ = electric displacement field $\stackrel{\to }{D}$ = gravitational displacement field $Q={Q}_{TOTAL}={Q}_{F}-{Q}_{B}$ $M={M}_{TOTAL}={M}_{F}+{M}_{B}$ $\rho ={\rho }_{TOTAL}={\rho }_{F}-{\rho }_{B}$ $\rho ={\rho }_{TOTAL}={\rho }_{F}+{\rho }_{B}$