# Casimir effect - gravitational influence?

Regarding the Casimir effect, is gravitational attraction too weak in order to explain the attraction between the plates?

In terms of order of magnitude, as noted in the reference in the comment (or also https://physics.info/gravitation-extended/practice.shtml), the gravity field is proportional to $$\mathbf{g}\sim \rho l G$$, where $$l$$ is the thickness of the plates, $$\rho$$ is the density of the plates, and $$G$$ the gravity constant, so the force per unit area $$A$$ is $$F_G/A \sim G \rho^2 l^2$$.
Regarding Casimir force, the derivation (https://en.wikipedia.org/wiki/Casimir_effect) shows that $$F_C/A \sim 10^{-2} h c r^{-4}$$, with $$h$$ the Planck constant and $$c$$ the speed of light and $$r$$ the distance between the two plates.
If we compare them : $$\frac{F_C}{F_G}=\frac{10^{-2} h c r^{-4}}{ G \rho^2 l^2}$$. You can see when gravity becomes insignificant with respect to Casimir effect.
• Still, the zero point energy of the hypothetical graviton should be $\frac{h\omega} {2}$like that of a photon. Commented Dec 17, 2018 at 22:43