#### hellfire

Science Advisor

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The force is inversely proportional to the fourth power of the distance between the Casimir plates:JesseM said:So I wonder, can the energy density between plates in the casimir effect go below the vacuum energy density by significantly more than 10^-9 joules per cubic meter? Does anyone know the equation for calculating the energy density between plates in terms of their size and separation? I found a bunch of pages that give an equation for the force (see here, for example), but I'm not sure how to translate this into energy density.

[tex]F \sim \frac{hc}{d^4}[/tex]

You can consider the energy as a negative work done by the vacuum (W ~ F d):

[tex]\frac{F}{A} = \frac{E}{V} = \rho_{casimir} \sim - \frac{hc}{d^4}[/tex]

The cosmological term is about:

[tex]\rho_{\Lambda} \sim 10^{-120}[/tex]

In Planck units. Between the Casimir plates one has:

[tex]\rho \sim \rho_{\Lambda} - \frac{hc}{d^4}[/tex]

[tex]\rho \sim 10^{-120} - \frac{1}{d^4}[/tex]

Therefore d must be less than 10

^{30}Planck lengths (10

^{-5}meters) to have a negative energy density for gravitational purposes. With this estimation one would conclude that every Casimir experiment deals with negative energy densities, as usual distances are about 1 micrometer.

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