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Old Jan 12th 2011, 01:05 PM   #1
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Casimir force and negative pressure

Vacuum with a constant energy density d_vac exerts a negative presure p_vac = - d_vac cē.

Between the plates of a Casimir experiment the energy density is less than d_vac, say d_cas < d_vac.

Thus, the pressure that is exerted by vacuum between the plates should be p_cas = - d_cas cē > d_vac cē = p_vac.

This means that p_cas > p_vac, the pressure between is plates is greater than the pressure outside.

The force between the plates should be repulsive.

The Casimir force is however attractive. Where is the mistake in my argument?
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Old Jan 17th 2011, 02:54 PM   #2
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I guess I found the answer by myself. The fact that p_vac = - d_cas cē, is related to the Lorentz invariance of vacuum. See http://www.astro.ucla.edu/~wright/Pvac_details.gif. However, inside the Casimir plates Lorentz invariance does not apply and therefore p_cas is unequal to - d_cas cē. Probably (I do not know however how to proceed to show it) p_cas < - d_cas cē, so that p_cas < p_vac and the force is therefore attractive.
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Old Jan 12th 2012, 01:06 AM   #3
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check for the magnitude of the pressure difference between the two regions i'e insi.

Originally Posted by tholan View Post
Vacuum with a constant energy density d_vac exerts a negative presure p_vac = - d_vac cē.

Between the plates of a Casimir experiment the energy density is less than d_vac, say d_cas < d_vac.

Thus, the pressure that is exerted by vacuum between the plates should be p_cas = - d_cas cē > d_vac cē = p_vac.

This means that p_cas > p_vac, the pressure between is plates is greater than the pressure outside.

The force between the plates should be repulsive.

The Casimir force is however attractive. Where is the mistake in my argument?
check for the magnitude of the pressure difference between the two regions i'e inside and outside the plates.
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