Robin,
When I say gas atoms see themselves as totally normal inside the cavity but time is accelerated inversely proportional to the cube of the spacing between Casimir plates I am simply applying a relativistic interpretation to the Casimir formula. That is to say the longer vacuum wavelengths are not suppressed between Casimir plates but rather space time transforms to allow the longer wavelengths to fit - As you pointed out the increase in energy density due to a large mass such as a black hole slows time (down shifting radiation) while a cavity suppresses energy density and therefore accelerates time from our perspective. In both cases it is based on equivalent acceleration but in the case of Casimir suppression it amplifies the rate at which it accumulates and then uses it as a reservoir to release abrupt negative acceleration (a ventori) where cavity geometry occurs between The plates. Since the energy density is even lower than the level outside the plates which accumulated the reservoir it is a negative energy density from our perspective. My premise is that the relativistic interpretation can escape the limits imposed by Liftshitz and others on Casimir plates through Lorentz contraction Of gas atoms inside the cavity. I think a Lorentz contracted gas atom can sidestep the fall off in Casimir force approaching a plate boundary and becomes even further contracted - allowing a scale down to Casimir dimensions that would appear to violate these limits from our perspective. A sort of Cascading effect where locally the gas atom still see the distance between the plates remaining near a maximum for Casimir force while from our perspective outside the cavity the atom could contract into cavities even smaller than an uncontracted atom without violating the limit from it's own local perspective. Regards Fran On Sat, 08 Jan 2011 14:39:22 -0800 mixtent said Where do you get this equation?
