Casimir Plates and Time Dilation Between Casimir Plates, the speed of light has been proposed to be faster than the speed of light in normal space.  This hypothetical effect is called the Scharnhorst Effect.
Scharnhorst Effect Wikipedia 

The Scharnhorst effect is a hypothetical phenomenon in which light signals travel slightly faster than $c$ between two closely spaced conducting plates. It was predicted by Klaus Scharnhorst & Gabriel Barton . They showed using quantum electrodynamics that the effective refractive index, at low frequencies, in the space between the plates was less than 1 (which by itself does not imply superluminal signaling). They were not able to show that the wavefront velocity exceeds c (which would imply superluminal signaling) but argued that it is plausible.

So a clock that was based on a light beam bouncing between mirrors, if that clock was placed in that region would run faster than normal. Does this mean that all clocks would run faster in this region?  
For instance, would a muon decay faster in the region between Casimir plates, than it normally would in a typical vacuum? 
Edit: I haven't seen any discussion of this idea in the literature when I looked around.  Any ideas?
 A: In the wiki link you give:

Owing to the Dirac sea, an empty space which appears to be a true vacuum is actually filled with virtual subatomic particles. These are called vacuum fluctuations. As a photon travels through a vacuum it interacts with these virtual particles, and is absorbed by them to give rise to a virtual electron–positron pair. This pair is unstable, and quickly annihilates to produce a photon like the one which was previously absorbed. The time the photon's energy spends as subluminal electron–positron pairs lowers the observed speed of light in a vacuum.

These vacuum fluctuations are the ones that give rise to the Lamb shift, a measurable effect.
This tells us the following: the speed of light we can measure in vacuum will be less than c, the speed coming from the classical electromagnetic field , because of the vacuum fluctuation corrections.
The velocity of light in vacuum classically given by Maxwell's equation  c2 = 1/(ε0μ0) will then be measured as less due to these fluctuations.
Going to the Scharnhorst effect, the modified vacuum between two charged plates, as the differences are calculated to be very small, 

A photon travelling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 10^36.

As the only comparison can be with the photon in the free vacuum, which also will be traveling at the limit allowed by the loop corrections of the free vacuum, there does not seem to be any reason to accept "faster than light"  photons. The observation is that the "vacuum" between the plates is closer to the vacuum of the classical electromagnetic theory than the one in the vacuum. After all in classical theory there is phase velocity and group velocity for light, and phase velocity can be faster than c, (in wave guides for example, for the same reasons as argued for the Scharnhorst effect) but cannot be used for signaling.

So a clock that was based on a light beam bouncing between mirrors, if that clock was placed in that region would run faster than normal. Does this mean that all clocks would run faster in this region? 

Note the smallness of the distance between the plates, what clock and what mirrors, what region?
If one goes to such details, for  an atomic clock for example between casimir plates, one would have to solve a different QED problem , including vacuum loops with respect to the atomic clock .
A: Stochastic Electro-Dynamics Physics is based on Planck's later work, rather than his preliminary paper.  Using that model in lieu of QED, we find that ZPE is the primary limiting factor in the speed of light. Apparently the Casimir effect reduces the ZPE between the two metal plates, hence light can be experimentally shown to move faster there.  However, so far it does not seem possible to create larger voids in the ZPE.
