Does a Photons Travel-Time decrease if it crosses a Dimension of less than Three?

[ranyart]

When a Photon travels at C, it is transversing a Three dimensional domain. In a Electromagnetic Domain, there are usually only two degree's of freedom, this translates to a Two-Dimensional Domain, do Photons travel through a reduced dimensional field at a 'Faster than light'? (when compared to the usual three-dimensional space, with 3-D matter obstructions).

[Terry Giblin]

Good question - I suppose it depends what you think a photon is?

[mathman]

Speed of light is usually interpreted as speed of light in a vacuum (no matter present). When photons travel through matter, they slow down. I don't see where dimension comes in.