The speed of light isn't constant. The speed of light through a certain material is constant, but the speed of light generally can vary massively.
The speed of light through a vacuum is believed to be the speed limit of the universe (i.e. the fastest you can go relative to space-time). However if a light photon goes from a vacuum into water, it will slow down. Scientists can even stop light momentarily: http://news.bbc.co.uk/1/hi/sci/tech/3308109.stm
No sure how this affects your question; I just wanted to point out the correction.
The speed of light through a vacuum is believed to be the speed limit of the universe (i.e. the fastest you can go relative to space-time). However if a light photon goes from a vacuum into water, it will slow down. Scientists can even stop light momentarily: http://news.bbc.co.uk/1/hi/sci/tech/3308109.stm
No sure how this affects your question; I just wanted to point out the correction.