Speed of light maybe not constant after all!:

Originally posted by KazetNagorra
I don't know how far you want to delve into quantum mechanics, but as an undergrad we used Griffiths' book Introduction to Quantum Mechanics. If you really want to get some intuition into quantum mechanical concepts, it's a good place to start. You would need some basic calculus and knowledge of simple differential equations to handle it.

I am currently watching Richard Feynman QED Lectures off youtube. Very interesting without any real maths required. I will consider getting a proper book on the subject at a later date as it is very interesting.
It does show how terribly out dated our school system is. Quantum mechanics has been the centre of physics for about 80 years (according to the lecture) yet I went up to A level physics without once learning any quantum mechanics. Everything I know of it I learn't outside school.

According to Feynman, photons can travel at all possible speeds. The 'speed of light' is just the most probable.