According to Einstein, light travels the same no matter which frame of reference you have, so in the case of what you are talking about, that would actually make a lot of sense. Hence the warping of space the nearer one gets to the speed of light. In your scenario, it is time which warps space. Also, it may be that the light is attached to an additional dimension of space, or time, or something in between(!), and it may be this which is warping time AND three-dimensional space.
(Should I have posted that in pseudo-science? They certainly don't teach that in high school.)