Let's say you're in a very fast car that can accelerate from zero to, eventually, 0.7c. I understand that as the car moves faster and faster, the driver will observe the light that hits him in the face to be of higher and higher frequency. This seems consistent with things becoming narrower in the direction of travel. But it seems inconsistent with things appearing to happen more slowly in time. According to Maxwell, the rate of change of the E field with respect to space must be equal and opposite to the rate of change of the B field with respect to time. So, the driver sees light of higher frequency as he goes faster, and thus greater rate of change of E with respect to space; therefore, I would expect him to also see a greater rate of change of B with respect to time. But if B is changing faster with respect to time, doesn't this contradict the idea that the observer sees things around him happening slower in time? What am I missing here?