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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?