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A motorist passes a red traffic-light (wavelength = 650 nm). The motorist’s velocity

makes an angle theta to the direction of light from the traffic light. Write down in four-

vector and matrix form the relationship between the four-momentum of a photon as

seen in the motorists’ rest frame, and as seen in the rest frame of the traffic light.

Using the above result or otherwise, assume that the motorist was travelling directly

towards the traffic-light, and is stopped by the police. The motorist tells the police-

officer that he observed the traffic-light as being green (wavelength = 500 nm). What

was the motorist’s speed as a fraction of the speed of light?

All i know is that the 4-vector for a photon is the same (px,py,pz,E/c) and that as the photon is massless, the magnitude is 0. However i am unsure if i am meant to be incorporating doppler shift into this ?

all help will be much appreciated!