Consider a photon of frequency vo v' emitted by a source at rest in frame K'. The photon is detected by an observer in frame K, where K and K' are related in the usual manner. (Note that this means that frame K' is moving either directly towards or away from K along the line of sight.) Derive the expression for the line-of-sight Doppler effect (i.e., for recession or approach only, not some arbitrary direction of motion) by considering the energy-momentum 4-vector of a photon, and requiring that it must transform from one inertial frame to another in the same way as any other 4-vector.

Consider a photon of frequency vo v' emitted by a source at rest in frame K'. The photon is detected by an observer in frame K, where K and K' are related in the usual manner. (Note that this means that frame K' is moving either directly towards or away from K along the line of sight.) Derive the expression for the line-of-sight Doppler effect (i.e., for recession or approach only, not some arbitrary direction of motion) by considering the energy-momentum 4-vector of a photon, and requiring that it must transform from one inertial frame to another in the same way as any other 4-vector.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter14: Special Theory Of Relativity

Section: Chapter Questions

Problem 14.41P

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