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The Elements of Relativity$
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David M. Wittman

Print publication date: 2018

Print ISBN-13: 9780199658633

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780199658633.001.0001

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Doppler Effect and Velocity Addition Law

Doppler Effect and Velocity Addition Law

(p.105) 9 Doppler Effect and Velocity Addition Law
The Elements of Relativity

David M. Wittman

Oxford University Press

We now pivot from relationships between frames to look at the effect of motion on communications between specific observers.This will help us look at the twin paradox in the next chapter, and will prove crucial to understanding the effects of gravity on time. Along the way, we develop an understanding of the Doppler effect; a key tool in many areas of modern science. We find that Doppler effects are reciprocal (Alice observes the same effect on Bob’s signals as Bob observes on Alice’s signals) and that Doppler effects compound over multiple frame changes. We then use the compounding of Doppler effects to deduce the algebraic formof the velocity addition law. We show that this Einstein velocity addition law reduces to the Galilean law at low speeds.

Keywords:   Doppler effect, velocity addition, reciprocity, time dilation, special relativity

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