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Velocity Transform

Velocity Transform. Differential position:. Divide all elements by dt’. Velocity Transform (continued). Velocity is NOT a four-vector. Adding Velocities. Tom. Dick. v 0 = b c =.9 c. L. Harry. v 0 = b c =.9 c. Tom’s velocity to Harry:. Dick’s velocity to Tom:.

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Velocity Transform

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  1. Velocity Transform Differential position: Divide all elements by dt’

  2. Velocity Transform (continued) Velocity is NOT a four-vector

  3. Adding Velocities Tom Dick v0=bc=.9c L Harry v0=bc=.9c Tom’s velocity to Harry: Dick’s velocity to Tom: Dick’s velocity to Harry:

  4. Pion Decay Pion decays to two photons in its rest frame: g p g Photons move atv=c. In frame where pion is moving withv=.99c, what are photons velocities? Something moving at the speed of light, moves at the speed of light in all frames.

  5. Stellar Aberrations In stationary system: In moving system: q v

  6. Stellar Aberrations (continued) In stationary system: In moving system: q v0

  7. “Proper” Velocities Try to make velocity a four-vector Position in rest frame: Velocity in rest frame: Transform this into moving frame: “Proper” velocity is a four-vector

  8. “Proper” Velocity (continued) • Square of velocity is the same in all reference frames. • For any frame except the rest frame, proper time is a computed quantity. • Proper times are different for particles with different velocities. Conclusion: Proper velocity is not very useful! (But we will use it anyway when we talk about Lagrangians.)

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