Transforming Four Velocities with the Lambda Matrix

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SUMMARY

The discussion focuses on the transformation of four velocities in Special Relativity (SR) using the lambda matrix. It confirms that four velocities, represented as Lorentz vectors, transform similarly to four positions under Lorentz transformations. The participants emphasize the application of the Einstein velocity addition law and suggest practical exercises with specific four vectors, such as (c, 0, 0, 0) and (γc, γv, 0, 0), to illustrate these transformations.

PREREQUISITES
  • Understanding of Special Relativity (SR)
  • Familiarity with Lorentz transformations
  • Knowledge of Einstein velocity addition law
  • Basic concepts of four-vectors
NEXT STEPS
  • Explore the mathematical derivation of Lorentz transformations
  • Practice transforming various four-vectors using the lambda matrix
  • Study the implications of four-velocity transformations in relativistic physics
  • Investigate the relationship between four-velocities and spacetime diagrams
USEFUL FOR

Physicists, students of relativity, and anyone interested in the mathematical foundations of Special Relativity and four-dimensional spacetime concepts.

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In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?
 
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GarageDweller said:
In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?

They're Lorentz vectors, so they transform as vectors under a Lorentz transformation. I.e. yes.
 
GarageDweller said:
In SR, I know we transform three velocities using the einstein velocity addition law.
However, in the case of four velocities, do they simply transform the same way as four positions? With the lambda matrix?

Yes. Try transforming the 4 vector (c,0,0,0) and see what you get. Then try transforming the 4 vector (γc, γv, 0, 0) and see what you get.
 

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