Derive u from v with Lorentz Transform

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SUMMARY

The discussion focuses on deriving the velocity u from the velocity v using the Lorentz transformation equation: u = (u - v) / (1 - vu/c²). Participants emphasize the importance of differentiating with respect to proper time to maintain Lorentz invariance. The distinction between u-time in the observed frame and v-time in the reference frame is crucial for accurate calculations. Understanding these concepts is essential for applying the Lorentz transformation correctly in relativistic physics.

PREREQUISITES
  • Understanding of Lorentz transformation equations
  • Familiarity with the concept of proper time in relativity
  • Basic knowledge of calculus, specifically differentiation
  • Awareness of relativistic velocity addition
NEXT STEPS
  • Study the derivation of the Lorentz transformation equations
  • Learn about proper time and its significance in relativity
  • Explore relativistic velocity addition and its implications
  • Practice differentiating functions involving Lorentz transformations
USEFUL FOR

Physicists, students of relativity, and anyone interested in understanding the mathematical foundations of Lorentz transformations and their applications in relativistic physics.

mntb
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derivating a from v (lorentz transform)
u is the velocity in the +x direction
u=(u-v)/(1-vu/c^2)
du? how do you du the right side of the eq? :confused:
 
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mntb said:
derivating a from v (lorentz transform)
u is the velocity in the +x direction
u=(u-v)/(1-vu/c^2)
du? how do you du the right side of the eq? :confused:

What are you taking the derivative with respect to? Note that the u-time in the observed frame is not the same as the v-time in the reference frame. If you want your derivative to be Lorentz invariant you have to differentiate with respect to proper time.
 

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