Lorentz Transformation Rapidity

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SUMMARY

The discussion centers on the relationship between rapidity and the relative angle of two frames in the context of Lorentz Transformation. It establishes that if tanh(Fi) equals v/c, then the relative angle, denoted as theta, can be expressed as tan(theta) = tanh(Fi) = v/c. The participants clarify that the "relative angle" refers specifically to the mathematical connection between rapidity and the angles of two reference frames, emphasizing the importance of understanding this relationship in the framework of special relativity.

PREREQUISITES
  • Understanding of Lorentz Transformation principles
  • Familiarity with hyperbolic functions, specifically tanh
  • Basic knowledge of rapidity in special relativity
  • Concept of relative motion between reference frames
NEXT STEPS
  • Study the mathematical derivation of Lorentz Transformation
  • Explore the implications of rapidity in relativistic physics
  • Investigate hyperbolic trigonometry and its applications in physics
  • Learn about the geometric interpretation of special relativity
USEFUL FOR

Physicists, students of relativity, and anyone interested in the mathematical foundations of special relativity and the relationship between rapidity and relative motion.

parsikoo
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Concerning Rapidity, if tanh(Fi) = v/c, can it be concluded in general that the relative angle of two frames in combination with Lorentz Transformation is tan(theta) = tanh(Fi) = v/c, where theta is the relative angle?
 
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What do you mean by the "relative angle"?
 
Yes,
\theta_{21} = \theta_{20}-\theta_{10}.
 
Fredrik said:
What do you mean by the "relative angle"?

I meants relative angle of the frames.
 
parsikoo said:
I meants relative angle of the frames.
That's what you said but what does it mean?
 
Simply the math connection between rapidity and the angle of two frames, not sure if this is clear?
 

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