I'm currently reading DF Lawden's book Introduction to Tensor

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Discussion Overview

The discussion revolves around the concepts presented in DF Lawden's book "Introduction to Tensor Calculus, Relativity and Cosmology," specifically focusing on the translation of inertial frames and the implications of using Minkowski's time coordinate in Lorentz transformations. Participants explore the mathematical representation of velocities and the potential for singularities in this context.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that Lawden's use of Minkowski's time coordinate leads to an expression for inertial frames moving at velocity u = -ictan(alpha), suggesting a possible implication of singularities at certain points, such as tan(90).
  • Another participant asks for clarification on the definition of the angle alpha.
  • A response indicates that alpha is defined as an imaginary angle length according to Lawden.
  • Another participant reiterates the initial claim about the Lorentz transformation and adds that the singularities occur when the velocity v equals the speed of light, c.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the mathematical framework, particularly regarding the existence of singularities. There is no consensus on the interpretation of these singularities or their significance.

Contextual Notes

The discussion includes assumptions about the definitions of terms like rapidity and the conditions under which singularities may arise, which remain unresolved.

jbowers9
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I'm currently reading DF Lawden's book Introduction to Tensor Calculus, Relativity and Cosmology. He coverss the idea of translation of inertial frames in the beginning and by using Minkowski's device for the time coordinate, x4 = ict, shows that inertial frames moving at velocity u = -ictan(alpha) in a Lorentz transformation are offset by -ictan(alpha). Doesn't this imply that there are singularities at certain points, ie tan90? thank you.
 
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An imaginary angle length according to Lawden.
 


jbowers9 said:
I'm currently reading DF Lawden's book Introduction to Tensor Calculus, Relativity and Cosmology. He coverss the idea of translation of inertial frames in the beginning and by using Minkowski's device for the time coordinate, x4 = ict, shows that inertial frames moving at velocity u = -ictan(alpha) in a Lorentz transformation are offset by -ictan(alpha). Doesn't this imply that there are singularities at certain points, ie tan90? thank you.
alpha is the so called rapidity (e.g. see http://en.wikipedia.org/wiki/Lorentz_transformation" )
The singularities are for v=c
 
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