Help: Lorentz transform for angles

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Discussion Overview

The discussion revolves around the Lorentz transformation of angles between two reference frames, specifically focusing on how angles and their trigonometric functions transform under special relativity. Participants explore the mathematical relationships and seek specific formulae to aid in calculations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests assistance in finding the Lorentz transform for angles from a primed to an unprimed system.
  • Another participant suggests considering a right triangle to define the tangent of the angle in the context of the transformation.
  • A participant mentions existing formulae that relate sine and tangent functions, indicating a desire for these specific transformations.
  • One participant challenges the need for transformations of trigonometric functions, arguing that the focus should be on the angle itself rather than its trigonometric representations.
  • Another participant expresses frustration at perceived condescension and reiterates the usefulness of having simple formulae for trigonometric transformations to simplify calculations.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and relevance of transforming trigonometric functions versus focusing solely on the angle transformation. There is no consensus on the best approach or the importance of specific formulae.

Contextual Notes

Some participants reference specific transformations, such as tan(theta) transforming to (1/gamma)*tan(theta'), but the discussion lacks clarity on the complete set of transformations for sine and cosine functions. The need for additional assumptions or definitions is implied but not explicitly stated.

Who May Find This Useful

This discussion may be useful for students or researchers interested in the mathematical aspects of special relativity, particularly those looking for insights into the transformation of angles and trigonometric functions in different reference frames.

Lorentzf
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Hi everybody,
I would need to find the lorentz transform for angles from primed to unprimed system. Could someone help fast?

Thanks a bunch, best,

Lorentzf
 
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Consider a right-triangle with legs:
x along the direction of motion and
y along a perpendicular direction.
Define tan (theta)=y/x in the frame of that triangle.
How do the legs transform?
 
Thanks, yes, that's what I do, but there are worked out formulae, with
sin(theta) as a function of tan(theta'/2) or something...
That's what I was looking for.

Thanks anyway, best,

Lorentzf
 
Lorentzf,

If you can't write the formula from the help that robphy gave, you don't deserve your username! ;-)
 
Dear all,
is this a place to help or to show off?
tan(theta)=(1/gamma)*tan(theta'), thanks a lot, I can see that, professors...
But there is a set of worked out, simple formulae also for the transformation of sinuses, cosinuses, etc. Of course I can do any calculation without, but they would be useful to simplify my life...

anyway,

Lorentzf
 
What use would it be to you knowing how the other "trigonometrical functions" would transform under a SLT...?You're interested in knowing how [itex]\theta[/itex] transforms,not [itex]\tan\theta,\sin\theta,\cos\theta,\arcsin\theta,\arccos\theta,...[/itex].

Daniel.
 
In order to simplify calculations...

Best wishes,

Lorentzf
 

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