Help: Lorentz transform for angles

In summary, Lorentzf is seeking help with finding the lorentz transform for angles from a primed to unprimed system. They are specifically looking for a set of formulae to transform trigonometric functions such as sine and cosine. Some users have provided helpful information, while others have questioned the usefulness of this knowledge.
  • #1
Lorentzf
4
0
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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  • #2
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?
 
  • #3
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
 
  • #4
Lorentzf,

If you can't write the formula from the help that robphy gave, you don't deserve your username! ;-)
 
  • #5
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
 
  • #6
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.
 
  • #7
In order to simplify calculations...

Best wishes,

Lorentzf
 

1. What is the Lorentz transform for angles?

The Lorentz transform for angles is a mathematical equation used in special relativity to calculate the difference in angles between two frames of reference moving relative to each other at high speeds.

2. How is the Lorentz transform for angles derived?

The Lorentz transform for angles is derived from the Lorentz transformation equations, which describe the relationship between space and time in special relativity. It is a result of the relativistic effects on angles due to the constant speed of light.

3. What is the significance of the Lorentz transform for angles?

The Lorentz transform for angles is significant because it helps us understand how angles are affected by the principles of special relativity, such as time dilation and length contraction. It allows us to accurately measure angles in different frames of reference and make predictions about how they will appear to observers moving at different speeds.

4. Can the Lorentz transform for angles be applied to any type of angle?

Yes, the Lorentz transform for angles can be applied to any type of angle, including 2D and 3D angles. It is a universal equation that takes into account the effects of special relativity on all types of angles.

5. How is the Lorentz transform for angles used in practical applications?

The Lorentz transform for angles is used in various practical applications, such as in particle accelerators and satellite navigation systems. It is also used in astronomy to measure the angles of celestial objects from different frames of reference. Additionally, it has applications in high-speed photography and in calculating the effects of motion on GPS signals.

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