Velocity Addition for Orthogonal Boosts in SR

In summary, the conversation discusses the search for a general formula to calculate the final velocity (w) resulting from a boost in the x direction followed by a boost in the y direction. The speaker is unsure which formula to use and questions whether the relativistic velocity addition formula (u+v)/(1+uv/c^2) applies. The responder states that this formula does not apply and suggests using different approaches depending on the individual's understanding of special relativity.
  • #1
tfhub
11
0
Hi,
is there any general formula to find out the final velocity w, happened by a boost in x direction forst and then to y direction?
I could find the boost matrices for both and I know it's not purely another boost, rather a boost and a rotation, but I am really confused which formula to use to find w.
does the relativistic velocity addition formula apply here ? (u+v)/(1+uv/c^2)?
 
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  • #2
No, it does not apply. It does not even have the correct low velocity limit.

There are some different ways of doing this, depending on your level of understanding. How much SR are you familiar with?
 

Related to Velocity Addition for Orthogonal Boosts in SR

1. What is velocity addition for orthogonal boosts in special relativity (SR)?

Velocity addition for orthogonal boosts in SR is a mathematical formula used to calculate the resulting velocity of an object when it undergoes multiple boosts in different directions. It takes into account the principles of special relativity, such as time dilation and length contraction, to accurately determine the final velocity.

2. Why is velocity addition for orthogonal boosts important in special relativity?

In special relativity, the laws of physics should be the same for all observers, regardless of their relative motion. Velocity addition for orthogonal boosts allows us to accurately predict the behavior of objects in different frames of reference, ensuring that the laws of physics remain consistent in all scenarios.

3. How is velocity addition for orthogonal boosts different from classical velocity addition?

In classical physics, velocities are simply added together, regardless of the direction of the boosts. However, in special relativity, the combined velocity is not simply the sum of the individual velocities. The formula for velocity addition for orthogonal boosts takes into account the relativistic effects of time and space, resulting in a different calculation.

4. Can velocity addition for orthogonal boosts be applied to any type of motion?

Yes, velocity addition for orthogonal boosts can be applied to any type of motion, as long as it follows the principles of special relativity. This includes both linear and circular motion, as well as motion in different directions.

5. How can velocity addition for orthogonal boosts be visualized?

Velocity addition for orthogonal boosts can be visualized using a spacetime diagram, which shows the relationship between time and space in different reference frames. This diagram can help illustrate the effects of velocity addition on an object's trajectory and velocity. There are also numerous online simulators and animations available to help visualize this concept.

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