Velocity Addition for Orthogonal Boosts in SR

Click For Summary
SUMMARY

The discussion centers on calculating the final velocity resulting from sequential boosts in orthogonal directions within the framework of Special Relativity (SR). The user inquires about the appropriate formula to apply, specifically questioning the applicability of the relativistic velocity addition formula, (u+v)/(1+uv/c^2). It is established that this formula is not suitable for the scenario described, as it fails to yield the correct low-velocity limit. The conversation highlights the need for understanding the relationship between boosts and rotations in SR.

PREREQUISITES
  • Understanding of Special Relativity (SR) principles
  • Familiarity with Lorentz transformations
  • Knowledge of boost matrices in SR
  • Basic concepts of rotational transformations in physics
NEXT STEPS
  • Study the derivation of the relativistic velocity addition formula
  • Explore the mathematical framework of Lorentz transformations
  • Investigate the relationship between boosts and rotations in Special Relativity
  • Learn about the implications of non-linear velocity addition in relativistic contexts
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in advanced concepts of Special Relativity and relativistic kinematics.

tfhub
Messages
9
Reaction score
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)?
 
Physics news on Phys.org
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?
 

Similar threads

Graduate Show Lagrangian is invariant under a Lorentz transformation without using generators
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Applying Velocity Addition in Rotating Frame: Is It Correct?
  • · Replies 18 ·
Replies
18
Views
2K
Graduate Relativistic Relative Velocity Comp.: Bini, D. et al. (1995)
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Gravitational Field Transformations Under Boosted Velocity
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Only Minkowski or Galilei from Commutative Velocity Composition
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why is the Lorentz Force always perpendicular to velocity?
  • · Replies 54 ·
2
Replies
54
Views
3K
Undergrad How do angular displacement and rapidity relate in special relativity?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Lorentz Boosts: Finding Speed, Coordinates & Rotation w/ Matrix Multiply
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Applying General Lorentz Boost to Multipartite Quantum State
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What assumptions underly the Lorentz transformation?
  • · Replies 120 ·
5
Replies
120
Views
10K