Thanks. I have in mind only the case of the standard arrangement.Eli Botkin said:A more general choice of the two coordinate frames' relative orientation and a more general relative velocity (rather than along a common X,X' axis) will not change the physics (what happens where and when). Time dilation and length contraction still appear. But the computations that show this will be more complicated.
Consider the standard arrangement of the involved inertial reference frames. The derivation of the LT starts with the transformation of the x(x') space coordinates and with the derivation of the time transformationEli Botkin said:In that case I don't understand what your question requires. Certainly not why the velocity is chosen along X, X' rather than Y, Y'. Please explain.
Are you asking why y=y'?bernhard.rothenstein said:Consider the standard arrangement of the involved inertial reference frames. The derivation of the LT starts with the transformation of the x(x') space coordinates and with the derivation of the time transformation
t=g(t'+Vx'/cc). Extending the problem to two space dimensions we add y=y' and derive the transformation of the Y(Y') component of the speed using the time transformation derived in the one space dimension approach considering that the time transformation is not affected by that.
Thanks for discussing with me the problem.
No.Meir Achuz said:Are you asking why y=y'?
Since Minkowski spacetime is an affine space it really does not matter how to describe parallel velocities. Any single direction or origin can be chosen.bernhard.rothenstein said:No.
What I am asking for is:
Starting from an one space dimension approach, textbooks derive the transformation for the x(x') and t(t') space and time coordinate . Going to two space dimensions it is stated that y=y' (a direct consequence of the principle of relativity) and in order to derive the transformation of the Y(Y') component of the velocity the time transformation derived in the case of one space dimension is used. Is there an explanation for that?
Because all events characterized by the same x coordinate are simultaneous? If so, should that fact be mentioned?
Regards
Velocity transformation is a mathematical concept used to describe how the velocity of a particle changes when observed from different reference frames. It takes into account the relative motion of the observer and the particle.
Velocity transformation is crucial in understanding particle motion because it allows us to accurately describe the movement of a particle from different perspectives. It helps us account for factors such as the observer's motion and the effects of relativity.
Velocity transformation is calculated using the Lorentz transformation equations, which take into account the speed of the observer and the speed of light. These equations are derived from Einstein's theory of special relativity.
Velocity transformation can be applied to any type of motion, as long as the motion is described using the principles of special relativity. It is commonly used in the field of particle physics, but can also be applied to everyday objects moving at high speeds.
Understanding velocity transformation allows scientists to accurately describe and predict the behavior of particles in motion. It is a crucial factor in many areas of research, such as particle accelerators, astrophysics, and quantum mechanics. It also helps to bridge the gap between classical and modern physics, leading to a deeper understanding of the universe.