Special Relativity Problem from Rindler

[Jason Williams]

Homework Statement

In the inertial frame $S'$ the standard lattice clocks all emit a 'flash' at noon. Prove that in $S$, this flash occurs on a plane orthogonal to the $x$-axis and traveling in the positive $x$-direction at speed $\frac{c^2}{v}$.

Homework Equations

Lorentz Transformations: $x' = \gamma(x-vt)$ and $t' = \gamma(t - \frac{vx}{c^2})$

The Attempt at a Solution

[/B]
The second part is relatively simple, set the flash to occur @ $t' = 0$ and then solve the corresponding Lorentz transformation equation to get $\frac{dx}{dt} = \frac{c^2}{v}$. The part I don't understand is show to show that it's orthogonal to the $x$-axis. I know you want to end up showing that $dx = 0$, I just can't manage to manipulate the Lorentz equations to get it in that form.

 

[MathematicalPhysicist]

Check my thread:
https://www.physicsforums.com/threads/a-few-questions-from-introduction-to-sr-by-rindler.163445/

 

[PeroK]

Homework Statement

In the inertial frame $S'$ the standard lattice clocks all emit a 'flash' at noon. Prove that in $S$, this flash occurs on a plane orthogonal to the $x$-axis and traveling in the positive $x$-direction at speed $\frac{c^2}{v}$.

Homework Equations

Lorentz Transformations: $x' = \gamma(x-vt)$ and $t' = \gamma(t - \frac{vx}{c^2})$

The Attempt at a Solution

[/B]
The second part is relatively simple, set the flash to occur @ $t' = 0$ and then solve the corresponding Lorentz transformation equation to get $\frac{dx}{dt} = \frac{c^2}{v}$. The part I don't understand is show to show that it's orthogonal to the $x$-axis. I know you want to end up showing that $dx = 0$, I just can't manage to manipulate the Lorentz equations to get it in that form.

I think you are looking at orthogonal the wrong way. It simply means a plane defined by the x-coordinate (where the y and z coordinates can be anything). Those are are the planes orthogonal to the x-axis.