Rocket Sends Light to Mirror: Event A to Event C Diagram

[morrobay]

https://www.cockcroft.ac.uk/wp-content/uploads/2015/10/gratus_RelWorksheet.pdf

Refer to diagram at top page 8 showing light signal reflected (Event A) back to rocket (Event C) on t'.axis.
If the space axis x' were drawn showing the position of rocket when the light signal was returned from
Event A would that be a mirror image of the diagram ie The x' axis added with the light path going to right and intersecting x' axis ?

 

[PeterDonis]

Do you have a question?

 

[morrobay]

See edit

 

[PeterDonis]

If the space axis x' were drawn showing the position of rocket when the light signal was returned from
Event A

Huh? The "space axis" shows all events that happen at time zero. It does not show all events that happen at some particular position.

The diagram at the bottom of page 8 shows the space axis $x'$, i.e., the line containing all events that happen at $t' = 0$.

The x' axis added with the light path going to right and intersecting x' axis ?

I have no idea what you mean by this.

 

[morrobay]

See page two in context of adding x' axis to show position of rocket when light is reflected back Event.
That is what I want to see: Position of rocket when reflected light hits it Event

 

[PeterDonis]

position of rocket when light is reflected back Event.

Position of rocket when reflected light hits it Event

These are two different events. Which one are you interested in?

In the diagram at the top of page 8, there is an event labeled A. Is that the one you mean?

 

[morrobay]

Event A is light striking mirror. I am interested in showing the rockets position in a
spacetime diagram when the reflected light (from Event A ) strikes rocket

 

[Ibix]

That's event C, isn't it? Event B is the rocket emitting the light and C is it returning. Just drop a vertical line to the x-axis to find its spatial position. Or, in general, a line parallel to the t axis of whatever frame you are interested in.

 

[morrobay]

A vertical line from Event C to x-axis only shows rockets position in rest frame. I am interested in the position of rocket in moving frame. Refer to lower diagram on page 2 that shows event from moving frame.

 

[Ibix]

Then drop a line parallel to the t' axis ("the t axis of whatever frame you are interested in"), as I said.

Since it rather looks like the moving frame is the rocket's rest frame, the result is trivial: the origin.

 

[Ibix]

If you don't know how to do that in general, let S be the frame whose axes are perpendicular on the diagram, and S' be the frame of interest. Your event A happens at $(X',T')$ as measured in S'. The line you want to draw is $x'=X'\ \forall\ t'$. The Lorentz transforms tell you that in S this is $X'=\gamma(x-vt)$ which you can easily rearrange and plot on your diagram.

 

[morrobay]

OK thanks then this would look like Event A shown in lower diagram on page 2. That would correspond to Event A on upper diagram page 8

 

[Ibix]

More or less. The lines you drop from any event will be parallel to the dashed lines in the diagram as long as you are interested in observer 2's rest frame, yes.