Minkowski space time graphs

[geordief]

Suppose I am an observer and ,as such am situated at the [x,t]=[0,0] event point on a Minkowski chart.

 

Now there is an event that occurs in my FoR at ,let's call it [X,T] (I have not worked out how to write mathematical equations here yet)

 

I would like to reset the Frame of Reference to be from the point of view of (a new observer situated at) this new event which does not share an origin with the first observer's.How does this new FoR view the first observer's worldlines ?. Is that quite simple to do ? (the different observers are not necessarily stationary wrt one another)

 

 

I have a second related question. Are there any alternative methods of graphically ordering the set of space time events or is the Minkowski graphs the only game in town?

 

 

 

*I mean the worldlines of other bodies as seen by the first observer (including of course his own) -how does this new observer see them ? At a minimum how does the new observer see(on his spacetime graph ) the x=0,t=0 lines of the original observer?

 

 

PS any links on the internet that address this question would be very helpful.

Edited April 28, 2016 by geordief

[elfmotat]

If the new frame with its origin at the event [math](t,x)=(T,X)[/math] in the first frame is moving with velocity [math]v[/math] w.r.t. the first frame, then the new coordinates are given by:

 

[math]t' = \frac{t-T-v(x-X)/c^2}{\sqrt{1-v^2/c^2}}[/math]

 

[math]x' = \frac{x-X-v(t-T)}{\sqrt{1-v^2/c^2}}[/math]

 

If they are stationary w.r.t. each other then [math]v=0[/math] and this reduces to:

 

[math]t' = t-T[/math]

 

[math]x' = x-X[/math]

[geordief]

Thanks. And if, on the Minkowski map the new origin was at (t,x) =(T,X) do I just get the same scenario as it was from (t,x)=(0,0) except that now the signs are reversed and the first FoR is in the past -in the bottom left hand quadrant?

 

Assuming ,of course that (T,X) are both positive.

[Markus Hanke]

@geordief, you might like this interactive Minkowski diagram generator - it's great for playing around with various parameters in order to get a "feel" for what is going on :

 

http://www.trell.org/div/minkowski.html

[studiot]

 

@geordief, you might like this interactive Minkowski diagram generator - it's great for playing around with various parameters in order to get a "feel" for what is going on :

 

http://www.trell.org.../minkowski.html

 

 

Like the linked diagram, thanks. +1

 

This is a good reason to visit SF, to be told about good work that others have done and we did not know about before.

[geordief]

@geordief, you might like this interactive Minkowski diagram generator - it's great for playing around with various parameters in order to get a "feel" for what is going on :

 

http://www.trell.org/div/minkowski.html

Hm. I don't know about "great". It is making my head hurt .

 

Seriously, though it is very useful. I am working through it at a snail's pace and hopefully ironing out my misconceptions one by one.