Where s the moving train on the embankment?

[Grimble]

Yes.
Ok, you got the embankment right in the embankment's frame, and the train in the train's frame. Time and space in the embankment frame are called (t,x), in the train frame (t',x').
Now some hints for corrections. Please make sure you understand why it has to look different.
1. From the embankment' frame, the train moves to the right (+x). That means that the embankment moves to the left in the train's frame (-x).
2. The line C' must cross the line B at t=0 (they align when A meets A', as seen in the embankment frame).
2'. The line C must cross the line B' at t'=0 (they align when A meets A', as seen in the train frame).
(I hope you see that these are two different conditions, not contradicting each other.)
3. The speed is much closer to c than you've drawn it. Try to get the inclination of the lines right, this will become important.

Hello, and thank you for your help in this forum.

I have tried to make the changes you describe but I seem to be getting in a bit of a muddle with them
Here is what I have done so far, but I must be getting confused somewhere - Help!
http://img19.imageshack.us/img19/6204/spdiagfig1.jpg
http://img191.imageshack.us/img191/6783/spdiagfig2.jpg

Grimble

 

[DrGreg]

Not bad, but in Fig 2, the A' B' and C' lines should all be parallel to the ct axis, not the x axis. It might also help you to compare the two diagrams if you continued Fig 2 downwards below the x' axis to before the event where A meets C'.

 

[Al68]

What do you mean by frame dependent? It has a nice sound to it and it is a nice easy image but what does it mean? How is something frame dependent?

A quantity is frame dependent if its value depends on the reference frame used, like kinetic energy, or length in SR.

Something may have different values in different frames, with things like kinetic energy or doppler effects we know why and how that works and we know, in each case, it is the view that changes not the object viewed.

Exactly. An object's length in SR is frame dependent, meaning it has a different value in different reference frames, but the object doesn't "change" just because we choose a different frame resulting in a different length.

Like you said, the kinetic energy of an object doesn't "change" just because it will have a different value if we choose a different reference frame. Same goes for length in SR.

 

[Ich]

OK, Grimble,

factor in DrGreg's comments and you're done with drawing.
There's one important thing I suspect you didn't consider:
The space points A,B,C,A',B',C' are actually lines in the diagram. You seemed to label certain events (i.e. points in the spacetime diagram) with these letters.
Do you see how (and why) these points are represented by lines?
That their intersection with the x/x'-axis selects 5 different events (one common to both intersections), and that we're talking about these different events when we talk about length contraction?

You should have some questions now, as to what you're supposed to be doing here. Ask them, otherwise I don't know where you're stuck.

 

[Grimble]

Not bad, but in Fig 2, the A' B' and C' lines should all be parallel to the ct axis, not the x axis. It might also help you to compare the two diagrams if you continued Fig 2 downwards below the x' axis to before the event where A meets C'.

Like this?

http://img64.imageshack.us/img64/4666/28262050.jpg

Grimble

 

[DrGreg]

Like this?

Yes, that looks good to me except for one small but important detail. You have x and −x the wrong way round in Fig 2.

It's worth pointing out the two red lines on your two diagrams don't represent the same thing. The first goes from left to right, the second goes from right to left. If you wanted, you could draw both lines on both diagrams.

Is it all making sense now?

 

[Grimble]

Yes, that looks good to me except for one small but important detail. You have x and −x the wrong way round in Fig 2.

It's worth pointing out the two red lines on your two diagrams don't represent the same thing. The first goes from left to right, the second goes from right to left. If you wanted, you could draw both lines on both diagrams.

Is it all making sense now?

http://img109.imageshack.us/img109/2534/spacedgms.jpg

Thank you, DrGreg, for your assistence. I believe this is right now?

Grimble

 

[Ich]

Ok, two things:

- You included an old version of fig. 1.
- I realize that you still have the wrong inclination of worldlines and x/x'-axis.

In order to answer your original question, you must draw accurate diagrams, with v=0.866.
I could provide the correct diagrams, but I think that would be counterproductive. Try it yourself. Ask if you're getting stuck.