# Space-Time diagram

1. Sep 25, 2008

### Ylle

Hello...

I have a little problem I hope you guys can help me with.
I'll write down the problem-text first, so it will be easier to point out the problem - hopefully.

Here it goes:
Event E0 has the following coordinates in some frame S:

x = 2 m
ct = 4 m

Locate E0 on a space-time diagram for frame S. Draw the lines that define the three invariant regions of space-time for E0. On the diagram, locate each of the follow events:

E1: x = 0, ct = 1 m
E2: x= 4 m, ct = 2 m
E3: x = 4 m, ct = 5 m

Specify whether each event is on the light cone of E0, in the past or the future of E=, or in the elsewhere. If E is within one of the light cones, find the speed (relative to S) of a frame in which E occurs at the same place as E0. If E is in the elsewhere of E0, find the speed if a frame in which it is simultaneous with E0.

First I draw my diagram, as you can see on the image, define the invariant regions (Past, future and 2x elsewhere), and locate the 3 events.

The next question is to specify where the events are happening.
I get:
E1 = The past
E2 = On the light cone
E3 = In the elsewhere

The next question is to find the speed (relative to S) of a frame in which E occurs at the same place as E0.

Then I draw the red line, and get the speed: (2/3)c

And that's what I got so far. The last part "If E is in the elsewhere of E0, find the speed if a frame in which it is simultaneous with E0." I cannot understand.
So maybe you can help me out ?

Thank you
- Ylle

Last edited: Sep 25, 2008
2. Sep 25, 2008

### Mentz114

You didn't post the diagram and I'm not going to redraw it. Use the 'Go advanced' and 'manage attachments'.

3. Sep 25, 2008

### yuiop

This looks suspiciously like homework and if it is, it is against the rules to post it here. (There is a special forum in PF for homework type questions with members eager to help). If you are just looking for guidance and understanding then maybe this will help:

Any two events that are contained anywhere in the region defined as the past and future light cone of your diagram can appear simultaneous in another reference frame with relative motion of less than c relative to the first reference frame. Any event E that is outside the past and future light cone (the elsewhere) of E0 can not appear to be simultaneous with E0 in any reference frame that has relative motion of less than lightspeed. These type of events are said to be "spacelike" in the texts. No real object or observer can travel from event E0 and arrive at event E because there is not enough time to do so if restricted to velocities of less than light speed. If event E is within the future light cone of E0 then there is enought time to travel from one event to other at sub light speed velocities. Because there is enought time to connect these type of events, these events are called "timelike" separated. If the velocity required to connect two events is exactly c (ie a photon could travel from one event to the other) then the speration is called "lightlike" and both events would be on the surface of a light cone which is sometimes called a "null worldline". I put these terms in here so you can look them up in Google or Wikipedia and perhaps learn more.

If two events are timelike or lightilke separated, then it is possible that one of the events is caused by the other. They are said to be "causally connected". If two events are spacelike separated (in the "elsewhere" of each other) then it not possible that one of the events is caused by the other.

Hope that helps :)

4. Sep 26, 2008

### Ylle

It was homework, but I posted in the wrong forum - sorry. I just didn't know how to delete my post.

But thanks anyways :D