*sigh* For being such a clever kid, you're having a hard time keeping up.
I'm gonna try to show you "why" I drew two Loedels when you think I only needed one. If you still don't get it, I'll look around for an interpreter.
- First, here's the table of events again. Note that there are nine of them that I'm interested in.
No. That is NOT a table of events. There *are* nine events:
1. When A1 is adjacent to B1
2. When A2 is adjacent to B1
3. When A3 is adjacent to B1
4. When A1 is adjacent to B2
5. When A2 is adjacent to B2
6. When A3 is adjacent to B2
7. When A1 is adjacent to B3
8. When A2 is adjacent to B3
9. When A3 is adjacent to B3
Furthermore, *everyone* agrees that Event 1 happens before Event 4 which happens before Event 7. Similarly for 2,5,8 and 3,6,9. Also, *everyone* agrees that 1 happens before 2 which is before 3. Similarly for 4,5,6 and 7,8,9.
But what *you* write for event 2 is a combination of *two* different events: my event 2 and my event 4. Remember that an event has both a time and a location. those two events have different locations.
- Next, is another Loedel for you. Most of it should be familiar to you.
- Note that I have identified the nine events with a "frame-independent" color: yellow. Do Loedels typically have frame-dependent colored lines and frame-independent boxes that identify events? No.
The lines are the space and time axes for the two spaceships. For example, the lines labeled as A1, A2, and A3 are three different fixed locations in spaceship A's frame. In the Loedel frame, however, the markers are NOT at rest, so you get these angled lines.
The same is true for the lines labeled B1, B2, B3, only they are for spaceship B.
The other blue lines are the lines that spaceship A sees as being simultaneous. So, being on one of these lines means spaceship A will see those events as happening at the same time. Similarly for the unlabeled red lines and spaceship B.
The events are simply events: locations in spacetime.
- Note also that three of the boxes have numbers in them: 1, 5, and 9. Those numbers correspond to events listed in the table. They happen to be events that both frames' observers describe identically. In other words, everybody in the spaceships agrees that when A1 is adjacent to B1, B1 is adjacent to A1; when A2 is adjacent to B2, B2 is adjacent to A2; and when A3 is adjacent to B3, B3 is adjacent to A3. And it so happens that everybody in the spaceships agrees on the chronological order of those three events, to wit: #1 happened first, #9 happened last, and #5 happened in the middle of all the events.
OK so far.
- Now, pray tell, what is the chronological order of the other six events? To show that order, please number the boxes and let me know when you're done. Thanks.
In what frame do you want the chronological order? In the frame of spaceship A? spaceship B? or in the Loedel frame?
The answers are different depending on which frame you mean. And, like I said, you have to be clear about what the events are. You seem to confuse the event when A1 and B2 are adjacent with the event where A2 and B1 are adjacent. They are at the same time *for spaceship A*, but are at different times for spaceship B and for the Loedel frame.
According to how I gave the events above, this is trivial. For example, the box you labeled as 1 is the event when the A1 and B1 lines intersect, so it is event 1.
Now, going by my designation of events above, the second row, left box is event 2, the right box is event 4, the left box on the third level is event 3, the right box is event 7, the left on the fourth level is event 6 and the right is event 8. Just look at which labeled lines are crossing and identify the number of that event.
The Loedel diagram is NOT a diagram from the frame of A or B. It is in the frame in which both A and B are moving at the same speed in opposite directions. That is the *definition* of the Loedel frame.
And, like I said above, we can read off the order of the events in each frame from this. For example, for spaceship A (blue lines), the event I have labeled 4 happens after 1. The events (notice the plural) 2 and 7 also happen on the same blue line (although it is not given) and so are simultaneous for spaceship A. Then event 5 happens, then 6 and 8 are simultaneous for A. Then 9.
For spaceship B, we use the unlabeled red lines. the sequence is 1, 2 and 3 simultaneous, 4, 5, 6 and 7, 8, 9.
For the Loedel frame, use horizontal lines for equal times, and find 1, 2 and 4, 3 and 5 and 7, 6 and 8, and finally 9.