« first day 

HRThomann
HRThomann
13:51
You wrote "What does B say that A's clock showed at THAT time? What does A say that B's clock showed at THAT time?".
What does B say at point H that A's clock showed? Is it 5/3 or 16/15? Is point F
You wrote "The relevant event is the event on A's worldline that B says is simultaneous with his meeting with C. The time coordinate of that event in A's frame is .4." This is point J. But B was meeting C at point H, which is connected to point F in your diagram.
What is the meaning of "simultaneous"? Does it mean the same interval value? The intervals of F, G, H and J are pairwise different.
Is is it correct to say: F is the point where B expects A to be as B passes C? "expect" means: from B's time and A's relative velocity.
What is wrong with the following argument: When B passed C, it learned that C's clock had run for 5/3. Also B knows that C's and A's clock are synchronous. So why to expect a different clock value for A?
WillO
WillO
14:33
A and C's clocks are synchronized in the A/C frame, not in the B frame.
"Simultaneous" means "having the same time coordinate."
In B's frame, J and G are simultaneous (they both take place at time .5). At J, A's clock reads .4. At G the signal is received. So in B's frame the following is true: "The signal is received when A's clock says .4".
HRThomann
HRThomann
14:50
Thanks. I finally understand:
(vt,t) in A is (0,-gamma*t) in B, (0,t) in A is (-vt,t)/gamma in B. The first one expresses A's view of B's motion, the second one B's view of A's motion. Both views reflect the same state of nature. The moving part is slower in the resting part's view. No contradictions!
A=(0,5/3) is (-5/4, 25/12) in B's view, and B=(0.4/3) is (1, 5/3) in A's view.
A=(0,5/3) is (-20/9, 4/3) in B and simultaneous with (0, 4/3) in B.
Correction: A=(0, 5/3) is simultaneous with (1, 5/3) in A, transforming to (4/5, 4/3) in frame B simultaneous with (0, 4/3) in B.
HRThomann
HRThomann
15:31
A=(0,5/3) is (-5/4, 25/12) in frame B, simultaneous with (1, 5/3) in A, transforming to (0, 4/3) simultaneous with (4/5, 4/3) in B.
1'048'576 thanks!
 
5 hours later…
WillO
WillO
20:14
I have not checked your arithmetic but what you are saying sounds just about certain to be correct. I'm glad this helped.
I have a textbook on relativity that will be published later this year. I can still add new material for the next month or so. I think I will add a version of this problem there. So I thank YOU as well.

« first day