Genady

This is how your logic goes: It's a genuine paradox: Atheist/"arelionist", whatever, state's as a matter of fact, there is no such thing as Santa. (Edit let's not get into semantics here.) So therefore, in a world without Santa, the children's books and the idea's therein have to be written by man and accepted by their fellow man. So therefore, if a lot of people, even in the face of cultural difference, say "that's an idea worth following". No Santa needed. Therefore, Santa has become a weapon for atheism/<insert word>.

Please, do. I'd prefer a fresh thread for this.

Yes. The interval between two events on B's timeline is the B's elapsed time between these two events. Likewise, the interval between two events on C's timeline is the C's elapsed time between these two events.

Generally, not. The metric of the diagram is not Euclidean. It has Minkowski metric. IOW, the "length" squared between two events on the diagram is not dt2+dx2. It is dt2-dx2. For example, the "length", called "interval", between any two events on a light line (450 line) is 0. IOW, the units on the lines belonging to different frames are not equal.

I don't get to that point because I can't get over the previous one.

Yes, it's correct. Notice the corrected expressions in my post. Sorry for that.

x=ct ct/x = 1 equivalently, c=1, v in units of c

The red line should not be parallel to the yellow line of the signal. The yellow lines have to be at 450.

It's your statement. You need to show, how the second part follows from the first.

The second part doesn't follow from the first.

"therefore" has been inserted here without a reason.

While you're resting, may I recommend these free and fun online presentations, which give good explanation for and practice in spacetime diagrams and Lorentz transformations (with Spanish subtitles available): Understanding Einstein: The Special Theory of Relativity | Coursera

It does not matter. A is not a midpoint in the B frame.

Yes, this is clear.

It looks incorrect. Why the three points A, B, and C are on a straight line? And why A is in the middle of that line?

@martillo, The spacetime diagrams are good for qualitative comparisons between events and frames, but to get quantitative comparisons you will have to calculate Lorentz transformations.

And A? Wait, D is signal reception...

I understand that event D is "Observer C receives the signal". What are the events A, B, and C on this diagram?

If you are assuming this, then B and C are not symmetrical, and I can prove it. Since they are not symmetrical, when they meet their clocks and beards will not be equal.

Yes, this is the problem. But we keep trying not to let him do this . PS. I have to go now. We'll be back in about an hour, I think. Otherwise, good night to all.

OK, but note that it is not the same v that appeared in the Lorentz Jr's calculations. So, we got the diagram with observers B and C which meet at some event up there and with C moving toward B with velocity v. What else do we know? Exactly. But in B frame, C moves toward A slower than A moves toward B and yet they meet all together. Thus, C has to be closer to A than B.

If they are equidistant from A in A then they are not equidistant from A in B, at any moment in B. So, what is v? Velocity of which frame relative to which frame? C relative to B? Something else?

I think it will be better if you answer, make mistakes, discuss, and fix them. We already know that Lorentz Jr knows how to solve this. What midpoint? In B frame?

What is A?

The velocity relative to what?