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It is best to avoid setting explicit colors. In dark mode your whole thing disappears:Sagittarius A-Star said:You describe 4 events (E1 ... E4).
E1: clock A shows 100s
E2: clock B shows 80s
E3: clock B shows 100s
E4: clock A shows 80s
I call the coordinates of frame A (x, y, z, t) and the coordinates of frame B (x', y', z', t').
1) => Events E1 and E2 happen simultaneous for observer A: ##\Delta t_{21} = t_2 - t_1 = 0s##.
But events E1 and E2 do not happen simultaneous for observer B, if they happen at different ##x## coordinates, according to the Lorentz-transformation: ##\Delta t'_{21} \neq 0s##.
2) => Events E3 and E4 happen simultaneous for observer B: ##\Delta t'_{43} = t'_4 - t'_3 = 0s ##.
But events E3 and E4 do not happen simultaneous for observer A, if they happen at different ##x'## coordinates, according to the Lorentz-transformation: ##\Delta t_{43} \neq 0s##.
So there is no contradiction.
The Lorentz transformation for time depends on ##\Delta x##:
##\Delta t '= \gamma (\Delta t - v \Delta x / c^2)##.
If ##\Delta t=0##, then ##\Delta t '= -\gamma v \Delta x / c^2##.
The inverse Lorentz transformation for time depends on ##\Delta x'##:
##\Delta t = \gamma (\Delta t' + v \Delta x' / c^2)##.
If ##\Delta t'=0##, then ##\Delta t = \gamma v \Delta x' / c^2##.
I can't stop coloring the text because I didn't color the text.A.T. said:@Sagittarius A-Star
Please stop coloring the text. It's unreadable in dark mode.
Interesting. There are explicit color directives in there. I wonder how they got there.Sagittarius A-Star said:I didn't color the text.
No. Now I deleted the color-commands.Dale said:Did you do some editing in another program and copy paste the result?
This happened occasionally pre-style update too, but the text wasn't completely invisible in the old dark style.Dale said:Interesting. There are explicit color directives in there. I wonder how they got there.
The alternative would be to invert all explicit colors, if the users mode doesn't match the poster's mode.Dale said:@Greg Bernhardt maybe something to think about. Instead of specifying explicit colors perhaps users could be given named colors like “highlight 1” that could be mapped appropriately.
I deleted the color-commands.A.T. said:OK, sorry. Did you maybe copy & paste the text? If yes, then look for a 'paste as plain / unformatted text' in the context menu of your browser.