(Quibble)
Almost correct. Mathematically that should be:
If ##Δx_A=0## then ##Δt_B>=Δt_A##
and
If ##Δx_B=0## then ##Δt_A>=Δt_B##.
And then, if they insist on having them both in one scenario, then clearly:
If ##Δx_A=Δx_B=0## then ##Δt_B>=Δt_A## and ##Δt_A>=Δt_B##,
and thus...
Nice diagram!
Fwiw, note that :
(*1) in the top figure, where Red touches the green car simultaneously with both hands, Green protests and says that Red is cheating because he does not touch his green car simultaneously. According to Green, Red touches the green car's front too late and the...
(Quibble) ... which will or will not falsify the postulates. I think that "validate" is too strong, as it might be interpreted as a synonym of "prove".
Measured time differences increase by a factor gamma, but c.t' = c.t.gamma only for x=0 (see Wikipedia Time dilation)
Measured distances decrease by a factor gamma, but x' = x/gamma only for t'=0 (see Wikipedia Length contraction)
Combining these two clearly distinct situations with two events...
To get a slope 1/2 between the horizontal and a line, you do *not* bisect the 45 degrees angle. Instead you draw a line with slope 1/2, which means climbing 1 unit for every 2 units of horizontal displacement. That gives an angle of 26.6 degrees, not one of 22.5 degrees.
See...
It means making a measurement that is simultaneous with the (x',t') = (0,0) event in my coordinates. You and the lamp post are moving in my frame, so I must make sure that I measure the distances to you and to the lamp post simultaneously. You are at distance x'=0 at my time t'=0, so I must...
"Moving with the arrow of time" is just fancy speak for "growing older". As far as we know, we can't grow younger, hence the "arrow". It points "where" we go.