Below is what Brent wrote to describe his plots: notice that he uses the
car moving at 0.8c. But respect to what? He doesn't say. And then he
contracts the car from the garage frame. Is garage frame moving or at rest?
He doesn't say. So much presumably ambiguous non standard terminology and
not a peep out of you. Let's do this; since this discussion has reached the
point of tedious worthlessness, let's terminate it. AG
"First note by comparing the two diagrams that the car is longer than the
garage, 12' vs 10'. So the car doesn't fit at small relative speed. What
does "fit" mean? It means that the event of the front of the car
coinciding with the right-hand end of the garage is after or at the same
time as the rear of the car coinciding with the left-had end of the
garage. In both diagrams the car is moving to the right at 0.8c so
\gamma=sqrt{1-0.8^2}=0.6. Consequently, in the car's reference frame, the
garage is contracted to 6' length and when the rear of the car is just
entering the garage, the front is *simultaneously*, in the car's reference
frame, already 6' beyond the right-hand end of the garage. Then in the
garage's reference frame the car's length is contracted to 0.6*12'=7.2' so
at the moment the front of the car coincides with the right end of the
garage, the rear of the car will simultaneously, in the garage reference
system, be 2.8' inside the garage as shown below."
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