On 12/11/2024 10:02 PM, Alan Grayson wrote:
On Tuesday, December 10, 2024 at 11:15:16 PM UTC-7 Brent Meeker wrote:
Do I not only have provide a diagram I also have to explain it in
detail just to end this silly thread??
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.
*If the car is contracted in garage's reference frame, why is the
car's length plotted at its initial value of 12' If this issue is so
silly, I'd think your diagram wouldn't raise this question. AG
*
*You raised the question. Can you point out where the car's length is
plotted as 12'?
Brent
*
Note that in the above diagram I have marked two simultaneous
events with small \delta's. The diagram below is just the Lorentz
transform of the one above. The two simultaneous \delta's are
also in the diagram below. You can confirm they are the same
events by referring to the time blips along the world lines, which
are also just the Lorentz transforms of those above. But clearly
the events marking the simultaneous locations of the rear and
front of the car above are NOT simultaneous in the garage frame
below. Conversely, the front and rear simultaneous locations of
the car below are not simultaneous in the above diagram, as the
reader is invited to confirm by plotting them. Simultaneity is
frame dependent.
Incidentally, when I was in graduate school this was still know as
the "Tank Trap Paradox". The idea was that if one dug a tank trap
shorter than the enemy tank, then the tank would just bridge the
hole, UNLESS the tank were going very fast in which its contracted
length would allow it to fall into the trap. This was being
explained to me by Jurgen Ehlers, whom you may correctly infer
from his name was a German professor recently hired at Univ
Texas. I said, "What is it with you Germans, illustrating things
with tank traps and cats in boxes with poison gas?" Jurgen who
was too young to have fought in the war didn't realize I was
pulling his leg and he was struck speechless.
Brent
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