On Tuesday, December 10, 2024 at 11:51:46 PM UTC-7 Quentin Anciaux wrote:
Le mer. 11 déc. 2024, 07:40, Alan Grayson <[email protected]> a écrit : 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?? *Yes you do. Providing plots without the numerical values in the LT, is useless. I can't tell if you're drawing plots to satisfy your biases, or if the numbers support the case you're making. Lesson learned; always do a real proof, which means supplying the arguments, or STFU. AG * Wake up, your ego will kill your brain. *I don't suppose you could explain the resolution clearly. Relying on slogans, which you have done throughout without knowing it, gets us nowhere. I am studying the numbers, and hoping this resolves the issue. 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. 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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/baf27506-6b0a-45a8-a0c5-475ce237e628n%40googlegroups.com.
