On Wednesday, December 11, 2024 at 1:51:00 AM UTC-7 Quentin Anciaux wrote:
Le mer. 11 déc. 2024, 09:46, Alan Grayson <[email protected]> a écrit : On Wednesday, December 11, 2024 at 1:39:54 AM UTC-7 Quentin Anciaux wrote: Le mer. 11 déc. 2024, 09:37, Alan Grayson <[email protected]> a écrit : On Wednesday, December 11, 2024 at 1:26:50 AM UTC-7 Quentin Anciaux wrote: In the thought experiment it always pass through the garage, just the following is frame dependent: the car is fully inside the garage and both doors are *simultaneously* closed, or part of the car is in the garage and doors are not simultaneously closed, in both view the car pass through the garage "undamaged", they just don't agree on the fact that the car was fully inside and both doors were simultaneously closed. Best to consider the garage like a covered bridge, open at both ends. IMO, there is only one reality. Therefore, however you want to define "fit", the car either fits or doesn't fit. There can be no ambiguity which is frame dependent. AG I give up... Maybe you should go to a monastery and meditate on this. I am not the kind of person who must be right, but on this issue I surely have made a provocative comment which must be taken seriously. AG You've just shown how stubborn and unwilling to understand you are. Believe what you want... Actually I'm not being stubborn. I just cannot imagine how seeing is not believing, in this case the car fitting or not fitting, each depending on different frame analyses. Maybe you're so committed to relativity that you can't imagine it being flawed. I admit; I don't know how relativity can satisfy what I see as basic logic and perception of the real world. AG Le mer. 11 déc. 2024, 09:16, Alan Grayson <[email protected]> a écrit : On Wednesday, December 11, 2024 at 12:44:05 AM UTC-7 Alan Grayson wrote: On Tuesday, December 10, 2024 at 11:40:10 PM UTC-7 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?? *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 * *Brent; your numbers check out. The car fits with ease from the pov of the garage frame, but not from the pov of the car frame. But this bothers me since we know that all frames are equivalent in SR. How then can two, so-called equivalent frames, gives different results? Using the LT, measurements in different frames generally differ, but here something more fundamental seems to be happening; namely, that the car fits and doesn't fit, depending on the frame being analyzed. AG * *What I'm getting at is this; if one could do the experiment with a real car, it would either fit, or wouldn't fit. Do you agree? But in SR, the result is frame dependent. How would you reconcile this apparent problem or contradiction? 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/ba1fa695-9cc1-441e-a063-f79a83831714n%40googlegroups.com.
