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... > 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/6ced1309-87f2-4fc2-aa4e-4e408169cdbdn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/6ced1309-87f2-4fc2-aa4e-4e408169cdbdn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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]. 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