On Saturday, December 7, 2024 at 4:16:38 AM UTC-7 Quentin Anciaux wrote:
I've already explained it to you last month, there is no contradiction, just non agreement on simultaneity... from the cars pov, the doors aren't closed simultaneously, that's it. I disagree with your conclusion. GIven the initial conditions of the scenario, the car cannot fit in the garage from the car's frame. And from the frame of the garage, the car can easily fit if its velocity is suffiently close to c. So, although I know that disagreements about simultaneity is the alleged solution to the apparent paradox, I don't see it as relevant. What we have are two frames which reach opposiite conclusions about whether the car can fit in the garage. This seems paradoxical to me, but perhaps I am mistaken. AG Le sam. 7 déc. 2024, 11:51, Alan Grayson <[email protected]> a écrit : On Wednesday, December 4, 2024 at 2:41:25 PM UTC-7 Jesse Mazer wrote: On Wed, Dec 4, 2024 at 4:06 PM Alan Grayson <[email protected]> wrote: In the case of a car whose rest length is greater than the length of the garage, from pov of the garage, the car *will fit inside* if its speed is sufficient fast due to length contraction of the car. But from the pov of the moving car, the length of garage will contract, as close to zero as one desires as its velocity approaches c, so the car *will NOT fit* *inside* the garage. Someone posted a link to an article which claimed, without proof, that this apparent contradiction can be resolved by the fact that simultaneity is frame dependent. I don't see how disagreements of simultaneity between frames solves this apparent paradox. AG Can you think of any way to define the meaning of the phrase "fit inside" other than by saying that the back end of the car is at a position inside the garage past the entrance "at the same time" as the front end of the car is at a position inside the garage but hasn't hit the back wall? (or hasn't passed through the back opening of the garage, if we imagine the garage as something like a covered bridge that's open on both ends) This way of defining it obviously depends on simultaneity, so different frames can disagree about whether there is any moment where such an event on the worldline of the back of the car is simultaneous with such an event on the worldline of the front of the car. Jesse Are you claiming that the apparent paradox can be resolved by accepting the fact that the car and garage frames have different conclusions about whether the car fits in the garage? AG -- 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/cf3fd800-48fb-451b-8eef-5f4dea84d408n%40googlegroups.com.
