On Saturday, December 7, 2024 at 3:51:30 AM UTC-7 Alan Grayson wrote:
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 Let me restate the problem where the car length is assumed to be longer than the garage length in the rest frame. So, the car can never fit in the garage when moving, since the garage length, which is initially smaller than the car's length, contracts. So there's no possibility of a perfect fit within the garage where simultaneity would apply. However, the car *can* fit in the garage, from the garage frame, since the car's length contracts. So, we have a situation where the car fits in the garage, but only from the garage frame. This seems paradoxical insofar as there's no objective reality of whether the car fits in the garage or not. 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/0049786e-adcd-4fea-b713-253243df1e8cn%40googlegroups.com.
