On Wed, Dec 4, 2024 at 11:43 PM Alan Grayson <[email protected]> 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 > > > Let's suppose that in the frame of the car, the front and back of the car > are simultaneously inside the garage at some speed v. How does this > account for the fact that the length of the garage schrinks arbitarily > close to zero as v approaches c, which ostensibly leads to, or tends to the > opposite conclusion? AG > > Assuming the car and garage are moving inertially, whenever there's a conflict over whether the car fits in the garage in the garage frame vs. the car frame, it's always the case that it fits in the garage frame (where the car's length is contracted relative to its rest length) but not in the car frame (where the garage's length is contracted relative to its rest length), never vice versa. So if the car fits in the car frame as in your scenario, it also fits in the garage frame. Of course whether or not it fits at a given value of v depends on the numerical details of the problem, for any v < c you can always build a garage whose rest length is sufficiently large compared to the car rest length so that the car will still fit in the car's rest frame despite the length contraction of the garage. Jesse -- 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/CAPCWU3JLoumLSD1e%3DeN8ovXbkkgfaOzEjPKyBZhA9UDac2%2BHyA%40mail.gmail.com.
