On Wednesday, December 4, 2024 at 10:57:16 PM UTC-7 Brent Meeker wrote:
On 12/4/2024 8:43 PM, 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 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 Think about what that mean operationally. You have a photon detector at the middle of the car and mirrors at each end of the car positioned to send photons from lights at each end of the garage. When the detector receives a photon from each direction at the same time that means the ends of your care are simultaneously at the ends of the garage IN THE CARS REFERENCE FRAME. Now think about what it means in the garage reference frame. Brent In garage's reference frame, it *might *mean the car does *not* fit in garage, or that it can't be concluded that it does fit. But the conclusion that it fits seems to contradict the fact that the length of the garage shrinks from the car's pov and was initially assume to be longer than the garage in the rest frame of the car. 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/d2ec116e-7745-4044-a921-d27440f84813n%40googlegroups.com.
