On Tuesday, December 17, 2024 at 8:26:00 AM UTC-7 Jesse Mazer wrote:
On Tue, Dec 17, 2024 at 4:10 AM Alan Grayson <[email protected]> wrote: On Wednesday, December 4, 2024 at 2:06:41 PM UTC-7 Alan Grayson 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 Let's go back to square one. The car fits in garage from the garage frame due to contraction of the car's length, which in rest frame is longer than the garage. And to get the fit we need to invoke simultaneity of the front and rear ends of the car. OTOH, from the frame of the car, which in rest frame is longer than the garage and won't fit within it, when the car is set in motion, the garage's length shrinks, so a possible fit becomes evev more impossible. It is claimed that this apparent paradox -- and I fail to see a paradox -- is resolved due to the disagreement of simultaneity between the frames. But I don't see any need to introduce simultaneity. >From the car's frame, the garage's length has *decreased *from its rest length, where it couldn't fit, and now imaging a fit is *worse* than the initial situation. So, what has simultaneity have to do with the solution? Apparently nothing! AG Simultaneity is relevant because if all frames shared the same definition of simultaneity, then a disagreement between frames about whether the car or garage was shorter would automatically imply a real physical disagreement in predictions about local events (like what clocks mounted to front and back of car read when they pass clocks mounted to front and back of garage), in which case it would be impossible for both frames' predictions to be correct if you tested the scenario. Jesse Using Brent's initial condiitons, in the rest frame the lengths of the car and garage are 12' and 10' respectively. There's no controversy that the car doesn't fit because it's longer. Now set the car in motion and use the gamma factor in SR, and it's even longer, so sane persons, and maybe even some not entirely sane, would conclude the car still cannot fit. AFAICT, disagreement about simultaneity has nothing to do with this conclusion, Similar logic can be applied to garage frame. Car length is contracted using gamma factor, so for v large enough, car will now fit in garage. Same conclusion using the gamma factor. For each frame we use the gamma factor to shorten the relevant length. 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/3ea4ac56-4331-4bc3-9a4e-6bb4c423126an%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/3ea4ac56-4331-4bc3-9a4e-6bb4c423126an%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]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/2d629018-eed2-41c4-829d-9c040e64f395n%40googlegroups.com.
