On Tuesday, December 17, 2024 at 1:03:57 PM UTC-7 Alan Grayson wrote:
On Tuesday, December 17, 2024 at 10:53:54 AM UTC-7 Jesse Mazer wrote: On Tue, Dec 17, 2024 at 12:25 PM Alan Grayson <[email protected]> wrote: 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. In Brent's scenario the two are never at rest relative to each other, I guess you are imagining one where they're initially at rest relative to each other and then one is accelerated? 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. *That's an error. Sorry for the confusion. When car is in motion, from car frame, for large enough v, garage contracts and car still won't fit. AG * Your phrase "Set the car in motion" would seem to indicate you're talking about the garage frame where the car is moving, and there the car is shortened. *Yes, in garage frame the car is shortened. AG* There is no inertial frame where the car is "even longer" than its rest length, are you maybe trying to say the *ratio* of car length to garage length is greater in the car's rest frame? *I never made that claim. AG* 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 I agree, you can use the gamma factor to show that in the car frame the car won't fit, and in the garage frame it will. *So you agree with my conclusion, and I never needed to invoke simultaneity. AG* But this doesn't address my comment that if it weren't for differences in simultaneity, different frames would actually be disagreeing in predictions about local physical events and thus at least one's predictions would be falsified. *I don't understand your comment because the two frames make predictions you agree with, so both are correct but differ in their outcomes, without invoking simultaneity. AG* Try to write down a non-relativistic theory where there is no disagreement about simultaneity, but where different inertial frames (related by a coordinate transformation where time coordinates t and t' always agree) each predict that objects in motion relative to themselves shrink in length--you can't do it! At least not if you want all frames to agree in predictions about local events like readings on clocks as they pass next to each other. 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/7063f1a1-4972-4bf2-a28d-747093c26b9cn%40googlegroups.com.
