On Tue, Dec 17, 2024 at 3:14 PM Alan Grayson <[email protected]> wrote:
> > > 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 * > Got it, thanks. > > 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 > <https://groups.google.com/d/msgid/everything-list/7063f1a1-4972-4bf2-a28d-747093c26b9cn%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]. 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