On Saturday, December 14, 2024 at 2:16:36 PM UTC-7 Jesse Mazer wrote: On Sat, Dec 14, 2024 at 12:34 PM Alan Grayson <[email protected]> wrote:
On Saturday, December 14, 2024 at 7:58:34 AM UTC-7 Jesse Mazer wrote: On Sat, Dec 14, 2024 at 5:27 AM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 1:35:54 AM UTC-7 Alan Grayson wrote: On Friday, December 13, 2024 at 8:48:39 PM UTC-7 Brent Meeker wrote: On 12/13/2024 7:02 PM, Alan Grayson wrote: On Friday, December 13, 2024 at 7:30:31 PM UTC-7 Brent Meeker wrote: On 12/13/2024 3:09 PM, Alan Grayson wrote: For some rest length frame parameters, there's a v, such that for velocities greater than v, won't the car fit in all garage frames, but in none of the car frames? If this is correct, what's the justification for saying the solution exists in one set of frames, but not in another? And what's the argument that in all of these frames, simultaneity of front and back of car is satisfied? TY, AG What could it possibly mean for the car *not to fit* in the car frame! *Have you ever tried to park a car? Use your brains and you'll figure it out. It's called the Lorentz Parking Paradox. You're trying to park a car of known rest length, in a garage of known rest length. Follow me so far? Now get the car moving and from the car's frame notice how the garage length Lorentz contracts. Follow me so far? At some v or greater, the length of the garage will be smaller than the car's rest length. When this happens most sane individuals will conclude that the car won't fit. * *OK, you meant the car will not fit in the garage, in the car's frame. * * Brent* *Maybe, just maybe, this apparent paradox cannot be resolved by solely analyzing what happens in space, but in spacetime. Tomorrow I will make an effort to fully understand your spacetime diagrams and see if they shed any light on this issue. The clue might be the fact that in relativity, ds^2 is frame invariant. And FWIW, I haven't seen any convincing arguments based solely on the frame non-invariance of simultaneity. It's often claimed this non-invariance solves the problem, but detailed proofs are woefully lacking. AG* *The reason a paradox seems to exist is because the frame observers witness contrary events; the garage observer sees the car fitting in the garage, whereas the car observer sees the car not fitting in the garage, when there's only one possible thing to observe. AG* "Events" in relativity generally refer to things that happen at a single point in spacetime, like the back end of the car passing by the front of the garage with the clocks mounted to each showing particular readings; the different frames do not disagree about any localized events in this sense. Did you understand my point about why the question "did the car fit" reduces to the question "did the event A of the back of the car passing the front of the garage happen before the event B of the front of the car reaching the back of the garage"? Jesse *Yes. In relativity measurements are generally not frame invariant, such as the E and B fields in EM. But this case seems different. Imagine two observers, one in car frame and the other in garage frame, and they're both viewing the car passing through the garage, now open on both ends. Ostensibly, the former sees the car fail to fit in the garage, the latter sees the opposite. I don't believe a rigorous definition of "fit" will resolve this contradiction. * Note that when we talk about what happens in a given frame this is not what any observer sees with their eyes, it's about when they judge various events to have happened once they factor out delays due to light transit time, or what times they assign events using local readings on synchronized clocks that were at the same position as the events when they occurred. For example, if in 2025 I see light from an event 5 light years away, and then on the same day and time in 2030 I see light from an event 10 light years away, I will say that in my frame both events happened simultaneously in 2020, even though I did not see them simultaneously in a visual sense. And if I had a set of clocks throughout space that were synchronized in my frame, when looking through my telescope I'd see that the clocks next to both events showed the same date and time in 2000 when the events happened. When you say 'I don't believe a rigorous definition of "fit" will resolve this contradiction', which of these is closer to your meaning? 1. If event A = "back of car passes through front door of garage" and B = "front of car reaches back of garage", then *even if* you grant that the question "does the car fit" is defined to be 100% equivalent to the question "does A happen before B", you still think an analysis of how simultaneity works in relativity which shows that the two frames can disagree about the order of A and B is *not* sufficient to resolve the paradox. *I just wrote a more detailed reply and it was lost. Yes, if both frames disagree about car fitting, IMO paradox is alive and well. I assume observers in each frame view the same phenomenon, so regardless of what relativity claims, they must see the same thing. This is different from the general case of different frames making different measurements, but I can't precisely explain in this case, the distinction between these two types of measurements. AG * 2. You grant that there is a good explanation for why different frames can disagree about the order of A and B, but you have an argument or strong intuition that the question "does A happen before B" is *not* equivalent in meaning to "does the car fit in the garage" *Not sure how to answer your question. I haven't thought about ordering. Nonetheless, any disagreement about whether car fits means the paradox is alive and well. AG * Jesse *OTOH, from the garage frame, the car's length is Lorentz contracted, so most sane individuals will conclude the car WILL fit in the garage. Thus, an apparent paradox, or shall we say a discrency of whether or not, the car can fit in garage, and from the pov of which frame? Final question: are you a sane individual? These questions might be totally ill-posed. If so, with your immensely superior intellect, I'm confident you'll be able to show us how; and if so, THAT WILL BE THE SOLUTION! AG* I don't even know that "the solution" means. *It means what I wrote above. Which frame, if any, can the car be fully contained within the garage? AG * What was the problem to be solved; *Read what I wrote, and better yet what other professionals write about this apparent paradox. AG* How to educate Alan? Simultaneity is a relation between EVENTS, not car parts. *I know that. Now tell me something I don't know. (Who said anything about car parts?) 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/7c122cdc-db23-411f-9407-0df3f19e8342n%40googlegroups.com.
