Le dim. 15 déc. 2024, 10:12, Alan Grayson <[email protected]> a écrit :
> > > On Sunday, December 15, 2024 at 1:51:21 AM UTC-7 Quentin Anciaux wrote: > > > > Le dim. 15 déc. 2024, 09:40, Alan Grayson <[email protected]> a écrit : > > > > On Saturday, December 14, 2024 at 11:27:37 PM UTC-7 Jesse Mazer wrote: > > On Sat, Dec 14, 2024 at 10:46 PM Alan Grayson <[email protected]> wrote: > > On Saturday, December 14, 2024 at 8:15:37 PM UTC-7 Jesse Mazer wrote: > > On Sat, Dec 14, 2024 at 9:46 PM Alan Grayson <[email protected]> wrote: > > 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 * > > > They see exactly the same local events. As I said before, if there are a > pair of clocks attached to either end of the garage which are synchronized > in the garage frame, and a pair of clocks attached to either end of the car > which are synchronized in the car frame, then in Brent's example they both > see that when the back of the car passes the front of the garage (event A), > the back car clock and front garage clock both read 0; and when the front > of the car reaches the back of the garage (event B), the front car clock > reads -7.5 and the back garage clock reads 3.5. The only difference is the > *convention* each frame adopts about which clocks are synchronized--the car > frame calls the car clocks "synchronized" and the garage clocks > "out-of-sync", and the garage frame calls the garage clocks "synchronized" > and the car clocks "out of sync". Thus, based on their different > conventions, the car frame says the event A happened later than event B (A > at time 0, B at time -7.5), and the garage frame says the event A happened > earlier than event B (A at time 0, B at time 3.5). > > Consider an analogy with disagreements about spatial coordinates. Say > there is a post on the ground, and two observers both define the x-axis of > their respective coordinate systems by rulers which touch the post, but the > two observers place the x=0 mark of their respective rulers 2 meters apart > from one another, so that the post is next to the 3 meter mark on the ruler > of observer #1, and next to the 5 meter mark on the ruler of observer #2. > The only difference is that they have different *conventions* for defining > the x-coordinate of objects on the ground, with each one defining > x-coordinate by markings on their own ruler. There is no disagreement about > the fact that the post is next to the 3 meter mark of observer #1's ruler > and next to the 5 meter mark of observer #2's ruler, but because of their > different conventions, this means observer #1 says "the post has position > x=3 meters" and observer #2 says "the post has position x=5 meters". Do you > think this is some deep physical contradiction, or would you agree it's a > mere difference in the convention used about which ruler to use when > assigning x-coordinates? If the latter, then why do you think the situation > with the garage and car is any different? All observers agree about what > all specific physical clocks read at event A and B, they merely differ on > their respective conventions about which clocks to use to assign > t-coordinates to events A and B. > > > 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 * > > > You haven't thought about it?? Disagreement about the ordering of these > two specific events (due to differences in simultaneity) is what Brent and > I have both been emphasizing as the fundamental resolution of the paradox, > have you not even understood that this is central to what we are arguing, > and considered in an open-minded way whether or not it makes sense? > > > *I meant I hadn't considered the ordering you postulated as effecting > simultaneity. By "fit", I always meant the ordering you described, and that > the paradox is alive and well under such ordering. * > > > By "the paradox is alive and well" do you just mean that the car rest > frame and the garage rest frame disagree about the order of those events A > and B? > > > *IIRC, I never discussed order of events; just contraction of lengths from > different frames. I thought it paradoxical that the frames could disagree > on whether the car could fit or not (and Brent gave the conditions for a > fit in a recent post). Now I am not so sure. Maybe the frames can disagree > about whether the car fits, and there's no problem. That seems to be the > consensus view on this MB and elsewhere. AG* > > > Please define fits into ? Fitting means the following two events are > simultaneous: the rear of the car is at or after the entrance while > simultaneously the front of the car is before or at the exit... so this > clearly depends on simultaneity... if you don't get it, then I think it’s > impossible to fit this idea in your brean whatever speed and enlarged > contraction factor applied to it. > > > *Firstly, I really don't need your snotty attitude. So, clean up your act > or STFU. FWIW, I know what simultaneity is, but what I'm not sure about is > how it allegedly solves the problem, if there is one, of the frames > disagreeing about whether the car fits in the garage. AG* > Do you or not agree with the definition of fitting into ? If yes, do you see how it involves simultaneity? If you disagree, please define fits into without using simultaneity. > -- > 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/b05316e5-04e1-4e77-9fd1-cd20399c5cb1n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/b05316e5-04e1-4e77-9fd1-cd20399c5cb1n%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/CAMW2kApfAnKKeiaZ%2BW4zRF32jb3wC6bPkodkYpNZQG5s2KeArA%40mail.gmail.com.
