Two points: I don't see what this has to do with the question on THIS thread, and I can't read your reference since it's way too small. AG
Here's my problem with the alleged solution to the Car Parking Paradox; diagreement about simultaneity means, IIUC, that the car can't fit and not fit AT THE SAME TIME. This is how Clark defined the paradox. Well, since every frame in SR has its own synchronized clocks, the concept of "at the same time" is meaningless when it is applied to two frames in SR, and the lack of simultaneity is a formal way of proving this. Now if the center of the garage has an observer situated there, and there's an observer in the car, the spacetime coordinates of the frames can be totally different in x and t when the observers are juxtaposed, yet from the pov of car observer, the car doesn't fit since it never does given the initial conditions of the paradox. OTOH, from the pov of garage observer the car always fits. So, when the car is at the center point of garage, the two observers are juxtaposed with different coordinates. but the observers have diametrically opposite conclusions. It doesn't matter that x and t, disagree with x' and t'. So, IMO, the paradox is alive and well. AG On Tuesday, February 4, 2025 at 12:13:44 PM UTC-7 Jesse Mazer wrote: > On Tue, Feb 4, 2025 at 1:39 PM Alan Grayson <[email protected]> wrote: > >> >> >> On Tuesday, February 4, 2025 at 9:43:18 AM UTC-7 Alan Grayson wrote: >> >> Since each reference frame has its own spacetime labels, what's the >> justification for plotting objects moving wrt different frames on the same >> spacetime grid? AG >> >> >> CORRECTION: >> >> Since each reference frame has its own spacetime labels, what's the >> justification f*or plotting a single object *moving wrt different frames >> on the same spacetime grid? AG >> > > > See my comment at > https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/22jbd5qZEAAJ > > >Alan: Yes, except we don't have to assume the moving rod has coordinates > in O2. AG > > >Jesse: Do you just mean it doesn't have *fixed* coordinates in O2, or do > you mean it isn't assigned coordinates at all in O2? If the latter, are you > imagining it's somehow invisible to the O2 observer? If so that's not how > things work in relativity, the rod is just an ordinary physical object, of > course the O2 observer is going to be able to measure it as it passes by > his own system of rulers and clocks, and say things like "when the clock > attached to the 3-light-second mark on my ruler showed a time of 5 seconds, > the back of the rod was passing right next to it (as seen in a photo taken > at that location at that moment, for example), therefore the worldline of > the back of the rod passes through the coordinates x=3 light seconds, t=5 > seconds in my coordinate system" > > In case my above comment about the O2 observer being "able to measure it > as it passes by his own system of rulers and clocks", you should be clear > on the idea that the coordinates of any given frame are generally defined > in textbooks in terms of local readings on a system of rulers and clocks > that are at rest in that frame (each clock permanently fixed to a > particular ruler-marking), with the clocks having been "synchronized" in > that frame using the Einstein clock synchronization convention (which has > the result that O1 will consider the O2's clocks to be out of sync with one > another as measured in O1's frame, and vice versa). So then if there's some > event, like a firecracker going off or the back of a car passing the front > of the garage, the observer just looks at a snapshot of the part of his > ruler/clock system that was right next to that event when it happened. If > for example the snapshot shows the firecracker going off next to the 12 > light-seconds mark on my ruler and the clock of mine that's attached to > that marking shows a time of 8 seconds in the snapshot, then I say the > firecracker happened at coordinates x=12 light seconds, t=8 seconds in my > frame. And you can imagine the ruler/clock systems of other observers are > sliding smoothly past my own ruler clock/system, so that for any given > event like the firecracker, each observer has a ruler-marking and > clock-reading of their own that was right next to that event when it > happened. > > Here for example are some pages from the textbook "Spacetime Physics" by > Edwin Taylor and John Wheeler which go over the concept: > > [image: spacetimephysicsp37.jpg] > [image: spacetimephysicsp38.jpg] > [image: spacetimephysicsp39.jpg] > > 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/e1d3176c-4c4e-4ddd-86b5-db9350d1d78cn%40googlegroups.com.
