On Tuesday, February 4, 2025 at 1:51:26 PM UTC-7 Jesse Mazer wrote:
On Tue, Feb 4, 2025 at 3:09 PM Alan Grayson <[email protected]> wrote: 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\ It has to do with your question "what's the justification for plotting a single object moving wrt different frames on the same spacetime grid?" The justification is that, as I said, each observer can certainly *measure* all the objects involved, it's not like different frames are parallel universes that each can only see objects at rest in that frame. They are just different ways of assigning coordinates to the same set of local physical facts about the same objects, like the firecracker exploding or the edge of one object passing next to the edge of another. I don't follow your meaning. I see each frame making independent measurements when the observers are juxtaposed, and reach different conclusions about fitting and not fitting. AG As for the text, did you try clicking on the images to expand them? I tried that. It didn't work. AG Anyway the reference was just to back up what I said in the paragraph above about each observer assigning coordinates with their own ruler/clock system, if you understood that part and have no objections then there's probably no need to read the textbook images. 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. Not if "at the same time" means both frame agreeing on a common notion of a single moment in time but disagreeing about what is happening at that moment (as you say they don't have a common notion of a single moment in time). But if John Clark did say that (I'd like to see the post to read his exact words), he might have meant something else like "there is at least one moment in the garage frame where the car is entirely inside the garage, but at no single moment in the car frame is the car wholly inside the garage", which doesn't require that they have a common definition of what events happen in a "single moment". 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 Does your statement "the paradox is alive and well" depend on that one phrase about fitting/not fitting "at the same time"? No. I stated that when juxtaposed, x, t and x', t' need not be identical. The disagreement about simultaneity just applies to the time coordinate, and it doen't matter if they are not identical when the observers are juxtaposed, which is the only thing the simutaneity argument shows. AG That isn't the usual way of formulating the paradox, you can just say they disagree about whether the car ever fits wholly inside the garage without any words like "at the same time", I was following Clark's definition of the paradox. I'm sure I'm not misrepresenting what he meant, which was the paradox is based on a misconception that the frames share the time coordinate value. AG so if you are getting hung up on those words I'd recommend you just write them off as a confusing and non-standard way of describing the problem. As I always say, it's usually made clear explicitly or implicitly that the "paradox" is about the danger that the disagreement about fitting would lead to a disagreement about local physical facts like whether the closing garage door hits the car, and the fact that the two frames don't agree on simultaneity (or don't agree on the ordering of non-simultaneous events with a spacelike separation) is the way to show how that danger is avoided, and both frames can be in complete agreement about all local physical facts despite the disagreement about whether the car ever fits. Jesse You can set up your clocks and rulers any way you want in both frames, and you'll find the car observer observes the car not filling and the garage observer observes it fitting, when the observers are juxtaposed, and x, t, need not be identical to x',t'. This is why I say the paradox is alive and well. Any objections? Also, FWIW, since each frame has its own distinct coordinates, it's an error to plot them using some coordinates x,t, when the frames use different coordinates. 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 <https://groups.google.com/d/msgid/everything-list/e1d3176c-4c4e-4ddd-86b5-db9350d1d78cn%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/bd23a281-47d1-48d7-91eb-534fbde6038fn%40googlegroups.com.
