On Tuesday, February 4, 2025 at 9:11:38 PM UTC-7 Jesse Mazer wrote:
On Tue, Feb 4, 2025 at 9:42 PM Alan Grayson <[email protected]> wrote: On Tuesday, February 4, 2025 at 5:02:00 PM UTC-7 Jesse Mazer wrote: On Tue, Feb 4, 2025 at 5:45 PM Alan Grayson <[email protected]> wrote: On Tuesday, February 4, 2025 at 2:50:03 PM UTC-7 Jesse Mazer wrote: On Tue, Feb 4, 2025 at 4:29 PM Alan Grayson <[email protected]> wrote: 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 Sure, they disagree about fitting, but each has a grid of coordinates covering the same region of spacetime, which is used to plot the paths of both the car and the garage in that region. Is that what you meant by "plotting a single object ... on the same spacetime grid", or did you mean something different? As for the text, did you try clicking on the images to expand them? I tried that. It didn't work. AG If you are looking at the site using a mouse or trackpad, try right-clicking on the images, and then when a menu pops up click an option like "open image in new window". If you're using a touch screen you can try just pressing down on an image with your finger until a menu like this pops up. 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 By "juxtaposed" do you mean when they assign coordinates to the same event, like the event of the back of the car passing the entrance of the garage, or the event of the front of the car passing the exit of the garage? I mean when juxtaposed they do any measurements necessary, to show car fitting in garage frame, but not car frame. For me this is a paradox. Presumably you disagree. AG If so, I'd agree the x, t assigned to each event by one observer will in general be different from the x', t' assigned to each event by the other observer, if that's all you're saying. 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'. Sure, if by "juxtaposed" you mean what I said above. This is why I say the paradox is alive and well. Any objections? I'd object to that because the mere fact that observers assign different coordinates doesn't seem like a "paradox" to me. That's not my claim. I am saying disagreement about simultaneity doesn't resolve the paradox because when juxtaposed, the times can be different, while the car fits in one frame and not in the other. AG So for you, the "paradox" is purely the idea that it fits in one frame but doesn't fit in another? Do you think it's a paradox that different observers assign a different velocity v and v' to the same object? No; I think from any frame, the object in that frame will be at rest, uncontracted, and will be in relative motion wrt the other frame. AG But *why* do you say it's non-paradoxical for different frames to disagree about velocity, but it is paradoxical for them to disagree about fitting? Is it just an intuitive reaction to the second that's different from your reaction to the first? To me they both seem like cases of "some statements about physical objects are frame-dependent, so different frames can disagree about them." I accept the fact that different frames can make different measurements, and the situation with v and v' might be an example of that, just like measurements of E and B fields differ in different frames due to the relative motion. What I don't accept is the argument using disagreement about simultaneity resolves the paradox. But WHAT IS "THE PARADOX"? Is it just that it fits in one frame and doesn't in another, with no additional argument about why anyone else but you should consider this fact alone to be a "paradox"? I have been ridiculed for taking that position, but ISTM that showing such a disagreement, just shows what we already knew; that clocks in different frames do not necessarily agree on the time something occurs. In my model, there's no reason to expect x and t to equal x' and t', The x and t associated with any specific *localized* event (i.e. an event occurring at a single point in spacetime) are not the same as the x' and t' associated with that same event, for the most part (except for the event at x=0, t=0), so in that sense I agree there's no reason to expect x and t to equal x' and t' for any specific localized event. But the car fitting or not fitting is not a specific localized event, it's a statement about a multiple different localized events that are considered simultaneous in a given frame (for example if there is a moment in a frame when the back of the car is at a localized point x1 inside the garage at the same t-coordinate as the front of the car being at a different localized point x2 inside the garage, then the car is considered to fit according to that frame). and yet with enough clocks and observers, the car will fit and not fit depending on which observer / frame is doing the measuring. So what has the disagreement about simultaneity yielded in resolving the paradox? Nothing! Moreover, IMO, the disagreement about fitting IS the parodox. If not, what do you think it is? AG OK, what if someone said "the disagreement about speed IS the paradox", but didn't have any additional argument about WHY they thought it was paradoxical for different frames to judge speeds of objects differently? Would you say they had any rational basis for their view that there was a paradox there? No, because I could point to relative velocity as the cause of the disagreement, ultimately on the invariance of the SoL, AG As to what *I* think the paradox is, this is something I have told you a million times including earlier on the other thread and I even repeated it earlier on this one, do you really not remember? Sure; it's when there are contradictory results at some local event. In the context of the alleged paradox, I don't see that the disagreement about simultaneity proves anything, since, if proven, it just tells us what we already knew; that fitting and not fillting don't occur at the same time. OTOH, if the observers observe different results when they're juxtaposed, it's a paradox IMO for the same reason as if Clark's definition for a paradox was manifested; different results at the same time. As for your last post on the other thread, I am still working on it. It will take some time before I respond, but I will. AG Jesse 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 Who has ever plotted two frames using the same coordinates? Brent gave two different diagrams, one showing how things look in the coordinates of the garage frame, and one showing how things look in the coordinates of the car frame. In each diagram he has two objects, car and garage, as seen from one frame, and then the other, even though the objects plotted are always observed from the pov of different frames. AG Yes, but so what? That isn't plotting trying to plot the perspective of two different FRAMES in the same graph (the 'error' you referred to above), each individual graph just plots two physical OBJECTS using a *single* frame's coordinates, say x,t. Do you have a problem with the latter? Do you think there is an error inherent in using a given frame to assign coordinates to an OBJECT that is moving relative to that frame, or that an observer in that frame would have any difficulty with making position and time measurements (using her own ruler/clock system) on objects moving relative to herself? Jesse Both diagrams showed the same objects (the car and the garage) and events (such as the back of the car passing the entrance of the garage), but the way different events lines up with the position and time axes of each frame were different, corresponding to a given event having different x,t coordinates in one frame from its x',t' coordinates in another frame. Jesse 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 <https://groups.google.com/d/msgid/everything-list/bd23a281-47d1-48d7-91eb-534fbde6038fn%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/a976d3d6-4495-4d37-9f5c-2d8853adf98bn%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/a976d3d6-4495-4d37-9f5c-2d8853adf98bn%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/b944834f-6438-4ab2-b3d1-a6660d9ff12cn%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/b944834f-6438-4ab2-b3d1-a6660d9ff12cn%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/9500fef7-e758-4f64-b629-72bf0b4d30c0n%40googlegroups.com.
