*In mathematics, functions have domains and ranges, standard terminology. A function maps domain sets to range sets. The image of a function is the set containing its range. Again, standard mathematical terminology. The contraction formula, derived for the LT, is a function. With me so far? AG*
*Now about the substance. If coordinate frame O2 is the domain of the formula function, the x values are elemments in its domain, and the x' values are elements in its range. The contraction formula is a mapping or correspondence from coordinate sets O2 to coordinate sets O1, the moving frame in relative motion wrt O2. That is, the contraction formula maps O2, the frame with no rod, to O1, the frame with the rod. You say, and I now agree, that there's no contraction of the one and only rod in O1. So what happened to contraction? So, AFAICT, contrary to what relativity claims, contraction doesn't exist! Note also what happens to the Parking Pardox. No contraction of any object in any frame. Paradox solved! Are we having fun yet? AG* On Sunday, February 2, 2025 at 7:52:55 PM UTC-7 Jesse Mazer wrote: > On Sun, Feb 2, 2025 at 8:17 PM Alan Grayson <[email protected]> wrote: > >> >> >> On Sunday, February 2, 2025 at 4:31:48 PM UTC-7 Jesse Mazer wrote: >> >> On Sun, Feb 2, 2025 at 5:08 PM Alan Grayson <[email protected]> wrote: >> >> On Sunday, February 2, 2025 at 2:43:09 PM UTC-7 Jesse Mazer wrote: >> >> On Sun, Feb 2, 2025 at 12:44 PM Alan Grayson <[email protected]> wrote: >> >> I will study your post and respond later. For now, let me say that the >> GPS situation is irrelevant. It just shows that time dilation is real. >> Nothing to do with length contraction. Also, after reading some of your >> earlier comments, I agree that in the frame containing the rod, its length >> is not contracted. This is the rest frame with the rod at the origin. The >> frame from which the LT is applied has an observer at the origin, but no >> rod, and is in relative motion compared to the frame with the rod. I hope >> you have no objections to this comment. If you have any objections, please >> let me know. AG >> >> >> Mostly sounds fine but the only thing I'd want to double check is that >> when you say "The frame from which the LT is applied has an observer at the >> origin, but no rod", do you just mean that the rod is not at rest in this >> observer's frame? The rod is still measurable and can be assigned >> coordinates with changing position as a function of time in this observer's >> frame (the observer you called O2 in your earlier post), agreed? >> >> >> I want two frames with the rod in one, which I thought was your initial >> model. The rod is situated and fixed at the origin, and there is no rod in >> the frame using the LT; >> >> >> But as I asked you repeatedly, when you say no rod "in" the O2 frame do >> you just mean there is no rod that's *at rest relative to* the O2 frame, or >> are you somehow denying that any given physical object like a rod is >> assigned coordinates by *all* frames including the O2 frame in which the >> rod is moving? >> >> > You still haven't answered this question, and it seems like it might be > important given some of your other phrases below... > > >> >> >> or if you prefer we can model the situation with a rod in each frame, at >> rest, both at origin, and their rest lengths are unimportant. >> >> >> No need for two rods, provided you agree above that the O2 frame still >> assigns coordinates to the rod even though the rod is not at rest in that >> frame. >> >> >> *OK. One rod, and frame with rod is given coordinates in both frames. For >> me, x ---> x' means a LT from frame with no rod, * >> > > Does "frame with no rod" just mean "frame with no rod at rest in it", or > are you somehow claiming there's a frame that doesn't "see" the rod at all > in terms of being able to measure it and assign coordinates to it? > > > >> *to frame with rod, and from this there's the implication of contraction >> in x' frame, with rod. Do you agree or not? AG* >> >> >> >> Drawing on the GPS situation, from any rod/frame applying the LT, the >> formula IMO predicts the measured length in the frame it is observing, >> >> >> GPS is distinct because the clocks don't just tick at their natural rate >> >> >> *They tick naturally and are then reset to presumably synchronize them >> with orbiting clock. AG* >> >> but are artificially adjusted, as I said. If the rod is at rest in O1 and >> moving relative to O2, can we assume we are initially given the coordinates >> of the rod as measured in O2, then then O2 frame is the one "applying" the >> LT to predict the coordinates in the frame O1, so that O1 would be "the >> frame it is observing" in your statement above? >> >> >> *Yes, except we don't have to assume the moving rod has coordinates in >> O2. AG * >> > > 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" > > > >> >> >> similar to the Earth bound clocks in GPS which predict the time delays in >> the orbiting clocks. For this reason, in the contraction case, the >> frame/observer applying the LT, doesn't predict the contraction in >> observer's own frame (which doesn't exist if there's one rod in the model), >> but in the frame with the rod. >> >> >> No, as my numerical example shows, if we start with the coordinates of >> the rod in O2 and use the LT to predict its coordinates in O1, we get a >> prediction of NO contraction of the rod in O1; the prediction will be that >> the rod has its "proper length" in the O1 frame. >> >> >> However, and this is where I get my prediction which you object to; in >> this frame, the frame with the rod, the only prediction possible is zero >> contraction. >> >> >> If you are talking about the type of calculation I describe above, I >> *agree* the prediction would be zero contraction in the O1 frame, which >> matches the fact that no contraction is MEASURED in the O1 frame. >> >> >> *Yes, this is what I've been saying. AG* >> >> >> It was you who claimed that there was some prediction using the LT that >> would conflict with the fact we both agree on that no contraction is >> measured in the frame where the rod is at rest. >> >> >> *I changed my pov when reading one of your previous posts. But since >> there's no contraction measured in frame where the rod exists* >> > > Are you saying the rod literally does not "exist" in other frames in the > sense of not being measured at all, or are you just saying the rod is not > at rest in other frames? If you're somehow saying the rod is not assigned > coordinates at all in the O2 frame, that doesn't make sense, see above. > > > >> * and is at rest (even though the frame is in relative motion), the LT >> has no other possible predictions, so it seems that length contraction >> never occurs!* >> > > Sure length contraction occurs, in the example it occurs for the O2 > observer who sees the rod in motion. If the rod has a proper length of 10 > light-seconds, and the O2 observer says the BACK of the rod passed by x=3 > and t=5 in his coordinate system, and the FRONT of the rod passed by x=11 > and t=5 in his system, then the distance between the front and back at the > single moment t=5 in this frame must be 11 - 3 = 8, so that's what the O2 > judges the rod's length to be, a length which is shorter than the rod's > proper length measured by the O1 observer. > > If you want to start from coordinates in one frame and then use the LT to > predict coordinates in another, and you're asking about how this could ever > lead to a prediction of contraction, one option would be to *start* from > the coordinates in O1's frame where the rod is at rest (unlike in my > numerical example where I started with the rod's coordinates in the frame > where the rod was moving), then apply the LT to *predict* the coordinates > in O2's frame where the rod is moving. If we did that instead of the > opposite, in that case we *would* get a prediction of a contracted length > in the predicted frame O2. I could give a different numerical example > illustrating this, if you would actually be interested in reading through > it. > > > >> * This is where the rubber hits the road in our disagreement about what >> the LT predicts, and what is measured. If contraction is never measured >> because it never occurs, the "predictions" of the LT are worthless to the >> point of not existing. I hope you're not going to tell me now, that x' in x >> --> x' refers to the frame applying the LT. AG* >> >> >> >> Hence, the LT doesn't do as you claim, and it doesn't function like the >> GPS situation. Moreover, I recall you used spacetime diagrams to show >> length *expansion *in your frame at relative speed, but never before >> have I heard or read of such a claim, which raises the proverbial red flag. >> AG >> >> >> As I stated repeatedly, by "expansion" I just meant the length would be >> predicted as larger in the second frame (O1 above) compared to the first >> frame where the rod was moving (O2 above), >> >> >> *How could that be if the result of the LT is x', not x?* >> > > In my numerical example I treated the primed frame as the one where the > rod is at rest, i.e. O1 in your terminology. So, going from x-->x' takes > you from O2 to O1. > > Also note however that the complete set of LT equations include both > x-->x' and x'-->x, so you're free to go in either direction. > > > >> * The rod is not contracted in O1 even though its moving relative to O2, >> and the length of the rod is not in the image of anything in O2?* >> > > If you want to do the LT from O2 to O1 you have to start with the > coordinates of the rod in O2, I don't know if that's what you mean by "the > image of anything" or if you just mean that we don't obtain the O2 > coordinates as a result of a LT. > > > >> * Remember; the LT prediction in O1 is no contraction. I think this is >> exactly where we disagree about what the formula predicts.* >> > > What do you think we are disagreeing about in terms of what the formula > predicts? I've said that if you start with the coordinates in O2 and use > the LT to predict O1, the prediction is no contraction in O1. > > Jesse > > > >> * Maybe in your reply we can finally resolve this issue. AG* >> >> I wasn't talking about expansion relative to the rod's proper length. The >> prediction will be that the rod has its proper length in frame O1, i.e. "no >> contraction" relative to the proper length. >> >> Jesse >> >> >> >> >> If you do agree, then I don't see any objections, and I'd note that this >> matches the type of scenario I was analyzing in my numerical example at >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/giZVF9PpDQAJ >> where I started from the unprimed frame of an observer who measures the rod >> to be moving at 0.8c, then used the LT to figure out the corresponding >> coordinates in the primed frame where the rod was at rest. >> >> Jesse >> >> >> >> >> On Sunday, February 2, 2025 at 8:27:46 AM UTC-7 Jesse Mazer wrote: >> >> On Sun, Feb 2, 2025 at 2:56 AM Alan Grayson <[email protected]> wrote: >> >> On Sunday, February 2, 2025 at 12:46:08 AM UTC-7 Alan Grayson wrote: >> >> On Saturday, February 1, 2025 at 9:50:28 PM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 11:10 PM Alan Grayson <[email protected]> wrote: >> >> >> >> On Saturday, February 1, 2025 at 8:11:53 PM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 6:42 PM Alan Grayson <[email protected]> wrote: >> >> >> >> On Saturday, February 1, 2025 at 4:33:24 PM UTC-7 Alan Grayson wrote: >> >> On Saturday, February 1, 2025 at 4:02:27 PM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 5:36 PM Alan Grayson <[email protected]> wrote: >> >> >> >> On Saturday, February 1, 2025 at 3:19:32 PM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 4:57 PM Alan Grayson <[email protected]> wrote: >> >> >> >> On Saturday, February 1, 2025 at 11:58:57 AM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 12:38 PM Alan Grayson <[email protected]> wrote: >> >> >> >> On Saturday, February 1, 2025 at 8:42:49 AM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 3:01 AM Alan Grayson <[email protected]> wrote: >> >> >> >> On Friday, January 31, 2025 at 11:35:08 PM UTC-7 Jesse Mazer wrote: >> >> On Sat, Feb 1, 2025 at 12:55 AM Alan Grayson <[email protected]> wrote: >> >> Any comment on this? >> >> >> *No. I'm not comfortable with spacetime diagrams. Further, since >> coordinates are irrelevant to length contraction (the V in the formula >> doesn't depend on coordinates), so I regard it as a distraction. AG * >> >> >> The "any comment this" above doesn't refer to any spacetime diagrams, >> it's referring to my comment right above it about how neither frame is >> typically designated as "moving" or "at rest" by textbooks, and how >> textbooks give both x --> x' equations and x' --> x equations side by side. >> Do you disagree with that? >> >> Maybe you were trying to respond to my second "any comment on this" about >> the textbook citation with the diagram below? If so you're free to ignore >> the actual diagram on p. 141 (apart from the little cartoons which clearly >> show the author is trying to indicate to the reader that the train is >> longer for the observer on the train than for the observer on the ground) >> and just note the parts of the text on p. 140 where he says the length of >> the train in the unprimed ground frame, AB, is shorter than the length of >> the train in the primed frame, CB. >> >> >> *All the textbooks and articles I've read about SR claim length >> contraction in any frame in relative motion as predicted by the LT from the >> pov of another frame in relative motion.* >> >> >> Can you point to any textbook or article that uses a phrase like that? I >> think what you will find is that they say the v that appears in the length >> contraction equation is just the velocity of the object in whatever frame >> you want to know the length in, without need to refer to any other frames. >> And if they do refer to multiple frames, they will say that the length of >> an object is contracted by sqrt(1 - v^2/c^2) in a frame that is moving at >> velocity v *relative to the object's own rest frame*. Do you disagree that >> most textbooks would phrase it in one of these two ways? >> >> >> *Why are you splitting hairs unnecessarily? Given relative motion, >> there's a symmetry with regard to length contraction, so I retained >> reference to the symmety. Whether that's exactly how it's stated in >> textbooks I can't say; nor does it matter. AG * >> >> >> If by "symmetry with regard to length contraction" you mean two frames >> with relative motion v will see the same length contraction factor sqrt(1 - >> v^2/c^2) for a given object, >> >> >> *By symmetry with regard to length contraction, I was thinking of two >> frames F1 ad F2 in relative motion, and from F1 the LT predicts length >> contraction in F2, and vice-versa, provided there are objects in each frame >> to contract, whether moving their respective frames or at rest therein. AG* >> >> >> >> Length contraction in this type of scenario needn't be symmetrical, >> though it could be for some special cases, like if the objects were each at >> rest in one of the two frames. Say object O1 is at rest in F1, and object >> O2 is at rest in F2. In that case the velocity of F2 relative to O1's rest >> frame (which gives the contraction of O1 in frame F2 by my definition) is >> equal to the velocity v of F2 relative to F1, and likewise the velocity of >> F1 relative to O2's rest frame (which gives the contraction of O2 in frame >> F1 by my definition) is equal to the velocity -v of F1 relative to F2. And >> since velocity is squared in the length contraction equation, here you do >> get the same contraction factor when you plug in v or -v. >> >> >> >> >> definition I gave would contradict this. Suppose you have two frames >> A and B, with B moving at velocity v relative to A, and you have a rod >> which is *at rest in B*, and therefore moving at velocity v >> relative to A. Then if you want to know the length of the rod in frame B, >> according to *my* definition above the velocity you should plug >> into the equation is *B's velocity relative to the rod's rest frame*, which >> is zero in this case since frame B *is* the rod's rest frame, so there is >> no length contraction of that rod in frame B. >> >> *I think your definition is wrong, or minimally confusing. If you want to >> predict the contraction of a rod at rest in frame B, you must calculate it >> from frame A assuming the frames are in relative motion with velocity V, >> which both frames share (since the motion is relative). AG* >> >> >> No, you don't need to do that at all, you just need the velocity of B >> relative to the rod's rest frame, or equivalently the velocity of the rod >> relative to B. Why are you so confident that you need to refer to another >> frame A that is neither the frame B that you want to know the length in, >> nor the rod's rest frame, if you can't point to any textbook or other >> source written by a physicist that says something like this? Did you ever >> take an actual class on relativity, or do an extended period of serious >> self-study, and are going on your memory of that? Or is it just an >> impression you've picked up from more sporadic reading? >> >> >> >> >> So, do you disagree that a textbook will say that if you want to know the >> length of an object in some frame S, the velocity you need to plug into the >> length contraction equation is the velocity of S relative to the OBJECT'S >> OWN REST FRAME, not relative to any other frame? >> >> >> *I disagree. It's the velocity of the other frame which must be plugged >> into the contraction equation; and assuming the motion is relative, it's >> the same V as the velocity of that other frame. * >> >> >> Here is a source that agrees with my definition, the textbook "Special >> Relativity" by T.M. Helliwell. First is an image showing all the main text >> on p. 54, then a zoomed in version on the part that says that "If an object >> has length D in its rest frame", then the length contraction equation d = >> D*sqrt(1 - v^2/c^2) is giving you the length "in a frame moving at speed v >> relative to the rest frame". You can see there is no mention of any other >> frame besides the frame we want to know the length in, and the object's >> rest frame. >> >> [image: helliwellp54.jpg] >> >> >> >> >> [image: helliwellp54zoom.jpg] >> >> >> *While this definition is correct, I think you're misinterpreting it. The >> rest frame the author mentions is in relative motion wrt the frame applying >> the LT. If there's relative motion, there must be (at least) two frames >> involved, which is why they're distinguished between unprimed and primed. >> The unprimed frame applies the LT to predict length contraction in the >> primed frame moving at relative speed v. And it is this v which is plugged >> into contraction formula. While the primed frame contains the object >> generally at rest therein (but not in your example), it's nevertheless in >> motiion wrt the unprimed frame, which makes the prediction of what the >> primed frame will measure. AG* >> >> >> How am I misinterpreting? The definition I stated myself already said you >> could consider two frames: the frame where you want to know the length >> contraction, and the object's rest frame. >> >> >> *Your error is subtle and it is incumbant on you to determine how it >> effects your analysis of the LT and its prediction of length contraction. >> The two frames you allude to, are in fact the same frame. In the moving >> frame in relative motion,* >> >> >> I don't know what this phrase means--are you going back on what you said >> earlier that singular designations like "moving frame" can be discarded >> because relative comparative terms are "superior"? If not and this was just >> a verbal slip, please specify "moving frame RELATIVE TO WHAT?" and >> "relative motion RELATIVE TO WHAT?" >> >> The two frames that I alluded to are the rest frame of an object, and the >> frame of an observer who has some velocity v relative to the object. And >> that's exactly what's being referred to in the textbook excerpt above, >> where say "an object has length D in its rest frame" and then talk about >> its length "in a frame moving at speed v relative to the rest frame." >> Clearly if v is nonzero these are not the same frame! >> >> >> >> * the proper length is unchanged, although it is resident in said frame.* >> >> >> Does "said frame" refer to the rest frame of the observer, or the rest >> frame of the object? And when you say "it is resident in said frame", does >> "it" refer to the object rather than the observer, and does "resident in" >> just mean "at rest in" or does it mean something else? >> >> >> *The only other frame is the one from which the LT is applied. If this >> other frame didn't exist, relative motion wouldn't exist. AG* >> >> >> I don't know what you mean by saying a frame doesn't "exist". Given a >> particular physical scenario in relativity stated in the coordinates of >> some frame, you are always *free* to choose any one of an infinite number >> of other frames to translate into, so those other frames always "exist" in >> the sense of being available to you if you wish. But a given textbook >> problem will only ask for calculations in some specific frames--if the >> problem doesn't REFER EXPLICITLY to some frame A, is that all you mean by >> saying that frame A "doesn't exist" in the problem? Hopefully you agree >> that the textbook author is not denying your freedom to refer to/use frame >> A if you want to! >> >> >> *It's very annoying. In the definition you added above, the author uses >> the phrase "rest frame" and presumably you understand it, but when I use it >> you find the phrase unintelligible, claiming I'm going back to some >> previous unintelligible language.* >> >> >> The author said "an object has length D in its rest frame" and then later >> in the same sentence referred to "a frame moving at speed v relative to the >> rest frame", so there was no doubt from that context it was referring to >> the object's rest frame. I didn't see any clear context like that in your >> use of phrases like "In the moving frame in relative motion". >> >> >> >> * Look at it this way; we have two OBSERVERS, O1 and O2, using different >> frames of reference, whose origins are moving wrt to each other at relative >> velocity v. The former contains a rod of fixed proper length which O1 can >> measure at any time and always gets the SAME measurement value L.* >> >> >> OK, so O1 is the object's rest frame. So, according to the textbook >> definition above, if O1 uses the length contraction equation to calculate >> the object's length in his frame, he should find no length contraction >> since O1 has a velocity of 0 relative to the object's rest frame; but if O2 >> uses the length contraction equation to calculate the length in *his* >> frame, he should find it's contracted by v, the speed of O2 relative to the >> object's rest frame (O1). Do you disagree? Keep in mind this question is >> just asking about the length contraction equation *as defined by the >> textbook*, not about the LT which is distinct from the length contraction >> equation. And of course you are free to claim the textbook is *wrong* if >> you like, I'm just asking if you AGREE or DISAGREE that this is what the >> textbook author would say we should predict about this situation, given his >> definition of how the length contraction equation works. >> >> >> Can you answer this agree/disagree question about what the textbook is >> saying we'd predict in your scenario if we use the length contraction >> equation rather than the LT? >> >> >> >> >> >> * These OBSERVERS are in relative motion. O2 uses the LT to calculate the >> contraction of L, presumably what O1 will measure.* >> >> >> If O2 starts with the coordinates of the rod in their own frame, and then >> uses the LT to translate to the coordinates of the rod in the O1 frame >> including its length in that frame, they will get the prediction that the >> rod has its proper length L in the O1 frame, that's what I showed you >> explicitly with my numerical example at >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/giZVF9PpDQAJ >> which you never responded to, or provided your own calculation to support >> your completely wrong claim that the prediction would be contraction in the >> O1 frame. Instead of giving a calculation/argument of your own, your lame >> excuse for not looking at my example was that it supposedly contradicted >> what textbooks would say or what would be predicted by the length >> contraction equation, but I've given you textbook citations that explicitly >> contradict this, and you've given no textbook sources (or other sources >> written by physicists, like web pages) to support your claims. All you have >> is repeated ASSERTIONS which seem to be based on nothing whatsoever but >> your own blind faith that if this is how you think the LT works, it must be >> true! >> >> >> >> * Notice that O1, the frame containing the rod of length L, NEVER >> MEASURES IT'S CONTRACTED VALUE. * >> >> >> THERE IS NO PREDICTION OF A CONTRACTED LENGTH IN O1, that's just your >> assertion which you haven't supported with any calculations or citations. >> >> >> *The calculation is very simple. Use the LT from O1 to get the >> contraction in O1. You'll get L since v in the formula is zero. AG* >> >> >> Yes, the idea that you'll get a length of L in O1 is exactly what I said >> in the comment you were responding to -- I wrote "THERE IS NO PREDICTION OF >> A CONTRACTED LENGTH IN O1", where by "contracted length" I meant any length >> *smaller* than the object's proper length L. Only in O2 where the object's >> velocity is non-zero is there a prediction of a contracted length. And this >> prediction, namely "contracted length in O2, no contracted length in O1", >> will hold regardless of whether you just use the length contraction formula >> in a given frame (see above), or if you are given the coordinates of the >> rod in one frame and then use the LT to translate to the other frame (as I >> did in my numerical example where the rod was at rest in one of the two >> frames I defined, and I started with the coordinates in the frame where the >> rod was moving and then used the LT to get its coordinates in the other >> frame where it was at rest). >> >> Jesse >> >> >> *Why are you wasting my time, playng games, and demanding a mathematical >> proof of something you know is true? AG* >> >> >> >> What do you think I "know is true"? Are you referring to the point above >> that there is NO prediction of the rod contracting in the rest frame of O1 >> (which is also the rod's rest frame), either if we use the length >> contraction formula or if we start with the coordinates in O2's frame and >> then use the LT to derive the coordinates in O1's frame? If you agree with >> that, great, that shows that there is absolutely no conflict between what >> is PREDICTED by the length contraction formula and the LT vs. what is >> MEASURED by the observer O1 using his own measuring instruments, both >> prediction and measurement say "no contraction of the rod in O1's frame". >> >> >> >> >> >> *NEVER! O1 always the rod's length as L . So we can call this "the rest >> frame". But O1 is in relative motion wrt O2, and is applying the LT, So we >> can ALSO call O1 the observer in the MOVING frame. So, O1 is resident in >> the rest frame AND the moving frame.* >> >> >> You understand that the LT has absolutely nothing to do with which frame >> we label as "the moving frame" or "the rest frame" right? The LT is >> mathematical, these verbal labels are totally irrelevant to calculating >> anything. >> >> >> *BS! The contraction formula is derived from the LT. Moreover, unless >> it's known from which frame we are calculating contraction,* >> >> >> I didn't say anything not knowing which frame we are calculating, I just >> said it doesn't matter which you label as "the moving frame" or "the rest >> frame" as you were doing above (non-comparative terms I thought you had >> agreed to drop, but I guess you are going back on the one example where you >> claimed you were willing to admit you were wrong about something). >> >> >> *I told you quite clearly. We need to distinguish the frame wherein the >> rod resides, from the frame applying the contraction formula.* >> >> >> I asked you clearly several times if you are using the language of the >> frame where the rod "resides" just to mean the frame in which the rod is at >> rest, or something else, and you never responded. If you do just mean the >> rest frame, then in the case of O1 using the length contraction formula, O1 >> *is* the rod's rest frame, that's why there is no contraction of the rod in >> that frame. If "frame wherein the rod resides" does NOT just mean the rod's >> rest frame, then you'd need to explain your meaning because I don't know >> what else that phrase might mean. >> >> >> * And in response you bring up your defacto claim that I've breached my >> commitment about proper language. AG* >> >> >> You can label the frame of O1 and the rod as "the moving frame" and the >> frame of O2 as "the rest frame", or you can label the frame of O1 and the >> rod as "the rest frame" and the frame of O2 as "the moving frame", these >> verbal labels make absolutely no difference if you are asked to calculate >> the answer to some frame-dependent quantitative question like "what is the >> length of the rod in O1's frame". Note that this question DOES clearly tell >> us what frame we are using, it just doesn't use any non-comparative terms >> for rest/motion. >> >> >> * we won't get any contraction! Now you know why the LT or contraction >> formula does NOT tell us what is actually MEASURED in the frame containing >> the rod. Are we done yet? AG* >> >> >> It does tell you what is measured--both the length contraction formula >> and the LT would PREDICT that the rod has its proper length L in the O1 >> frame, which you seemed to agree with above when you said "Use the LT from >> O1 to get the contraction in O1. You'll get L since v in the formula is >> zero." Do you not agree that the observer O1 who sees the rod at rest would >> also MEASURE the rod to have length L? Isn't that a perfect agreement >> between PREDICTION and MEASUREMENT? >> >> >> *No, definitely not. You've moved the goal post. The question is whether >> the contraction formula, when applied from a frame NOT containing the rod, >> makes a correct PREDICTION of what the frame containing the rod will >> actually measure.* >> >> >> That doesn't make sense, how could the length contraction formula be >> "applied" in one frame A to make a prediction about what a different frame >> B would measure? The contraction formula is only designed to answer >> the question "if you have a rod of proper length L whose rest frame is >> moving at speed v relative to some frame A, what is its length of the rod >> in that frame A?" The formula simply isn't designed to translate between >> the coordinates of different frames, are you talking about the LT instead? >> >> If you are talking about the LT, I already showed you with a numerical >> example that if you start with the coordinates of a rod which is moving in >> the unprimed frame (a frame 'not containing the rod', assuming by 'not >> containing' you just mean 'not at rest in'), then use the LT to translate >> to a primed frame where the rod is at rest (i.e. the frame containing the >> rod), you get the PREDICTION that in the primed frame the rod has its >> maximum length, i.e its proper length, which is also what is MEASURED by >> observers in the primed frame. If you still disagree with that statement >> about the prediction based on the LT, you have presented no calculations of >> your own or citations to back up your disagreement, nor have you even >> looked at my example to see if you could find a flaw in it. >> >> >> >> * Admit it. This frame NEVER measures the rod contracted! AG * >> >> >> Why are you asking me to "admit" that when I have said it all along? The >> frame O1 where the rod is at rest never measures the rod as contracted, in >> perfect agreement with what is PREDICTED if you use either the length >> contraction formula or the LT to calculate the length of the rod in the >> frame O1 where it is at rest, since neither of those calculations will >> predict it as contracted in O1. >> >> >> >> *This is a worthless discussion. You refuse to admit that the contraction >> formula, derived from the LT, and applied by a frame in relative motion wrt >> the frame containing the rod, in that frame, wherein the rod resides, NEVER >> measures its length contracted.* >> >> >> I don't "refuse to admit" that, I have literally agreed with that point >> about what is MEASURED over and over and over and over and over and over >> again (you really seem to have serious problems with either reading >> comprehension or memory, I'm sure I could find at least 10 previous posts >> where I have said this) and I've also told you over and over and over and >> over and over and over again that our dispute is about whether this >> agreed-upon measurement result conflicts with what is PREDICTED by either >> the length contraction formula or the LT equations. I say there is no >> conflict, because all forms of relativistic prediction will ALSO tell you >> that there is no length contraction of the rod in its rest frame! >> >> >> *BS! You surely have NOT repeatedly stated what you now claim.* >> >> >> I have, many times, repeated the point that the match between predictions >> and measurements means a match between the fact that there is NO measured >> contraction of an object in the frame where it's at rest, and the fact that >> "no contraction of the object in its own rest frame" is exactly what is >> PREDICTED by any correct application of the length contraction equation or >> the LT. Honestly, I wonder if you have some genuine problems with the >> transfer of information from short-term memory to long-term memory, >> especially when it conflicts with ideas you are fixated on (if you are over >> 65, it might actually be worth it to ask a doctor if they have any tests of >> short-term-->long-term memory transfer). This sort of issue with me >> repeating things over and over and you acting like it's totally new >> information to you has happened with a number of different issues, it was >> also what caused me to give up in frustration on the "ATTN: Jesse" thread >> where we were discussing the garage paradox and kept asking the same >> question about what the "paradox" actually was, and I again gave you my >> answer which and told you it was something I had already "said a million >> time", and in the post at >> https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/bqjNoR6-BQAJ >> you said 'Why don't you copy and paste what you "have said a million times" >> and maybe the alleged truth value will get through'. >> >> Anywhere here are a bunch of examples (both from this thread and the >> earlier "Questions about the Lorentz Transform" thread) where I've repeated >> variants of this same point that our disagreement is not about what is >> MEASURED in the object's rest frame, that I agree the rod is not measured >> to be contracted in the rod's own rest frame, rather our disagreement is >> about whether this measurement is any different from what is PREDICTED by >> the LT or length contraction equation: >> >> Post #1 >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/WN9AFWN8DAAJ >> >> Jesse: The LT simply doesn't "imply" there would be any length >> contraction of the rod "in the frame of the rod", so your premise here is >> completely wrong … Whatever the LT implies about lengths/times in a >> specific inertial frame, it always corresponds exactly to what would >> actually be measured using a system of rulers and clocks which are at rest >> in that frame (the clocks synchronized by the Einstein convention), no >> exceptions. >> >> >> >> Post #2 >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/-P-uereKDAAJ >> >> Alan: That's NOT my claim but what those allegedly knowledgeable about SR >> claim; that the results of the LT give us what is actually MEASURED in the >> target frame. In fact, that's what you claimed in some post on this >> subject. AG >> >> Jesse: Yes, that's what I still claim. The premise of yours that is wrong >> is that when we apply the LT we predict the rod is CONTRACTED in its own >> rest frame. >> >> >> >> Post #3 >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/pkGIai6eDAAJ >> >> Alan: What I claimed is that you can't MEASURE the contraction in its own >> frame. You claim it's possible. >> >> Jesse: No, I never claimed you could "measure the contraction in its own >> frame", I claim it is *not* contracted in its own inertial frame according >> to the LT, so there is no predicted contraction to measure. >> >> >> >> Post #4 >> https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/ximYgKzKDAAJ >> >> Alan: As I clearly recall, you claimed the LT gives us what is actually >> MEASURED in the target frame, and I objected. If there's no physical >> contraction that can be MEASURED in the target frame, then it's reasonable >> to say the LT gives how the situation APPEARS from the pov of the source >> frame. Nonetheless, I think the result is physically real in the target >> frame even if it can't be measured. AG >> >> Jesse: No, what is measured matches exactly with what is predicted by the >> LT. I say that (1) The LT predicts there is *no* physical contraction of >> the rod in the rod's frame (i.e. the inertial frame where the rod has a >> velocity of 0), and (2) measurements show there is no physical contraction >> of the rod in the rod's frame. You apparently assume (1a) the LT predicts >> there *is* physical contraction of the rod in the rod's frame, and that's >> why you think there is a conflict with (2). If so, the problem is just that >> (1a) is false as a statement about what the LT predict. >> >> >> Post #5 >> https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/8iY_fUUlCQAJ >> >> Jesse: But if you use the LT to transform into a "target frame" where an >> object has a velocity of zero (like the rod in your earlier example), the >> LT doesn't *predict* any time dilation or length contraction of the object >> in that frame, that's what I told you repeatedly >> >> >> Post #6 >> https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/FbbF0L3fBwAJ >> >> Alan: The LT doesn't do what you claimed it does; tell us, or PREDICTS, >> what the target frame will MEASURE. AG >> >> Jesse: That's just an empty assertion with no reasoning to back it up. If >> you think my previous statement somehow supports it, you must have some >> basic misunderstanding of what I wrote -- what I said was that for an >> object with v_rt = 0, the LT predicts the object will have its MAXIMUM >> length in the target frame, NOT be contracted, and measurements in the >> target frame would match this prediction. >> >> … >> >> Jesse: if an object is at rest in the target frame then THE LT DOES NOT >> PREDICT ANY LENGTH CONTRACTION/TIME DILATION OF THAT OBJECT IN THE TARGET >> FRAME, so there is NO CONFLICT with the fact that measurements of that >> object in the target frame will show no length contraction/time dilation. >> >> >> Post #7 >> https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/wRt33LvjBwAJ >> >> Alan: All along you've claimed the LT predicts what is actually measured >> in the target frame. Now you deny this >> >> Jesse: No I don't, and I have no idea what previous statement of mine you >> could possibly read as denying it. >> >> … >> >> Alan: But you claimed that the LT gives us what is measured in the target >> frame, and I claimed it does not. Now you agree with me, but deny your >> original claim. >> >> Jesse: No, I don't agree with you on this and never have. You seem to >> have some major reading comprehension problems here, but what I have been >> saying over and over again (including in the comment immediately above that >> you are somehow misreading as supporting your assertion) is the combination >> of these two claims: >> >> 1. When dealing with a case like the rod which is moving in the source >> frame but where it has velocity v_rt = 0 in the target frame, what the LT >> predicts is that THERE IS NO CONTRACTION OF THE ROD IN THE TARGET FRAME, >> instead the LT predicts the rod is LONGER in the target frame than the >> source frame. >> >> 2. What will be actually measured in the target frame is that THERE IS NO >> CONTRACTION OF THE ROD IN THE TARGET FRAME, instead the rod will be >> measured to be LONGER in the target frame than the source frame. >> >> Assuming for the sake of argument that 1 and 2 are both correct, do you >> think they would indicate a conflict between the LT's predictions and >> actual measurements, yes or no? If you agree they don't conflict but you >> just think either 1 or 2 is incorrect, you will need to provide some >> REASONING, not just empty assertions that there is a conflict. It would >> help if you would follow my request in the previous comment: "If you think >> there is *any* scenario involving inertial frames (not non-inertial >> coordinate systems like GPS) where LT's prediction about the target frame >> doesn't match what's measured in the target frame, please give at least >> some minimal details of what scenario you are imagining (like the rod/Earth >> scenario), specifying the velocity of the *object* in the target frame >> (like v_rt for the rod) separately from the relative v between the two >> frames being related by the LT." >> >> >> Post #8 >> https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/ZGeJ3ZY7EAAJ >> >> Alan: Notice that O1, the frame containing the rod of length L, NEVER >> MEASURES IT'S CONTRACTED VALUE. >> >> Jesse: THERE IS NO PREDICTION OF A CONTRACTED LENGTH IN O1, that's just >> your assertion which you haven't supported with any calculations or >> citations. >> >> >> >> >> >> * What you've repeatedly claimed is that the formula makes flawless >> predictions, but if not about measurements, then about what?* >> >> >> Flawless predictions about measurements, including the fact that a rod >> will show no contraction when measured in its own rest frame. >> >> >> >> * Moreover, you've reduced the concept of contraction to pure >> vacuousness, since you now say the formula only predicts accurately in the >> rest frame,* >> >> >> I never said anything of the kind. If the rod is at rest in observer O1's >> frame and moving in observer O2's frame as you specified, the formulas >> accurately predict that the rod is NOT contracted in O1's frame, and that >> it IS contracted in O2's frame. (I'm not sure if "the rest frame" in your >> statement refers here to the rest frame of some specific object or >> observer, or if you are back to old mistaken idea that it somehow matters >> to the answer to physical questions/calculations which frame we designate >> as 'the rest frame' in a non comparative way) >> >> >> >> * whereas it doesn't from the pov of a rod in relative motion. I would >> agree that the concept is pure nonsense if your pov is valid, except that >> the GPS case establishes that there's something real about contraction. AG * >> >> >> *The GPS case shows there's something real about time dilation,* >> >> >> As I told you before, the GPS case deals with clocks that have been >> *artificially* sped up relative to normal clocks following the same >> spacetime trajectory, in order to keep them synchronized in an >> Earth-centered frame. An analogy would be if we had a bunch of rubber >> rulers with a machine that had clamps on either end that could artificially >> stretch them by whatever desired factor, so for example if the rubber ruler >> had been stretched by a factor of 1.5, an observer in the rubber ruler's >> rest frame could hold a normal rigid ruler up to them and see that the "1 >> meter" and "2 meter" marks on the rubber ruler were actually 1.5 meters >> apart as measured by the normal rigid ruler. If a bunch of these rubber >> rulers were flying around in space, someone could then set the machines to >> artificially stretch the rulers depending on their velocity relative to the >> Earth rest frame, in just the right way as to "compensate" for their >> Lorentz contraction in the Earth frame, so that as measured in the Earth >> frame every ruler would still have the correct Earth-frame distance between >> any pair of markings (for example, a rubber ruler moving at 0.6c would have >> been stretched in its own rest frame by a factor of 1.25 to contract for >> the length contraction factor of 1/1.25, and thus the Earth observer would >> still measure the distance between the "1 meter" and "2 meter" marks as 1 >> meter using his own rigid rulers at rest in the Earth frame). Do you think >> this would demonstrate anything interesting about length contraction, and >> if so what? If you think it would just be a gimmick that doesn't tell us >> anything new about physics, then you should say the same about GPS clocks. >> >> >> >> * but since contraction and dilation both derive from the LT, I conclude >> contraction must also be real, but since it's never actually measured, I >> can't claim I understand what's going on. The only thing I'm sure about is >> that your pov reduces contraction to pure vacuousness. AG * >> >> >> If you think there's a conflict between prediction and measurement, that >> means you think a person could correctly follow the rules for applying the >> length contraction equation or the LT equations and end up with a false >> prediction that there IS contraction of the rod in the frame O1 where the >> rod is at rest, right? If so, THAT'S what I've been clearly disputing all >> along, not your statement about what is measured. >> >> >> *No, I never claimed that; rather that since contraction is never >> measured except in the rest frame,* >> >> >> Again, are you back to using "the rest frame" in a non >> comparative/relative way? If not, WHOSE REST FRAME? There is certainly no >> contraction of the rod in the rod's rest frame, which is also O1's rest >> frame. There is contraction of the rod in O2's frame since the rod has >> nonzero velocity in that frame. Both of these could be measured, and would >> match what would be predicted if either O1 or O2 used the length >> contraction equation to predict length in their own frame. And these would >> also match what would be predicted if you started with the coordinates of >> the rod in O1's frame and then used the LT to predict what would be >> measured in O2's frame, or if you started with the coordinates of the rod >> in O2's frame and then used the LT to predict what would be measured in >> O1's frame. >> >> >> >> * the general prediction for observers in relative motion wrt the object, >> makes no sense. You claim it makes sense since we can use the formula in >> the rest frame.* >> >> >> Again, I don't know what you mean by "the rest frame". Every frame used >> in a problem can be considered the rest frame of SOME object or observer, >> as with the two frames in your formulation which you stated as the rest >> frames of observers O1 and O2. But we don't need to label any of them as >> "the rest frame" in a non-comparative sense. >> >> >> * So what? Why is contraction (and dilation) featured as revolutionary >> resultsof SR if it's never measured. * >> >> >> >> Length contraction/time dilation of an OBJECT which is moving relative to >> a given OBSERVER can be measured in that observer's rest frame. Taking >> observer O2 in your example, the rod would be measured as contracted in >> O2's rest frame since the rod is not at rest in that frame, and likewise if >> there was a clock at rest in the O1 frame then it would be measured as >> running slow in O2's rest frame. >> >> 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/ee28352d-d9cd-42cb-aa31-d789f808af61n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/ee28352d-d9cd-42cb-aa31-d789f808af61n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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