Stupidity really has no limits 😔 Le dim. 9 févr. 2025, 01:17, Alan Grayson <[email protected]> a écrit :
> > > On Saturday, February 8, 2025 at 3:20:43 PM UTC-7 Alan Grayson wrote: > > On Saturday, February 8, 2025 at 9:23:11 AM UTC-7 Jesse Mazer wrote: > > On Sat, Feb 8, 2025 at 9:35 AM Alan Grayson <[email protected]> wrote: > > > > On Saturday, February 8, 2025 at 12:29:55 AM UTC-7 Alan Grayson wrote: > > The way I see it there are two frames f1 and f2, *one *rod located at the > origin of f1, fixed in f1, but moving wrt f2. Of course, frames are > coordinate systems and our single rod has coordinates in both frames, but > only *EXISTS* in one frame, f1. > > > Is "only exists in one frame" just a synonym for "only has one frame as > its rest frame" or does it mean anything more? You agree the single rod can > be assigned coordinates in both frames, so presumably you agree the > observer in f2 is still able to see and measure the rod. > > > > So, using the formula from the pov of f2, the proper length of the rod in > f1 is L, which is contracted to L'. > > > Yes, that's what I said in point #1 above. > > > Since the rod is fixed in f1, its length is* never* contracted from the > pov of an observer in f1, > > > Yes, that's what I said in point #2 above. > > > but is always contracted from the pov of an observer in f2, which sees the > rod moving with velocity v. > > > Yes, that again agrees with point #1. > > > The bottom line is the what is calculated by f2's observer is NEVER > measured by f1's observer. > > > Calculated using the length contraction equation, or calculated using the > LT? "What is calculated by f2's observer" using the length contraction > equation is just the length in the f2 frame (assuming the f2 observer > inputs the velocity v of the rod in their own frame), not any prediction > about what is measured in f1. > > > *The simplist way to model this problem is to assume a symmetric > situation, a rod in each frame of the same rest length, located at the > respective origins, located at the center of each rod. Then, using the > contraction formula, and assuming a relative velocity of v, observers > within each frame, will measure the rod within each frame as having a non > contracted length, whereas the calculated length of the moving rod it's > observing will be calculated as contracted.* > > > You can introduce a second rod if you like, but then I would request that > you have different names for the two rods--say the rod at rest in O1's > frame (f1) is called R1, and the rod at rest in O2's frame (f2) is called > R2--and that when you make a statement about what any observer predicts > about the length of a rod, you specify which rod you are talking about by > name. Note that if we describe the rods this way, the previous discussion > was only about the rod R1 at rest in f1, there was no rod R2 in that > scenario. I think it would be simpler to stick to that scenario with one > rod viewed in two different frames, but we can also talk about the second > rod R2 if you feel it's essential. > > > > * Neither observer measures the rod in its own frame as contracted,* > > > Yes, that agrees with the previous discussion where we just had the rod > R1, and the observer O1 did not predict it as contracted according to the > length contraction formula (this was point #2 on my list of 4 points which > you agreed with. BTW, you didn't respond to my earlier argument that you > should have no reason to object to point #3, see the argument I made in the > two paragraphs beginning with my comment "I've asked you a bunch of times > before about what you mean when you say there is 'no rod'." Do you intend > to respond to that?) > > > * but the rod from the perspective of either frame using the formula is > calculated as contracted.* > > > This is the sort of phrase I would want to avoid because it doesn't > specify which rod is being predicted in which frame using which formula. > Using the length contraction equation, we get the prediction that the rod > R1 is contracted on O2's frame, but that the rod R2 has no contraction in > O2's frame; and the length contraction equation also gives us the > symmetrical prediction that the rod R2 is contracted in O1's frame, but > that the rod R1 has no contraction in O1's frame. And I claim that if we > start with the equations of motion for both R1 and R2 in one frame and use > the LT formula to predict R1 and R2 in the other frame, we get the same > predictions as above; for example if we take the coordinates of both rods > in O1's frame as input, and use the LT to translate to O2's frame as > output, we again get the prediction that the rod R1 is contracted in O2's > frame, but that the rod R2 has no contraction in O2's frame. > > > * For this reason I claim the contraction formula never predicts what it > calculates as the measurement in the target or image frame.* > > > If by "target or image frame" you mean the same thing as what I call the > "output" of the LT (you seemed to deny this is what you meant by 'target > frame' in an earlier post, but you never explained what I got wrong), then > I would deny that there's any disagreement between the LT prediction and > the measurement, see the paragraph above. Do you disagree with my claim in > the last sentence that "if we take the coordinates of both rods in O1's > frame as input, and use the LT to translate to O2's frame as output, we > again get the prediction that the rod R1 is contracted in O2's frame, but > that the rod R2 has no contraction in O2's frame"? Or do you agree with > that, but think that this prediction differs from what O2 actually measures > for R1 and R2? > > > > * Also, if one of the frames does NOT have a rod, I mean that the > contraction formula cannot be applied, since without a rod, the proper or > rest frame length is undefined, or if you prefer equals zero.* > > > But you still aren't defining what you mean by vague phrases like "the rod > doesn't exist in one frame" or "one of the frames does not have a rod", I > keep asking you over and over and over and over again if you're just saying > there is no rod *at rest in* the frame you're referring to, or if you mean > something different, but you never answer. > > In our previous scenario where there was just one rod R1 at rest in O1's > frame, would you say that O2 doesn't "have a rod" because there is no > second rod at rest in O2's frame? But if that's all you mean, surely you > can't be claiming that there is anything wrong with O2 applying the length > contraction formula to find the length in his own frame of that rod R1 > despite the fact that R1 isn't at rest in O2? You had no problem with this > when I stated it as point #1 in my list of 4 points from before. > > It seems like you're just exploiting the verbal ambiguity between O2 > "having a rod" in the sense of there being a rod at rest in O2, vs. "having > a rod" in the sense of having the values of L and v associated with some > rod to plug into the length contraction formula. But these are totally > different meanings, and this ambiguity would never arise if you would just > give me a straight answer to my question asking you to define what you mean > by such phrases. > > > * A frame without a rod presumably knows the coordinates of the rod in a > frame which has a rod, and I think you're trying to show below that when > the LT is applied to the coordinates of the rod in any moving frame, will > show that my conclusion about contraction and measurement in the symmetric > situation is mistaken. I need to further study your example using the LT to > make an intelligent comment. AG* > > In contrast, the LT equations *can* be used to predict what is measured in > f1 if you are given the coordinates of the rod in f2, and in this case the > prediction will agree with my point #2 above that says the rod has no > contraction in f1. > > > > *If so, then the LT and contraction formula disagree in their predictions > since from the pov of f2, f1 is moving and must be contracted from the pov > of f2. I'll have to study further what the LT predicts. AG * > > > *My conjecture is that you might have lost the fact of motion between f1 > and f2 when you used the rod's coordinates in f2 and the LT to calculate > the measured value of rod in f1 and got its rest length. I suggest you > review what you did, and if you don't find this error, I will study your > results in detail. AG* > > > No, I didn't lose that. The equations of motion in the unprimed f2 frame > described a rod R1 which is moving at 0.6c in the +x direction of the f2 > frame, then I used the LT equations to translate R1's coordinates to a > primed f1 frame which is also moving at 0.6c in the +x direction relative > to the f2 frame. In this case the LT equations for x-->x' and t-->t' look > like this (using units of light-seconds for length and seconds for time so > that c=1): > > x' = 1.25*(x - 0.6*t) > t' = 1.25*(t - 0.6*x) > > The 0.6 in these equations represents the relative velocity of 0.6c > between f1 and f2, and the 1.25 is the gamma factor which is also based on > that relative velocity (since 1/sqrt[1 - 0.6c^2/c^] = 1/(1 - 0.36) = 1/0.64 > = 1.25). So yes, please study that numerical example and see if you agree > with all the steps, and if not tell me where you disagree. > > Jesse > > > *Let me make a constructive criticism; don't parse my comments. Read them > in their entirety before responding. And make better use of your > imagination in understanding my comments, which are quite clear and not at > all ambiguous as you claim. AG* > > > *Congratulations to us! We've proven that SR has a fatal irreparable flaw; > specifically, that the LT, using coordinate transformations, predicts the > rest length of a rod in f1 as calculated from f2, where the frames have non > zero relative velocity v; whereas the contraction formula derived from the > LT, always predicts a contracted length under the same conditions, and > never the rest length. Where shall we publish? AG * > > > > You can, of course, reverse the frames which do the calculations, but you > can't get symmetric results because *there is NO rod in f2's frame *for > which the formula can be applied. > > > If by "no rod in f2's frame" you just mean no rod *at rest* in f2's frame, > and if "the formula" in your statement refers to the LT rather than the > length contraction formula, then I would just point out that the LT > equations do not *require* that an object be at rest in the input frame to > predict the coordinates of the same object in the output frame. See my > numerical example a few posts back, where I gave these coordinates for the > front and back of a moving rod in the unprimed frame (corresponding to what > you're calling the f2 frame): > > Back of the rod: x = 0.6c*t > Front of the rod: x = 8 + 0.6c*t > > Do you AGREE/DISAGREE that these equations for position as a function of > time describe a rod which is *not* at rest in f2? For example, at t=0 the > equations tell you that the back of the rod is at x=0 and the front of the > rod is at x=8, then 5 seconds later at t=5 the equations tell you the back > of the rod is at x=3 and the front of the rod is at x=11, so the whole rod > has moved forward by 3 light-seconds in those 5 seconds. So maybe the rod > doesn't "exist" in this frame f2 according to your idiosyncratic phrasing, > but it is clearly being *described* in terms of the coordinates of f2, and > that description includes the fact that it is moving relative to f2. > > If we look at the set of spacetime coordinates that the front or back of > rod will pass through in this frame, we can perfectly well use those > unprimed coordinates as inputs for the x-->x' and t-->t' Lorentz > transformation equations, and get the set of primed coordinates the front > and back of the rod pass through in the f1 frame as output. For example if > you take x=3, t=5 for a point the back end passes through, you can plug > those values into the LT equations x' = 1.25*(x - 0.6*t) and t' = 1.25*(t - > 0.6*x), and get x'=0, t'=4 as. output. Do you AGREE/DISAGREE that the LT > can be used this way? > > 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/49ff3541-2e6f-4f0d-91f8-d5077889fe3an%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/49ff3541-2e6f-4f0d-91f8-d5077889fe3an%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]. 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