I realize the argument must have moved from the original claim of a paradox which was complete contrived nonsense, unphysical contrived experimental model, to how 'parallels' transport when they're measured to be parallel in the local proper frame where the measurement is made. They're co-moving because they're at rest with respect to each other in the local proper frame where the measurement is made. The Ricci tensor is an invariant. http://math.ucr.edu/home/baez/gr/outline2.html I added the link for those who don't seem to understand what invariant means in relativity theory. Any derivation using relativity theory has to recover the exact same physics as the tensor equations Einstein included in the GR model. I'm not to sure about the non co-moving example you gave. I'm just going to guess. The example you gave isn't an invariant in the theory. It would be frame dependent. These problems can be solved using invariants. The theory can be completely expressed without the use of any coordinate system. So I really don't pay much attention to the algebraic manipulations which conclude the physics is frame dependent. The original post claimed co-moving parallels measured in the local proper frame of the parallels isn't an invariant based on the measurements contrived for the remote coordinate frame.
Bruce, I find your quote of my post confusing as to what you are referring to. Actually, the original post of this thread was about two objects which had relative motion and happened to be parallel in a particular frame, so they wouldn't be co-moving. I don't see that general relativity needs to be introduced into this thread. Tach keeps going back to the case of parallel objects which are comoving which is not an interesting case if you know anything about linear transformations like the Lorentz transform. Nor does it apply to the question raised in the other thread about objects which are parallel in one frame but not comoving.
But they are comoving as soon as they collide. The fact that you put a set of blinders on doesn't change the facts. So, you failed to show any mathematical error in the derivation I posted and now you are outright denying the physics part. For your information, all three(!) threads generated by Pete and Fednis48 pertain to the physics of the collision.
My naive understanding (from relativity experts who are forever telling the "cranks" that frames of references are not necessarily associated with any object as such), is that both the box frames and the rods in the animations CAN be "virtual" for purposes of illustrating essentials. Even if Tach objects and says that the rods themselves "will collide", it has already been suggested somewhere that we offset the rods by minuscule distance between them so they pass side-by-side but going in opposite directions. It seems silly for anyone to pick on trivial inconsequentials like this in a thought experiment just to avoid the obvious results if SR is applied correctly. Which can only be found out if all participate in the honest debate not play games forever? Any "crank" listening in to this "debate" between supposed SR experts may be forgiven for thinking that 100 yrs of Special Relativity has made no dent even in the mainstream confusions let alone the "cranks" confusions. Tach, moderators, isn't it about time that Tach answered all pertinent questions without manufacturing obfuscating and evasive strawmen? Wouldn't any "crank" have by this time been asked to summarize his position or else be banned? If this goes on much longer without honest engagement, and instead continues with the tactics of insult and obfuscation, then all "cranks" viewing this will be immune from banning because it is allowed ad nauseum here. I ask that Tach and all concerned make efforts to bring this debate to a proper conclusion based on their summation of their SR "understandings" and without any more rubbish taunts and evasions. Either SR is explicable and valid, or it is just another confusion riddled fantasy. Which is it? So far it seems that the experts can't decide one way or the other even after 100 yrs! Theory should be better explained and understood than this seems so far. Moderators can you please do something before this site becomes a laughing stock? I came here hoping to learn, but so far the only "lessons" I have had from this is that tactics and obfuscation are more important than science.
This is NOT the scenario is being discussed. The rods collide. If you want to make up your own scenario, open another thread. You not posting would be a good first step. This thread can be sorted out between me, Pete and rpenner.
Reference frames are all important to SR, aren't they? Those frames are "virtual" not necessarily "objects". The best way to analyze the experiment is to come to agreement about the "virtual line" along which they would have "collided". And the best way to see that "virtual collision line" is to allow the frames to pass through each other as animated. Or are you claiming that frames of references are "objects" which "collide"? /Edit: The games you play are not a good omen for "sorting out" anything between you and anyone else? Maybe if you stopped the games and spoke plainly and summarized what the "correct" SR analysis is in your view, we would all be less confused?
Nope, because in realty , the rods DO NOT pass through each other, they collide and STOP. There are no games but you have some serious comprehension problems.
Trivial objection from you. They may be offset by minuscule insignificant amount like I said. They can pass each other and be instantaneously co-located but instantaneously going in opposite directions. If a "crank" had made the same objection you are making, you would have asked moderators to ban them because they were "nuts" or whatever. Stop the games and trivial strawmen and just sort it out honestly. How many posts does it need for you to summarize the "correct" analysis" according to 100 yrs of SR "expert understandings" which surely must be absolutely superior to my own naive understandings so far? Get on with it and stop confusing everyone please?
The "collision" may be "virtual" as each point on the rod length passes its counterpart on the other rod, for illustrative and analysis purposes providing a "line of collision" which would have been produced as they passed each other. Do you get that? Then you can work out the consequences of an actual collision after you have "sorted out" the SR essentials. Do you get that?
Real experimenters work out the SR essentials in theory. Then, if they can, they conduct the experiment to see what happens in fact. Do you object to the theoretical stage? If so, have you an experiment result in fact to present for debate? Or is this discussion and exercise still in the theoretical assumptions and constructions according to SR theory stage?
The experiment being discussed is the collision between a rod and a flat surface. If you want to discuss rods passing through each other, please open a different thread, this is not what we are discussing in this thread.
Pete's third animated illustration (which you also referenced) is about the rods being parallel and moving in opposite directions. If they are slightly offset they will not collide, but the essential point shown by their parallelism is that IF they had collided they would have met all along their lengths without any bending. What is your problem?
Still trying hard to get noticed, I can see Please Register or Log in to view the hidden image! You should take a cue from the fact that rpenner did not argue and you should have stayed submersed. Even better, you could try finishing the exercise with the carousel deviation. Better use for your time, you might learn a little.
Hells bells, RJ Beery, you beat me to it. I was just going to come back with that after Tach's next response was in. I was going to point out that if the rods miss each other by an infinitesimal offset, then they never collide in fact. So Tach's "as soon as they collide" would never be a real physical event", only a virtual one he is using as a theoretical collision line of all points which are still moving in fact in opposite directions if they are offset. So the SR essentials must also cover that "missing each other" case as well as the "actual collision" case, yes? I am waiting for the games to stop and the experts sort out what the general case is to be understood as in SR theory basis. My naive understandings so far are all at sea until the final expert word is in one way or the other. I don't care which way. Just as long as it is sorted out properly before hell freezes over?
