Q-reeus,
You want to silence everyone. Now Schmelzer has taken up again, I will give it a rest. But so far you have failed to establish your argument cogently.
Best wishes with your efforts.
Simple geometric proof GR's GW's are impossible
- Thread starter Q-reeus
- Start date
Q-reeus,
You want to silence everyone. Now Schmelzer has taken up again, I will give it a rest. But so far you have failed to establish your argument cogently.
Best wishes with your efforts.
Wrong thinking at best, continued malicious misrepresentation most likely. Any non-zero azimuthal 'strains' h_φφ, and meridian 'strains' h_θθ are self-contradictory on two levels at least, as stated clearly beginning in #1 (even though h_φφ, h_θθ nomenclature wasn't explicitly used there).
Firstly, each such spatial metric 'strain' separately would violate the explicitly purely transverse character supposedly applying.
Most bleeding obvious in the particular case of equatorial plane, where indeed only u=2πr fulfills GR GW solution requirement of 'purely transverse'. In TT gauge, which is what is typically applied to a local patch, this is obscured. Proper length of rulers and a bead array deform in unison. Once a global view is taken, on a coordinate basis where h_φφ, h_θθ have a direct application, there is simply no room for any necessarily axially symmetric, purely transverse, non-zero h_φφ 'strain'. Only by allowing radial 'breathing' - and such is not allowed within GR GW physical solution.
One wishes nevertheless to allow such radial 'breathing'? Then read again the passage in #94:
Secondly, relaxing the pure transverse GR solution requirement and allowing radial motions i.e. longitudinal wave character, has the h_φφ, h_θθ 'strains' in mutual conflict. Since at a moment t when say h_φφ is +ve (outward 'breathing'), at that same location h_θθ is -ve (inward 'breathing'). Integrated over a spherical shell, there is literally nowhere net deformations of such strains could make sense. This is not QM - beads can't be in two places, and having conflicting motions, at once.
What's a poor bead to do? My advice to such a confused bead - ignore the stupid, impossible demands of the theory. Don't 'stress' as another disingenuous poster imagines is a relevant consideration.
The problem is essentially identical to that of considering what purely transverse mechanical strains are possible on a rigid thin spherical shell. Which matters were worked out in detail way back in the 1880's by Rayleigh and Love and others.
It was shown that only pure torsional modes, and linear combinations of such, can fulfill that requirement. If any of those workers were told that the GR GW 'purely transverse' 'pure shear' solutions, mapped on a coordinate basis to the mechanical counterpart, could qualify, they would justly laugh such a claim out of the room.
See above. Go to coordinate basis, not proper TT-gauge basis, and try and argue your non-zero h_φφ, or h_θθ for that matter, makes any sense.
And here is the real 'ultimate challenge' no-one has been game to attempt. My very first reference in #1 - Feynman's famous beads on a stick.
No pretense now that scenario as per https://s26.postimg.org/axee7pdmh/GR_GW_paradox_2.png is 'incomprehensible'.
If I have somehow misunderstood the situation, and Feynman had it right, here's what to do to settle it.
Just take a straight plan view of linear oscillator case, a single slice through equatorial plane. So oscillator axis is perpendicular to page/screen. A billion Feynman's each holding their locally straight stick tangent to the r >> λ, far-field equator line, are distributed uniformly around that equator line. As are the beads on those sticks. The sticks are touching end to end and ever so slightly curved so as to form a huge, perfectly circular hoop overall, centred about oscillator axis. (Yes, this is essentially a repeat of what was in #1)
Show that beads moving azimuthally along those sticks is logically coherent.
Post it here, with diagram, this thread. That would be end of story. Something that should have happened back around post #2 - if it were possible. So let's see who will finally bite. I predict no-one will.
expletives deleted
Registered Senior Member
The God:
Schmelzer:
The God:
What is the point, in principle, of following maths to absurd result which initial logical analysis of the real situation in geometric terms already described shows is inevitable if the maths is followed without regard to the logical (or illogical as the case may be) basis for the maths in the first place?
@ Schmelzer:
How does the 'strain' aspect even come into consideration if the GR GW perturbation is supposed to occur and travel at light speed? The usual tidal stresses issue would arise if the alleged GW GW perturbation was traveling at much less than light speed along with the masses that generate Gravity and the masses that are affected by the gravity wells. But if weak far field GR GW perturbations allegedly exist and travel at light speed, any 'stresses' would be over even before the inertial structures of the test masses could respond and a strain can establish and persist long enough to be discerned above the inherent parametric instabilities already being desperately controlled for in the aLIGO system.
That is my observations on your respective objections to Q-reeus's OP and arguments as made. I have no further comments. Thankyou for your discussions, The God, Schmelzer and Q-reeus.
Schmelzer:
The God:
What is the point, in principle, of following maths to absurd result which initial logical analysis of the real situation in geometric terms already described shows is inevitable if the maths is followed without regard to the logical (or illogical as the case may be) basis for the maths in the first place?
@ Schmelzer:
How does the 'strain' aspect even come into consideration if the GR GW perturbation is supposed to occur and travel at light speed? The usual tidal stresses issue would arise if the alleged GW GW perturbation was traveling at much less than light speed along with the masses that generate Gravity and the masses that are affected by the gravity wells. But if weak far field GR GW perturbations allegedly exist and travel at light speed, any 'stresses' would be over even before the inertial structures of the test masses could respond and a strain can establish and persist long enough to be discerned above the inherent parametric instabilities already being desperately controlled for in the aLIGO system.
That is my observations on your respective objections to Q-reeus's OP and arguments as made. I have no further comments. Thankyou for your discussions, The God, Schmelzer and Q-reeus.
Schmelzer
Valued Senior Member
ED, I don't understand why you think your question has anything to do with my arguments. I have not talked nor about strain, nor about tidal stresses, nor about the speed of waves.
The justification for this makes no sense. Because the GR equations do not contain any "solution requirement of 'purely transverse'". There are simply many solutions which, according to GR, are indistinguishable by observation, and therefore, by the positivist spacetime interpretation, do not define different solutions. So that we have a quite large class of equivalent solutions. The question if one can choose one solution from every class, and if, then how, is a quite secondary one of no fundamental importance.
For waves, the TT gauge defines such a possibility. If this gauge makes sense outside the consideration of plane waves or not is nothing even worth to care about. Because this gauge is a pragmatic choice of no fundamental importance at all. So, once there simply is no such fundamental solution requirement, it also cannot require any $u=2\pi r$.
But, whatever, does from the TT requirement follow that $u=2\pi r$? Of course, not. Let's consider, for simplicity, the surface of a sphere as an example of a curved geometry with $u\neq 2\pi r$. And usual water waves on that surface. If one starts them at the North pole, their highs and lows will have, by symmetry, equal distance to the North pole, fixed surface points move up and down, the wave moves South, so everything transversal. If the wave is up, the circumference will be a little bit greater, it it is down lower, but in any way it will not be $u < 2\pi r$ where r is the distance on the surface from the North pole.
The funny thing is that what I have, namely "seems quite clearly based on the assumption that the Euclidean u=2πr holds exactly", is admitted to be essentially correct.
The justification for this makes no sense. Because the GR equations do not contain any "solution requirement of 'purely transverse'". There are simply many solutions which, according to GR, are indistinguishable by observation, and therefore, by the positivist spacetime interpretation, do not define different solutions. So that we have a quite large class of equivalent solutions. The question if one can choose one solution from every class, and if, then how, is a quite secondary one of no fundamental importance.
For waves, the TT gauge defines such a possibility. If this gauge makes sense outside the consideration of plane waves or not is nothing even worth to care about. Because this gauge is a pragmatic choice of no fundamental importance at all. So, once there simply is no such fundamental solution requirement, it also cannot require any $u=2\pi r$.
But, whatever, does from the TT requirement follow that $u=2\pi r$? Of course, not. Let's consider, for simplicity, the surface of a sphere as an example of a curved geometry with $u\neq 2\pi r$. And usual water waves on that surface. If one starts them at the North pole, their highs and lows will have, by symmetry, equal distance to the North pole, fixed surface points move up and down, the wave moves South, so everything transversal. If the wave is up, the circumference will be a little bit greater, it it is down lower, but in any way it will not be $u < 2\pi r$ where r is the distance on the surface from the North pole.
What animal is this "coordinate basis"?
'Admitted' for sound reasons already covered. And see below.
Let's see. Just one example of many - read 2nd para under "Quadrupole formulae" sub-heading here: http://www.tapir.caltech.edu/~teviet/Waves/gwave_details.html
Why bore with a thousand other examples. Some contentious individuals like to play with their 'legitimate solutions' as 'counterexamples' having nothing whatsoever to do with either standard GR treatment of GW's or that pertaining to OP scenario. Their problem.
If some reputable article(s) claiming that for any actual physically generated GR variety GW, an appreciable longitudinal GW component exists in far-field, specifically cite such.
See above. Generalities presumably including everything e.g. static mass solutions, or even absurd non-physical solutions, are not relevant to OP.
Of course TT gauge choice per se does not require u=2πr, but global geometry - axial symmetry - does impose that restriction given GR's pure shear GW form.
And surface water waves propagating from a North pole have what to do with notional axially symmetric, purely transverse pure shear GR GW's? Some loose analogue that misses the real point entirely. I quoted in #222 a passage from #94 for a reason, to squash idle inferences that allowing longitudinal motions could be a legitimate out.
That would be adoption of the same one referring to say a static Schwarzschild exterior metric. You know, where the reference is considered to be 'at infinity' thus asymptotically in a flat Minkowski metric. Metric disturbances further in are referenced to those 'at infinity'. So-called coordinate values. A global perspective.
Well, since I claim only a global viespoint highlights the issue re GR GW's, it's appropriate to take that 'at infinity' as reference, and note that for a field point much further in but still far-field wrt linear oscillator source, metric perturbations h_φφ, h_θθ, naturally read as the supposed axially symmetric 'global strains' induced by a passing GW, in direct analogy to spherically symmetric Schwarzschild static ones.
I find it interesting what wasn't responded to in my #222. The last passage. The 'ultimate challenge'. My prediction of zero respondents to that seems to be right.
And just for some comic relief, here's a variant on that theme. Instead of Feynman's sticks and beads, why not insert an end-to-end touching circular array of one's favourite bar-type resonant GW detectors? That should be just as much fun to ponder. Or maybe a headache to stress over.
ANY TAKERS?
Schmelzer
Valued Senior Member
Can you distinguish a result about GR GWs from a requirement for GR GWs?
There is no fundamental requirement that GWs have to be TT. This is a only particular gauge, that's all. A gauge which is of no fundamental importance, because it is usually defined only for small disturbances $g_{mn} = \eta_{mn}+h_{mn}$.
A longitudinal component can be there, simply because nobody forbids it. But one would be unable to distinguish it from the solution in TT gauge. Because, at least locally and for small waves, in every equivalence class of metrics there is one which fulfills the TT gauge condition.
But let's now, simply to explain the difference, assume that this property (there is one and only one field with TT gauge in every equivalence class) holds only approximately, not exactly, and not even globally (for those who know more about GR, this is just for the sake of the argument). Would this be a problem for GR? Not at all. It would be a problem only for the domain of applicability of the TT gauge.
This is the first point where you clearly do not understand nor GR, nor the role of the TT gauge in GR.
These "generalities" are relevant for everything. Once you confuse a particular gauge condition for a particular class of approximate solutions with a fundamental requirement for all solutions, this invalidates your construction completely. Because without a fundamental requirement of GR violated by the transversal GWs you have no problem for GR.
It does not, as shown by my waves on a sphere example. The waves start from the North pole and then arrive at the equator at the same time, nice axial symmetry of the construction.
This is a forum mainly read by laymen, in a really professional forum I would not use it, but you would be unable to understand my text. We have axial symmetry in the example. We have $u<2\pi r$ in the example. We have nice transversal waves in the example. And the distances as measured on the water surface (with waves) would even define a metric, simply with one dimension less. To add one more dimension is locally not a problem too - simply take the water depth as the third spatial dimension.
So, nothing relevant for the discussion is missed.
And forget yet about longitudinal motions. We can start to talk about them after you have understood the role of TT gauge, and no longer confuse it with an a priori restriction for consistent GR solutions.
Sounds like another blackout in your GR education. "Coordinate values" are simply values depending on the particular choice of coordinates, like in "coordinate speed of light". It has nothing to do with infinity. If you have seen this in some textbook in another context, link please.
It seems I have identified now already two points where your GR education, hm, .... is not adequate (the role of the TT gauge, and of "coordinate values") and one where you are wrong about what follows from the TT gauge ($u=2\pi r$ does not). I do not think it makes sense to study your "challenge" before solving these issues. I would guess that after resolving them, or at least two of them, you will remove your "challenge" yourself after understanding your error. And I also guess we will be unable to resolve even a single one, judging from your behavior up to now.
But, whatever, even if I'm wrong about this, I promise to take a look at it if we resolve two of these three issues. (Ok, that's cheap, given that I expect none will be resolved anyway.)
Disingenuous tripe. That which I quoted, relevant to far-field, obviously weak GW's which is all that is of interest, point blank states the accepted position. Only transverse components are present. Nit pick over technicalities bringing in general case not just far-field, if you wish.
He he he. See above.
So an admission of playing BS games is slipped in. Right.
So, deal with my challenge, and let's see how all that talk washes up.
Really and truly? So, you will now demonstrate how by dispatching my challenge with ease, right?
Poor and misleading example. From the start, such water waves violate analogous transverse requirement by being radial displacement waves! Instead, proper analogy would be comparison to torsional surface shear waves as studied by Rayleigh, Lamb, Love etc.
Wrong. That example fails to convey the true situation as I explained above. Those 'nice transversal' waves are not transversal.
Wrong.
See remarks on that very point in CALTECH article I quoted last post.
What I stated on that matter was relevant and correct. Do not try and trap me with nitpicking technicalities.
None of such pedantic nitpicking over fine details is relevant. Your style though.
COP OUT. I do not intend to keep playing your stupid games, having to keep rebutting intentionally skewed criticisms. Nor keep copping your veiled insults. None of your criticisms deal in any significant way with OP scenario. And the acid test of that is....
You cannot meet that simple. direct challenge in #222. Doing so would blow all your spurious guff out of the water. And we both know it. Chaff tossing the preferred strategy, rather than having to plainly admit that. Easier, and safer, to go on raising spurious issues where you consider me vulnerable on technicalities.
Again, I say you cannot coherently answer that direct, simple challenge in #222, or variant in last part of #226. Preferring to keep playing the same game as The God has descended to. 'Counter-challenges' tossed back. Which I always 'fail'. Hence you never have to deliver your end. Interesting common ground.
Schmelzer
Valued Senior Member
Of course, it is an accepted position, that the TT gauge indeed chooses one solution out of each equivalence class for weak field gravitational waves. And I do not question this accepted position at all.
The difference which you don't get is about something completely different. It is that this particular question - if the TT gauge chooses one field out of each equivalence class or not - is completely irrelevant for GR as a physical theory. It is, at best, a question about the place of the TT gauge for the consideration of GR GWs. Even if you would be correct about everything else, the result would be only that the TT gauge is worse than usually assumed.
I don't know, simply because I have not yet tried to make sense of it. You see, I'm in a situation comparable to a teacher in communication with a pupil who is yet unable to multiply integer who claims that some integral is wrong. Would you care if this claim makes sense?
No. In the example, we have surface wave moving from the North pole toward the South. What changes here is $\theta$. The waves themselves are waves in r. $r=\sin(\theta-ct)$.
You think I will look for an article in some other post .... Sorry, the point was about our discussion here, so make it here. I read your replies, on everything else you cannot rely (too much off-topic in your discussions with others).
In other words, you have nothing to reply and refuse to discuss the point itself.
Such is live. You may prefer paddoboy's cheap personal attacks. If you prefer to argue with a professional scientist, you have to live with nitpicking. Because science is nitpicking. Every peer review of a scientific article is nitpicking. Because every minor detail should be correct, and if the reviewer finds one reason to nitpick, the best you can hope for is an admission to resubmit a corrected version.
I do not have to and do not plan to. Given that in this posting you have openly refused to even consider one of your errors (about the "coordinate values") , simply repeated your point without any progress about the second (the role of the TT gauge as a gauge condition vs. a fundamental requirement), and completely misinterpreted the third one (the surface waves example), there is not much hope that we will be able to resolve even a single issue, and, as I have explained, it makes sense to consider your challenge only if at least two of them have been resolved.
It is your choice if you want to accept criteria similar to professional peer review or not. If not, you have failed, feel free to talk with paddoboy, he will be the appropriate conversationalist for you. If you accept this, live with the nitpicking, accept it as legitimate, answer it, and correct the errors which have been found by the "nitpicking about technicalities".
expletives deleted
Registered Senior Member
Schmelzer:
I'm sorry, Schmelzer, the relevant comment should have been addressed to PhysBang, not you! I must have been pondering on your arguments when I typed that incorrect address name. I can't go back and edit the name now, so I will quote it below as it should have read in the opening address:
My apologies, Schmelzer. Thankyou very much for bringing that to my attention. Best.
I'm sorry, Schmelzer, the relevant comment should have been addressed to PhysBang, not you! I must have been pondering on your arguments when I typed that incorrect address name. I can't go back and edit the name now, so I will quote it below as it should have read in the opening address:
My apologies, Schmelzer. Thankyou very much for bringing that to my attention. Best.
Schmelzer,
Although not fit on Q-reeus and almost below the belt and condescending, still I liked your teacher-pupil analogy in general. I hope you are not copy-righting it, I would like to use it at appropriate places.
Your very same post is quite condescending to Q-reeus and very dismissive to Paddoboy.
Although not fit on Q-reeus and almost below the belt and condescending, still I liked your teacher-pupil analogy in general. I hope you are not copy-righting it, I would like to use it at appropriate places.
Your very same post is quite condescending to Q-reeus and very dismissive to Paddoboy.
The constant refrain, from the start. 'I cannot make sense of it blah blah blah'. How amusing. Feigning imbecile level comprehension, just as earlier on.
The simple question - could a GR variety GW logically exist, and act as per scenario such that Feynman's famous beads really move along the stick(s). Response - 'incomprehensible words', or 'I have not thought about it'. Sure thing. Sure.
Which nicely sums up and nicely reveals your nasty condescending attitude. The genius whose beautiful, perfect ether theory an ungrateful world rejected. And the hurt over that is imo manifesting right here. Unfortunately. The rest of #229 just invites another futile round of arguing over things of no importance to OP issue.
But thanks for providing a revealing indelible record here. Able to be recalled for future reference.
Last edited:
Schmelzer
Valued Senior Member
Ok, let's summarize. The following errors have been identified:
1.) A misinterpretation of the TT gauge - a particular gauge suitable for small gravitational waves on a Minkowski background without fundamental importance - as a fundamental requirement of GR.
2.) The claim that transversal waves would require $u=2\pi r$, which has been falsified by a simple counterexample.
3.) A confusion about the role of coordinates in GR, leading to meaningless talk about a "coordinate basis" and "coordinate values".
Q-reeus refuses to correct them.
It is not that he made some errors - everybody makes them, me too - but this refusal to discuss them, combined with personal attacks, which leads to disdain toward him.
1.) A misinterpretation of the TT gauge - a particular gauge suitable for small gravitational waves on a Minkowski background without fundamental importance - as a fundamental requirement of GR.
2.) The claim that transversal waves would require $u=2\pi r$, which has been falsified by a simple counterexample.
3.) A confusion about the role of coordinates in GR, leading to meaningless talk about a "coordinate basis" and "coordinate values".
Q-reeus refuses to correct them.
It is not that he made some errors - everybody makes them, me too - but this refusal to discuss them, combined with personal attacks, which leads to disdain toward him.
False accusation. Nowhere have I stated or implied TT gauge was somehow 'fundamental to GR'. But easy accusation to claim.
False accusation. My actual claim, in proper context, was last given in #222. Persistent misrepresentation notwithstanding.
And the 'simple counterexample' - water waves on a spherical surface, is falsely claimed to show by analogy, that in OP scenario, presence of a longitudinal component is ok. Not so. The analogy breaks down from the start. A purely transverse solution: http://www.tapir.caltech.edu/~teviet/Waves/gwave_details.html
is just that.
I stated the meaning - as analogous to that for exterior Schwarzschild metric. From
https://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric
Ooh - 'infinitely far' - Schmelzer doesn't like that sort of 'meaningless talk'. Better get straight onto author of that piece!
Supposing all such lies were even true. That Schmelzer has from the beginning refused to deal with actual OP argument is THE issue not faced. I made an argument, a simple one. He and others simply refuse to face it. THAT IS THE ISSUE.
One right back at me. Oh, it hurts so much!
So, once more. After maybe dozens of attempts to illicit a straight answer:
Will, or rather logically can, a GR GW, generated by a linear quadrupole radiator, induce Feynman's beads to move along the transversely oriented stick, as all of GR community believes so?
Some deep psychological block prevents committing to a simple YES or NO?
Schmelzer
Valued Senior Member
For example in #94 "GR GW's are allowed only purely transverse pure shear spatial metric perturbations" or in #222 "Only by allowing radial 'breathing' - and such is not allowed within GR GW physical solution" you clearly claim that there has to be something which does not allow longitudinal GWs in GR. But there is no such thing which does not allow them. There is only a gauge condition, which chooses among the many equivalent and equally allowed GWs the ones without longitudinal component.
First, you have not shown that the analogy is somehow wrong. I have made a specification how what is defined by the water surface defines a spacetime metric. You have given no counterargument to show that it somehow breaks down. The example shows that there may be transversal waves but nonetheless $u<2\pi r$.
Just to explain: A 2D surface embedded in 3D space defines a 2D metric on this surface. Once it changes in time, it defines a 2+1 dimensional spacetime. It is easy to extend this 2+1 dimensional spacetime to a 3+1 dimensional one by adding another trivial cylinder coordinate. So we have here already an example of a transversal wave starting from the North pole and we have $u<2\pi r$.
It made no sense.
Nonsense. Ok, the third point about the coordinates was a side issue, and can be simply solved by ignoring everything you have said about "coordinate basis". But as the first, as the second point are deadly objections to the whole OP argument.
Just to quote #222: "Most bleeding obvious in the particular case of equatorial plane, where indeed only u=2πr fulfills GR GW solution requirement of 'purely transverse'. " Wrong, shown by my counterexample.
And to quote #1: "GR's and similar tensor gravity theories brand of pure tensor GW's are logical absurdities." A statement about GR. Not one about some possible problem with the TT gauge which, even if it would really exist, would not be a logical problem of GR at all, but only one for this particular gauge condition. So, as a statement about GR it is simply wrong.
And you keep ignoring the relevant application is to far-field situation only, as specified at outset in #1.
You were asked in #226:
So - cite! Far-field case.
I expected a logical response. Water wave amplitude is in the radial r direction - orthogonal to sphere surface. What it means to be a water wave. Only the phase front is truly transverse. Hence absurd to claim, as you do, that such a wave is 2D. In GW case, far-field components are pure transverse. So, as stated, no proper analogy.
See above.
See above.
That quote from #226 again:
So - cite! Far-field case.
And, continued failure to answer the simple yes/no question - will the beads move along the stick. Gee, must be a really tough one! Actually, making it perfectly obvious you are entirely unwilling to answer with a straight yes or no. Being perfectly aware of the bind either answer would lead to. Cowardly. Don't waste further time with nonsense diversionary tactics. Just admit to being too scared to answer.
Schmelzer
Valued Senior Member
The point being? As if this would matter that you apply some incorrect reasoning only to far field situations. It does not change the fact that all you could attack is only a gauge condition of no fundamental importance. Thus, the consequence cannot be some logical error with GR GWs.
The surface of the water has how many dimensions? IMHO two. You can parametrize them with the angles $\theta, \varphi$. Then, on this 2-dimensional surface you have a metric. Simply the minimal distances as measured on the surface with geodetics.
Now, the most trivial way to define this 2D surface is by the radius. Say, $r= r_0 + \sin(\theta - ct)$. Nothing depends on $\varphi$ on this 2D surface.
Your fantasies about me being scared are really funny.
Ignoring the other diversionary nonsense in #237, it is no fantasy. As proven by the record. Never once game to commit to a simple yes or no. How is that not being - ok let's ease things a bit - and label it 'continued extreme reticence'? That various other onlookers on this forum seems afflicted with the same malady is no excuse for you to cop out too.
So, one again. Will Feynman's beads move via GR GW, as per scenario in #1? With recaps in e.g. #94, #222, #234. It's not like there is anything 'incomprehensible' being asked. Was Feynman right, or wrong?
Last edited:
Say, Feynman was wrong. How does that make GR wrong ?
Feynman resolved an issue whether energy can be transferred through GR, for that he gave some though experiment and it is quite likely GR supporters squeezed it. Period.
There is a local oscillation as mathematically shown and the same was claimed to have been detected.
You are making a thumping statement that beads cannot move under GR GW type considered so GR must go.....despite my repeated urging not even once you pin pointed the error in maths. You are saying look entire GR is bad so it is irrelevant to pin point the error in the maths...thats no argument.
Nothing there hits the mark. I cannot help your deep failure to grasp the geometric constraint that is evident by simple inspection of axially symmetric scenario in #1.
We have gone over it all too many times for anything to change. You have a profound and evidently incurable comprehension issue.
Still, one more try with The God. If you agree Feynman's beads will move along the stick (assume zero friction - just that there is some motion along stick), extend the situation as per e.g. last passage of #222. Still can't see the to me obvious dilemma? If not, and I have tried to convey it many times without ever getting through, please keep out of this thread.