Simple geometric proof GR's GW's are impossible

[Schmelzer]

And you think this helps you to avoid to answer the questions?

1.) Given that $\eta_{mn}$ is a trivial vacuum solution of GR, do you agree that the metric computed above from this using the coordinate transformation $x^m \to x^m + f^m(x,t)$ is also a vacuum solution of GR?
2.) Do you agree that above have curvature tensor 0?
3.) Do you agree that the $h_{mn}(x,t)$ computed above look (approximately) like waves, once the $f^m(x,t)$ are solutions of the wave equation $\square f^m(x,t)=0$, thus, like gravitational waves?
4.) Do you agree that these four types of gravitational waves are the four types of waves which, according to the Living Review article, are not present in GR?

All these solutions obtained in this way are valid vacuum solutions of the GR equations, as valid as $\eta_{mn}$ itself. They are indistinguishable from the vacuum by observation? Ok, big deal. They are, anyway, solutions of the equations. Which is what matters.

And this is the whole problem of your argument: They are all legal and legitimate solutions of the Einstein equations. Even if they have longitudinal components. They are not forbidden.

I have to admit that I have not checked if the TT gauge is a global one. I would guess it is, but I'm not sure, and I'm too lazy to check. If not, then, indeed, it could be possible that for such a global solution there will be always, somewhere, a place where it has some longitudinal component. Would this matter? Not. Because even without the TT gauge the solution would be a valid GR solution.

 

[Q-reeus]

Seems certain imo vexatious folks here just won't let up. In one case claiming that GR solutions having no possible physical basis are nonetheless terribly relevant to OP issue. The same individual who many times expresses disdain for other 'legitimate' GR solutions yielding wormholes, CTC's, Reissner-Nordstrom or Kerr-Newman exotica allowing e.g. 'safe' trips to 'parallel universes' and so on. Hmm.... So, given I have no interest in wasting time on such BS diversions (well answering here is sort of doing that, but that much I have little choice in), here's an 'easy' way for my relentless critics to soundly refute me. And if doable, I will humbly concede defeat.

OP i.e. post #1 presents in illustration (direct link again: https://s26.postimg.org/axee7pdmh/GR_GW_paradox_2.png) the model I claim allows an unequivocal proof GR's accepted, physically real - owing to source as described - GW's are logically impossible. Far field analysis of monochromatic linear mass-quadrupole oscillator.

Well then. Let any of my highly qualified, mathematically proficient critics set up their own equivalent model version, and show that the accepted by GR community GW field solution (you know - owing to an actual matter source) is perfectly self-consistent. As determined on both a local and global basis. THAT should put upstart me in my place - good and proper! So go to it critics. Let's see who finishes up with egg on their face. If not up to it - can't be bothered etc., then just don't bother me with further nonsense postings. Fair enough?

 

[Schmelzer]

Seems certain imo vexatious folks here just won't let up. In one case claiming that GR solutions having no possible physical basis are nonetheless terribly relevant to OP issue. The same individual who many times expresses disdain for other 'legitimate' GR solutions yielding wormholes, CTC's, Reissner-Nordstrom or Kerr-Newman exotica allowing e.g. 'safe' trips to 'parallel universes' and so on. Hmm....

I would have similar concerns if you would claim that all these wormhole exotica are not GR solutions. They are, as well as gravitational waves.

Your claim that there exist no GR GW solutions is simply mathematically wrong. And has nothing to do with the question if GR is a good physical theory.

Well then. Let any of my highly qualified, mathematically proficient critics set up their own equivalent model version, and show that the accepted by GR community GW field solution (you know - owing to an actual matter source) is perfectly self-consistent. As determined on both a local and global basis. THAT should put upstart me in my place - good and proper! So go to it critics. Let's see who finishes up with egg on their face. If not up to it - can't be bothered etc., then just don't bother me with further nonsense postings. Fair enough?

It is impossible, as long as you do not even clarify what is - iyo - a consistent solution. I have given you some examples of solutions which are consistent GR solutions, and asked you if you accept that they are. You refuse to answer.

So, the challenge would be to define some Q-reeus-consistent GW solutions, where nobody knows what this "Q-reeus-consistent" means.

 

[Schmelzer]

It appears you have the wrong impression about what form the "falsification" may come in. It comes in, first and foremost, when objective scientific method is applied to scrutinize a hypothesis or incumbent theory (if it has got as far as the latter status) for self-inconsistencies according to logic and known physical possibilities. If that scrutiny does uncover self-inconsistencies, then there is no actual requirement for the "falsifier" to provide alternative equal to or better than the so falsified hypothesis or theory. The provision or postulation of an alternative hypothesis or theory is a separate step altogether.

In fact, there is an even more subtle point.

The distinction between recognizing that some theory is false, and the question if it remains the incumbent one.

In fact, almost nobody doubts that GR is false. For some very obvious reasons: It is not a quantum theory, it has singularities. Does it follow that GR would be simply thrown away? No. Because predictions based on pure GR computations are fine. To replace it with another theory, this other theory should be somewhere better in its computations. So, sometimes the incumbent theory remains incumbent even if it is known to be wrong.

 

[Q-reeus]

In #134 the following mischaracterization (mild term) was stated:

Your claim that there exist no GR GW solutions is simply mathematically wrong. And has nothing to do with the question if GR is a good physical theory.

In reality not once have I suggested such. From the start, and consistently throughout this thoroughly side-tracked thread, my claim was GR certainly does provide extremely well-known solutions predicting GW's. I even cited in #31, just to answer a useless criticism, a typical article setting out the derivation and final form of such solutions. In particular, one pertinent to the OP scenario - for a linear quadrupole oscillator. See also #22, where GR solutions are obviously, clearly taken by myself as a given.

It was clearly stated over and over, the issue is one of the logical inconsistency of such solutions (in particular, that relating to a linear quadrupole oscillator), as revealed via global geometric constraints. NOT that 'no GR GW solutions exist'. Continually inventing false claims serves only to further tarnish the reputation of the inventor of such.

It is impossible, as long as you do not even clarify what is - iyo - a consistent solution.

Another foolish mischaracterization. My aim, again stated and summarized in #97 (see also #99), is crystal clear. As also made clear there, again, it was suggested attention be given to G4v as a currently viable candidate. Given the imo admissable vector character of G4v's predicted GW's. There was absolutely no onus on me to have provided even that much. Sole responsibility was to make good on title claim - why GR's GW solutions cannot work. And that imo was indeed accomplished in #1. That it was done without any recourse or need of maths, but solely based on the - well understood by many - spatial metric character of such purportedly viable GR variety GW's (revealed owing to the axial symmetry involved), seems to have greatly disturbed certain folk. Too bad.

I have given you some examples of solutions which are consistent GR solutions, and asked you if you accept that they are. You refuse to answer.

See #86, which lists the relevant history, thus real intent, of even bringing up such consistent GHOST (i.e non-physical thus irrelevant to OP) solutions. Tiresome repetition.

So, the challenge would be to define some Q-reeus-consistent GW solutions, where nobody knows what this "Q-reeus-consistent" means.

See above. It seems the vexatious poster will go to any lengths to avoid taking up the very clear challenge set out in #101. Which, since it directly deals with viability of OP, would be the logical course of action.
Logic and honest objectivity has taken very much a back seat this sadly trashed thread, beginning with current post #2 this thread. Even more so, the original post #2 now banished to Cesspool.

 

[PhysBang]

Does it take a huge IQ to figure out that the beads in the equatorial hoop, purely by symmetry, cannot have any motions along the hoop? The 'sticky beads' are stuck, even if perfectly frictionless! Dilation/contraction along lines of latitude makes zero sense. Something obvious when viewed globally ('forest view'), only seemingly sensible if viewed as a local perturbation ('tree level' view i.e. the small ellipses). Feynman got it badly wrong.

I'll say, again, that I'm afraid that it takes more that simply saying that the beads are stuck. I suspect that no argument that they are stuck will be forthcoming, but since this is the key point of the argument of the OP, it would be nice to actually see the argument delivered.

 

[Q-reeus]

I'll say, again, that I'm afraid that it takes more that simply saying that the beads are stuck. I suspect that no argument that they are stuck will be forthcoming, but since this is the key point of the argument of the OP, it would be nice to actually see the argument delivered.

I did expect there a bare minimum of comprehension of the symmetry constraint owing to circular (more generally axial) geometry/symmetry. The onus is on the reader to argue that the beads could logically have circumferential motions induced. It was further elaborated in #62.
ONCE AGAIN. THE ONUS IS ON THE READER TO LOGICALLY JUSTIFY PERIPHERAL BEAD MOTIONS - GIVEN THE KNOWN CHARACTER OF GR VARIETY GW's - SUPPOSEDLY GENERATED BY A LINEAR QUADRUPOLE OSCILLATOR!

But further, the most pertinent, telling counterargument to my OP claim is set out in #101. Not up to it, or can't be bothered? If the latter, simply do not bother to make any further skew criticisms. #101 is THE appropriate way to rebuff me. Take it up, or defacto concede there is no legit counterargument to make.

 

[Schmelzer]

IFrom the start, and consistently throughout this thoroughly side-tracked thread, my claim was GR certainly does provide extremely well-known solutions predicting GW's. I even cited in #31, just to answer a useless criticism, a typical article setting out the derivation and final form of such solutions. In particular, one pertinent to the OP scenario - for a linear quadrupole oscillator. See also #22, where GR solutions are obviously, clearly taken by myself as a given.

It was clearly stated over and over, the issue is one of the logical inconsistency of such solutions (in particular, that relating to a linear quadrupole oscillator), as revealed via global geometric constraints. NOT that 'no GR GW solutions exist'. Continually inventing false claims serves only to further tarnish the reputation of the inventor of such.

That's the whole problem. It is not possible to understand what you really mean, I have to guess wildly, and no wonder that the result is misunderstanding. Its not me who has named this thread "Simple geometric proof GR's GW's are impossible".

If a solution exists, that means, we have some functions $g_{mn}(x,t)$ which fulfill (at least the linear approximation of) the Einstein equations. Once they exist, and once they are really solutions of the Einstein equation, what could a "logical inconsistency" mean? I have no idea. For me, a logical inconsistent solution is not a solution at all, thus, it can only mean that no solutions exist. My hypothesis was that you may somehow think that they exist only locally but cannot be combined into a consistent global solution, so that the global solution does not exist. This hypothesis you have rejected now too. So I have to admit that I'm completely lost.

Nor the OP, nor your challenge makes any sense to me.

 

[PhysBang]

I did expect there a bare minimum of comprehension of the symmetry constraint owing to circular (more generally axial) geometry/symmetry. The onus is on the reader to argue that the beads could logically have circumferential motions induced. It was further elaborated in #62.
ONCE AGAIN. THE ONUS IS ON THE READER TO LOGICALLY JUSTIFY PERIPHERAL BEAD MOTIONS - GIVEN THE KNOWN CHARACTER OF GR VARIETY GW's - SUPPOSEDLY GENERATED BY A LINEAR QUADRUPOLE OSCILLATOR!

But further, the most pertinent, telling counterargument to my OP claim is set out in #101. Not up to it, or can't be bothered? If the latter, simply do not bother to make any further skew criticisms. #101 is THE appropriate way to rebuff me. Take it up, or defacto concede there is no legit counterargument to make.

If there is some constraint that prevents these beads from moving, will they experience some sort of deforming stress?

I find it funny that the burden is on the defender of GR to "disprove" an uncompleted argument against it. We know that GR works to a high degree or accuracy, some hypothetical problem not attached to a positive theory able to describe physical systems is not a serious problem.

 

[Q-reeus]

That's the whole problem. It is not possible to understand what you really mean, I have to guess wildly, and no wonder that the result is misunderstanding. Its not me who has named this thread "Simple geometric proof GR's GW's are impossible".

The now oft repeated assertion that a clear presentation (maybe too uncluttered with unnecessary maths for the tastes/needs of some), complete with clear illustration of physical arrangement and far-field bounding spherical surface of interest, is somehow 'impossible to understand', 'incomprehensible', etc. etc., is both exceedingly disingenuous, and likely to poison the minds of only those with very poor comprehension skills. Unfortunately there seems to be plenty here in that category. I won't even give it a 'nice try'.

If a solution exists, that means, we have some functions gmn(x,t) which fulfill (at least the linear approximation of) the Einstein equations. Once they exist, and once they are really solutions of the Einstein equation, what could a "logical inconsistency" mean? I have no idea.

So you keep claiming. Picking an example/counterexample you are known to have derided as inadmissible on presumably logical grounds: the formally correct Godel CTC solution:
https://en.wikipedia.org/wiki/Closed_timelike_curve
IS DEEMED BY RATIONAL FOLK AS INADMISSIBLE - BASED ON E.G. GRANDFATHER PARADOX. So you now renounce that former scepticism? Based on your above words? Please DO make up your mind.

For me, a logical inconsistent solution is not a solution at all, thus, it can only mean that no solutions exist.

See above.

My hypothesis was that you may somehow think that they exist only locally but cannot be combined into a consistent global solution, so that the global solution does not exist.

Faulty logic. Faulty presentation. My actual position has been crystal clear from the outset, and oft repeated owing to such continued misrepresentation as above.
THE GR GW SOLUTION(S) ONLY SEEMINGLY MAKE SENSE WHEN VIEWED LOCALLY. THAT THEY CANNOT MAKE SENSE WHEN VIEWED GLOBALLY MEANS THE SOLUTION THEREFORE FAILS ALTOGETHER ON GEOMETRIC GROUNDS. IT MAKES NO SENSE TO THEN TALK OF 'VALID' LOCAL SOLUTION VS INVALID GLOBAL SOLUTION. THE LATTER NECESSARILY RULES OUT THE FORMER AS WELL. THE SOLUTION IS FORMALLY CORRECT AND THERE, BUT FAILS TO MEET CONSISTENCY CRITERIA. DUH!

This hypothesis you have rejected now too. So I have to admit that I'm completely lost.

Continually, relentlessly inventing and promoting straw-man arguments does not help to get un-lost.

Nor the OP, nor your challenge makes any sense to me.

see above.
Bottom-line - signals via above nonsense arguments that 'it's not worth while' to take up challenge in #101 - WHICH IS THE ONLY TRUE AND APPROPRIATE WAY TO REFUTE ME!

 

[Q-reeus]

If there is some constraint that prevents these beads from moving, will they experience some sort of deforming stress?

You are playing games. Just read #62 yet again. There is no excuse for such evident mind-game tactics.

I find it funny that the burden is on the defender of GR to "disprove" an uncompleted argument against it. We know that GR works to a high degree or accuracy, some hypothetical problem not attached to a positive theory able to describe physical systems is not a serious problem.

Repeating verbatim final words of #141:
Bottom-line - signals via above nonsense arguments that 'it's not worth while' to take up challenge in #101 - WHICH IS THE ONLY TRUE AND APPROPRIATE WAY TO REFUTE ME!

 

[Schmelzer]

Hey, I have an idea how this curious argument makes sense. If one takes the informal picture too serious, one may think that there is simply no place for oscillations of the circumference, because the length of the circumference is fixed by the geometry, by $u=2\pi r$, and once the waves are not longitudinal, it means, r is not oscillating but fixed.

If one thinks this way, all the oscillations which remain allowed are those which do not disturb the fixed Euclidean geometry, thus, those which are equivalent to coordinate transformations. Thus, only those which do not change the curvature, because the curvature is predefined by the fixed Euclidean geometry and trivial. Thus, those which are non-trivial, and lead to real, observable effects in GR are forbidden, the longitudinal ones, which can be obtained also via coordinate transformations, are, instead, allowed.

 

[Q-reeus]

Hey, I have an idea how this curious argument makes sense.

He he he. Innocent sounding start. Now for the disingenuous caricature:

If one takes the informal picture too serious, one may think that there is simply no place for oscillations of the circumference, because the length of the circumference is fixed by the geometry, by u=2πr, and once the waves are not longitudinal, it means, r is not oscillating but fixed.

Actually what is logically imposed by the accepted character of GR's TT GW's. As set out in #1. The only 'viable resolution' - within GR paradigm - is indeed a sterile, unperturbed far-field metric. Just as Eddington maintained. One has to reject the accepted GW solutions as internally inconsistent. But poster now pretends this is a rather naive 'Euclidean geometry' mistaken viewpoint:

If one thinks this way, all the oscillations which remain allowed are those which do not disturb the fixed Euclidean geometry, thus, those which are equivalent to coordinate transformations. Thus, only those which do not change the curvature, because the curvature is predefined by the fixed Euclidean geometry and trivial.

Gee, how silly to 'think that way'! Or partly that way. Because the proposed next 'logical step' seems to yours truly to be somewhat insane. Having 'exposed and summarily dispatched' OP 'naive outlook', that next 'logical step' is to suggest reintroducing those BS, admittedly unphysical, entirely sterile formal mathematical solutions first raised in #30:

Thus, those which are non-trivial, and lead to real, observable effects in GR are forbidden, the longitudinal ones, which can be obtained also via coordinate transformations, are, instead, allowed.

Err, I guess there is some logical flow there, somehow.
Anyway, getting back to my #141, can't help but notice that having easily dispatched a cheap argument in #139:

For me, a logical inconsistent solution is not a solution at all, thus, it can only mean that no solutions exist.

, by quoting example of Godel metric with pathological CTC's, poster now chooses to deflect attention from that issue, with the caricature as per above described.

What else to add here. Oh, I know. How about, the poster simply finally take up challenge ('suggestion' if that seems too confrontational) of #101. Applying his superior professional scientist skills to such a trivial task, I anxiously await the devastating knock-out blow that will surely deliver! I've a hunch it might be a very long wait though.

 

[Schmelzer]

Picking an example/counterexample you are known to have derided as inadmissible on presumably logical grounds: the formally correct Godel CTC solution:
https://en.wikipedia.org/wiki/Closed_timelike_curve
IS DEEMED BY RATIONAL FOLK AS INADMISSIBLE - BASED ON E.G. GRANDFATHER PARADOX. So you now renounce that former scepticism?

Don't cry. Fine, I reject the Gödel-like solutions too, for similar reasons, but I have not seen yet any such philosophical argument which makes sense against the GW solutions. By the way, the grandfather paradox is not what I would name a logical inconsistency, it is an incompatibility with causality and freedom of choice. If on accepts fatalism (which one has anyway, if one accepts the block universe seriously) then no logical problem arises. It is a quite strange and counterintuitive philosophy. But I would not name it logically inconsistent.

My actual position has been crystal clear from the outset, and oft repeated owing to such continued misrepresentation as above.

I think you have to understand that what seems crystal clear to you may remain completely unclear to other people.

There is, in fact, a whole domain of human knowledge named "pedagogy" which cares mainly about one question: How to teach things which are crystal clear (say, all the mathematics, and all the sciences taught in school) so that other people can understand them.

Then, you have to learn the fact that your behavior - crying and personal attacks against those who do not understand you - may be the typical one in American internet, but is not helpful at all. At best your attacks will be returned. Other people simply stop to argue with you because of an obvious lack of civilization on your side. What will be certainly never the result is that people after such attacks start to agree with you.

The strange mixture of an answer to the argument and the usual polemics makes it hard, close to impossible, to understand if my last guess was closer to the original idea or not.

The only 'viable resolution' - within GR paradigm - is indeed a sterile, unperturbed far-field metric. Just as Eddington maintained. One has to reject the accepted GW solutions as internally inconsistent. But poster now pretends this is a rather naive 'Euclidean geometry' mistaken viewpoint: ... Gee, how silly to 'think that way'!

This one could interpret, after removing polemics, like some sort of acceptance that I have guessed correctly, combined with a rejection of my rejection. Let's try, without polemics, to ask some questions to clarify this:

So, indeed, you think that the only global "logically consistent" (whatever this means) GR solutions have a "sterile, unperturbed", far field metric?
Does "sterile, unperturbed" mean static?
Does it mean Euclidean? Or at least Euclidean in the far field, outside some large enough sphere?

 

[Q-reeus]

So, indeed, you think that the only global "logically consistent" (whatever this means) GR solutions have a "sterile, unperturbed", far field metric?

Your partially accurate caricature suggested as much. You know perfectly well, the axial symmetry, together with purported GW TT character, demands any time-varying far-field azimuthal, axial metric perturbations h_φφ, h_zz (taking particular case of equatorial plane here, but for arbitrary latitudes, replace h_zz with h_θθ) are geometrically restrained to be unvarying thus zero. So no perturbation. So just an asymptotic flat Minkowski metric in the far-field - no self-consistent GR GW signature possible. And of course by definition of being TT GW's, h_rr always zero.

Does "sterile, unperturbed" mean static?

See above.

Does it mean Euclidean? Or at least Euclidean in the far field, outside some large enough sphere?

See above.
And stop trying to play aloof, as though your whole approach has been anything but a wrecking attempt from the go.
Are you now prepared to do as asked in #101 or not? If yes then get on with it and deliver. If no - give a brief reason why you are not prepared to settle the issue unequivocally that way. No more stupid diversionary questions of me. The rest of your post is not worth responding to.

 

[Schmelzer]

I ask questions not with the purpose to have to guess again, reading some text above. So yes or no? For the first question, one can guess it means a "yes", but for the second (the second two) questions this is not clear at all.

The brief reason why I do not accept your challenge is that it is described in words which are much too uncertain and diffuse. Especially it is yet completely unclear what is the meaning of the phrase "perfectly self-consistent" which you have used in your challenge.

That's why I ask questions: Your answer gives me much more precise information about what you think is a "perfectly self-consistent" solution and what is not. Once I have found a sufficiently large number of clear answers of type "a solution with properties XYZ is perfectly self-consistent" as well as "a solution with properties XYZ is logically inconsistent" I may be able to able to prove that GW solutions which are "perfectly self-consistent" exist. Alternatively, the result could be that every GR solution which differs from the Minkowski metric, thus, every non-trivial gravitational field, would have to be, IYO, logically inconsistent. Or something between. Or to show that several of your claims contradict each other. Whatever, I would have a base to start some arguments.

 

[Q-reeus]

I ask questions not with the purpose to have to guess again, reading some text above. So yes or no? For the first question, one can guess it means a "yes", but for the second (the second two) questions this is not clear at all.

The brief reason why I do not accept your challenge is that it is described in words which are much too uncertain and diffuse. Especially it is yet completely unclear what is the meaning of the phrase "perfectly self-consistent" which you have used in your challenge.

That's why I ask questions: Your answer gives me much more precise information about what you think is a "perfectly self-consistent" solution and what is not. Once I have found a sufficiently large number of clear answers of type "a solution with properties XYZ is perfectly self-consistent" as well as "a solution with properties XYZ is logically inconsistent" I may be able to able to prove that GW solutions which are "perfectly self-consistent" exist. Alternatively, the result could be that every GR solution which differs from the Minkowski metric, thus, every non-trivial gravitational field, would have to be, IYO, logically inconsistent. Or something between. Or to show that several of your claims contradict each other. Whatever, I would have a base to start some arguments.

That is not a genuine response. What is not clear about that asked in #101? Which would if acted on cut through all this chaff tossing. You cannot figure how to apply the well known far-field field solutions for the simplest and most symmetric GW source possible - linear quadrupole oscillator? Really?! Then it is hopeless and best end it on that sad note.

 

[Schmelzer]

I see you refuse to answer even simple questions. So it makes no sense. Whatever I would write, you could write a similar "that is not a genuine response" answer.

I have asked some questions in #145 and again #147.

 

[PhysBang]

You are playing games. Just read #62 yet again. There is no excuse for such evident mind-game tactics.

That post merely continues to ignore internal stress. You created a model where a certain kind of motion cannot be done but you chose to ignore all other kinds of energy transformations. This is why we should not take your argument seriously. If you want to have a real argument, then show that there can be no transfer of energy in your scenario.

As it stands now and since the original post, you have nothing to refute.

 

[Q-reeus]

I see you refuse to answer even simple questions. So it makes no sense. Whatever I would write, you could write a similar "that is not a genuine response" answer.

I have asked some questions in #145 and again #147.

As you wish. I reminded paddoboy a while ago - every word in every post forms a permanent record, available for any future reference.