Simple geometric proof GR's GW's are impossible

[Schmelzer]

Admirably summing up your entire personal 'applied philosophy', as practiced at SF. One day, you may admit even to yourself that the claim in #247:
is false in all respects. But any such admission will not appear here. Do have another nice day.

Any argument about the content of the two serious problems I have identified in your #1 OP? (If my vague summary about what I think about the importance of Feynman's side remark is correct or not is completely irrelevant for these points.)

 

[The God]

I accept you truly believe all that, and that it makes coherent sense. Doesn't to me. So - live and let live. OK?

I have never been incoherent....certainly not in this case.

Take it this way...
You are claiming that GR is BS, you have a picture and some qualitative argument to support your claim.
I am just asking you, very humbly, pin point the mathematical step which is incorrect in GR. I have referred you to the right maths also. Is it too much of asking? You have taken more than 150 posts on this thread, still you have not been able to pin point where the flaw is, in GR maths.

Explaining of your theory is over in no more than 10 spread posts, rest all are just short of abuses.

 

[Q-reeus]

Any argument about the content of the two serious problems I have identified in your #1 OP? (If my vague summary about what I think about the importance of Feynman's side remark is correct or not is completely irrelevant for these points.)

Such distractive 'important points' are irrelevant to central issue of OP topic, and given your continual refusal to give a straight yes or no to relevant question on that, I suggest to drop this now. With a seeming preference for endless argument in the political/ideological arenas here, why not just concentrate where the 'buzz' over point scoring in angry exchanges is 'normal'?

 

[Q-reeus]

I have never been incoherent....certainly not in this case.

Not in your mind. But to me yes. After hundreds of posts, enough were spent trying to convey what is relevant and central, without success. That this just keeps going round in circles may not bother you but I'm sick of it. And caricature 'summaries' as per your last post is the confirmation nothing relevant will ever get through. Can you not take a hint and simply quit posting here?

 

[The God]

You are right....i must go from this thread, I feel sad that a false theory could not be falsified. Nice effort.

 

[Q-reeus]

You are right....i must go from this thread, I feel sad that a false theory could not be falsified. Nice effort.

Thanks for ending on a nice note.

 

[Schmelzer]

Such distractive 'important points' are irrelevant to central issue of OP topic, and given your continual refusal to give a straight yes or no to relevant question on that, I suggest to drop this now.

Ok, once you are not interested to discuss the weak points of your OP, and suggest to drop them, the question is solved. The OP is no longer defended, so no point for further argumentation.

 

[Q-reeus]

Ok, once you are not interested to discuss the weak points of your OP, and suggest to drop them, the question is solved. The OP is no longer defended, so no point for further argumentation.

And I won't bother defending against that. Better things to spend one's time on. Bye bye.

 

[Q-reeus]

For an amusing, some might describe as informative, PhysicsForums Mk II attempt at tackling GR GW's globally, but carefully always confined to the case of orbiting binaries:
https://www.physicsforums.com/threads/linearized-metric-for-gw-emitting-orbiting-bodies.880101/
Which as per #31 here, is a follow-on from the Mk I attempt at:
https://www.physicsforums.com/threads/modeling-the-effects-of-gw-and-the-earth-frame.878289/

The chances any of those participants aren't aware of this hugely sabotaged thread is imo pretty slim. Yet I predict they will steadfastly avoid taking the obvious and sensible step. Ditch the binary system in favour of analyzing the linear quadrupole oscillator scenario. Where axial symmetry reveals, not obscures, the fundamental dilemma for GR GW's. Could a site committed to GR ever allow that? He he he. But then I might have them all wrong. Still, one GR expert participant in above two PhysicsForums threads, was also very much involved back in 2012 as per my #58 here.

Above is more or less intended as my parting observations here. Earlier participants are encouraged to NOT come back in for yet more futile engagements.

 

[paddoboy]

Another reply, rather lengthy and supporting what I believe most already believe, at least with the "conspiracy" nonsense being inferred..........

Dear Barry,

My name is Maximiliano Isi and I am a member of the LIGO Laboratory at the California Institute of Technology. I also happen to be the author of one of the papers cited at the end of your message. Thank you for your interesting email and apologies for the belated reply.

It is absolutely true that our observations do not allow us to fully rule out the existence of non-GR physics. This is just a consequence of the fact that experimental observations have the power to disprove theories, but not to prove them: scientific theories are falsifiable, but not demonstrable. The best we can do is to say that our measurements agree with GR up to some (high) confidence level. It is in that precise sense that we mean "Einstein was right" (a misleading phrase: we don't know whether GR is fully accurate, we just cannot prove it wrong with what we have seen).

We have several methods to make quantitative statements about the agreement between the GR prediction and the signals we measure, but I won't describe them here in detail. Note that in order to find signals in the detector noise we use templates that tell us what the waves look like, and those templates are the output of highly–advanced super-computer simulations of GR dynamics; this means that the signal cannot be too different from the GR prediction or we wouldn't have seen it at all!

Now, agreement with GR is not exclusive: an alternative theory might explain our observation just as well as GR or even better. Given any two competing theories (with different predictions), we can always ask which one is favored by our data, and we have well-established statistical methods to make quantitative statements to answer. Unfortunately, however, the mathematics of GW emission and propagation has only been worked out for very few of the viable alternatives to GR and in most of those cases the theories are similar enough to GR that the signals we'd expect to see are practically indistinguishable. The reason for this is that computing GW waveforms for interesting sources is an extremely complicated mathematical problem and (as mentioned above) it takes super-computers to do it even in GR, the theory we know best (and most alternatives are intrinsically more complicated).

So far this has all been about the relation between theory and experiment. However, most of the text in your message alluded to potential logical inconsistencies within GR itself. Since the main point relies on a thought experiment, let me begin to address this by clarifying that, although thought experiments can be a very useful tool, they are not proper logical arguments in themselves and do not formally tell us anything about the the validity of a theory. This is because natural language is too ambiguous to express formal statements: GR (as every other physical theory) is a mathematical framework and we need mathematics to discuss it properly. This is evident when you consider how both quantum mechanics and special relativity are full of paradoxes that seem to point to contradictions that go away when expressed mathematically. Paradoxes point to the inadequacies of our intuitions, not to those of the theory.

That said, I'd like to point out a few potential flaws in the argument presented in your email, without actually going into mathematical detail:

First, Feynman's sticky bead argument played an important role in re-igniting interest in GWs at a point in history when it wasn't clear whether they were real at all; however, the argument is not a core part of the GR framework and is usually not even referred to in modern treatments of the topic—our understanding of GR has come a long way since the 50's!

Second, our intuitions about space and time do not jive well with GR. Because spacetime can be curved, the fact that circumference of the loop in the example decreases does not say much about the radius. For example, imagine you went in a circle around a massive object (say, Sun) and measured the distance travelled (call it c, for circumference), and then travelled radially inwards towards the center and measured that distance too (call it r, for radius), then you would find that c < 2*pi*r because the massive body curve the spacetime around it. This is all to say that a shrinking circumference does not imply a shrinking radius (at least not in all frames).

Third and last, it seems to be implied in the text you quote that the existence of longitudinal gravitational waves would be in conflict with GR; however, this is only true in a narrow sense that needs to be explained. According to GR, at any point in space-time one should be able to find a particular form of the GW equations (the technical term for this freedom in the eqs. is gauge, think of it as a frame of reference though it's not the same) in which the wave can be expressed as the combination of two independent polarizations transverse to the direction of propagation. Notice some key aspects of this statement: there is a specific choice of gauge (or frame of reference, if you wish) in which the equations take this particularly nice form, and that choice can only be defined locally (i.e. a choice that works nicely in one point in space, will be bad somewhere else). This means that if you choose an arbitrary frame of reference, chances are the wave will not look transverse, though you could always switch to the specific frame and gauge which will make the waves look nice at that point (this is the so called transverse-traceless gauge). The bottom line is that you might think that you have longitudinal waves, but you can always explain that as a combination of independent, transverse waves.

Finally, I would like to add a few words about Carver Mead's G4v theory. Unlike most alternatives to GR, Carver's theory makes markedly different predictions than GR with respect to the polarization content of GWs. However, the relative orientation of our detectors makes LIGO not really good at distinguishing different polarizations in transient (short-lived) signals like the ones we have observed so far. Furthermore, we don't have a full prediction of what the GW trace of the merger of two compact objects would look like in G4v (Carver is working on it), so we cannot make a statement about which theory, if any, is favored by the data. So we will have to wait for more detections and more theoretical work until we are able to make a statement about G4v.

Once again, thank you very much for a very thought-provoking email and for your interest in LIGO and gravitational waves in general. By all means, do let me know if you would like me to clarify any of the points above or if you have any questions.

Best,
Maximiliano Isi
--------------------
California Institute of Technology
LIGO Laboratory, MC 100-36
Pasadena, CA 91125

 

[Q-reeus]

First, Feynman's sticky bead argument played an important role in re-igniting interest in GWs at a point in history when it wasn't clear whether they were real at all; however, the argument is not a core part of the GR framework and is usually not even referred to in modern treatments of the topic—our understanding of GR has come a long way since the 50's!

That Feynman's sticky bead argument is not a core component of GR was never an issue, so the point is irrelevant. What is relevant is that applied to the scenario in OP, it becomes manifestly obvious circumferential 'bead motions' are illogical on purely geometric symmetry grounds. Hence Feynman's bead argument collapses entirely. The good Prof. Isi failed to address anywhere that key finding!

Second, our intuitions about space and time do not jive well with GR. Because spacetime can be curved, the fact that circumference of the loop in the example decreases does not say much about the radius. For example, imagine you went in a circle around a massive object (say, Sun) and measured the distance travelled (call it c, for circumference), and then travelled radially inwards towards the center and measured that distance too (call it r, for radius), then you would find that c < 2*pi*r because the massive body curve the spacetime around it. This is all to say that a shrinking circumference does not imply a shrinking radius (at least not in all frames).

Exterior Schwarzschild metric in it's standard form is indeed anisotropic and non-Euclidean as stated. But in that standard form, it's exclusively the radial spatial metric that shrinks on a coordinate basis, and that is a monotonic integrated effect over all space exterior to the mass source. Which is a total contrast to the case of supposedly purely transverse pure shear far-field GR GW's. Where in the far-field there is periodic, sinusoidal variation, and in only the transverse spatial metric components. The two cases could hardly be more different! And that doesn't even begin to address the matter of conflicting overall deformations owing to integrated h_φφ, h_θθ, oppositely signed 'strains'.

Third and last, it seems to be implied in the text you quote that the existence of longitudinal gravitational waves would be in conflict with GR; however, this is only true in a narrow sense that needs to be explained. According to GR, at any point in space-time one should be able to find a particular form of the GW equations (the technical term for this freedom in the eqs. is gauge, think of it as a frame of reference though it's not the same) in which the wave can be expressed as the combination of two independent polarizations transverse to the direction of propagation. Notice some key aspects of this statement: there is a specific choice of gauge (or frame of reference, if you wish) in which the equations take this particularly nice form, and that choice can only be defined locally (i.e. a choice that works nicely in one point in space, will be bad somewhere else). This means that if you choose an arbitrary frame of reference, chances are the wave will not look transverse, though you could always switch to the specific frame and gauge which will make the waves look nice at that point (this is the so called transverse-traceless gauge). The bottom line is that you might think that you have longitudinal waves, but you can always explain that as a combination of independent, transverse waves.

I made the point in earlier posts - the obvious choice to get a global perspective is from the coordinate perspective. That is, metric perturbations h_φφ, h_θθ, are referenced to notional asymptotically flat very far field spacetime metric values. The observation point being static wrt the source (or time averaged centre of energy in oscillator case) Which is the very same perspective from which standard form Schwarzschild metric is evaluated. There is then any room for a far-field longitudinal wave component? If so, one has a theory of GW's different to GR's.

The other points raised in #270 re G4v etc. are peripheral and basically restate that which I already covered much earlier this thread.
It cannot be emphasized enough - the fundamental character of GR GW's is transverse shear. I have quoted various sources before e.g Living Reviews that point blank state GR allows ONLY transverse pure shear GW's. If it were not so, and a far-field GR longitudinal component is physically 'really' there, where is there any reference to aLIGO etc. making provision for such? Being periodic, a GR longitudinal wave should have an impact comparable to transverse modulations. Any citations?

Next post, I will paste relevant content of latest version of an email I have begun posting to certain individuals - and Prof. Isi is now on that list! I await a detailed response with interest. Which would be a first. As #290 amounts to the best feedback so far, given it's failure to address the core finding in OP, that is saying something about just how pathetic has been the overall reaction to date.

 

[Q-reeus]

As stated last post, below is a core part of the latest revision of an email 'flyer' being sent out to various folks. Red highlight emphasizes that which is evidently strictly taboo topic. I wonder why!
****************************************************************************************************************************************************************
This may seem a silly question, but have you ever bothered to check if those elegant GR solutions for GW's, apparently making good sense viewed on a far-field small patch basis, e.g.
https://en.wikipedia.org/wiki/Gravitational_wave#Effects_of_passing
, still make sense on a far-field global view?

I contend a severe consistency problem, obscured in the usual orbiting binary scenario, is acutely evident in the simplest possible axially symmetric system. That of a linear quadrupole radiator. One asks what kind of ostensibly purely transverse, far-field metric deformations can act on an imaginary spherical shell centred about the linear radiator. Here is a link to a bare bones illustration I used in a below linked to forum thread:
https://s26.postimg.org/axee7pdmh/GR_GW_paradox_2.png

At rock bottom, all one need ask is can there logically be an axially symmetric azimuthal 'strain' h_φφ (usual spherical coordinates r, φ, θ) - locally tangent to any given line of latitude e.g. equator line? Given that in far-field, GR GW's are exclusively transverse and pure shear in character?

To claim that a circular hoop can undergo uniform circumferential strain without an accompanying radial expansion/contraction is laughably illogical. Yet the parallel in the linear radiator GW case has somehow never been noticed. And it's easily seen that relaxing the strictly transverse character of GR GW's to allow radial 'breathing', cannot resolve things in favour of transverse strains declining in amplitude in a 1/r radiation field manner. Instead, transverse strains decline as 1/r^2, and one has overwhelmingly radial i.e. longitudinal far-field 1/r displacement amplitudes. Which I do not believe a credible way out, for a number of reasons, including the following.

The situation just becomes worse when polar strains h_θθ acting along meridian lines of that imaginary spherical shell is considered. As you are no doubt aware, at any given local patch and any given instant t, h_φφ, h_θθ strains have equal amplitude but opposite sign ('+' polarizations - applying to axially symmetric linear oscillator). Hence, while say at t = t_0, latitude lines notionally want to 'breathe' outwards, meridian lines notionally want to 'breathe' inwards. And vice versa other half cycle. This is not QM - an initially static test particle can't both move in and out nor be in two places at the same time!

It was always a puzzle as to why one never sees a global view of the h_φφ, h_θθ strains in any of the many online illustrations and animations. Typically just cartoon 'water wave' depictions, and then only for binary case. Strange indeed!

Back in 2012 I first discovered and aired this issue in a forum thread, but that was a bad move ending in a life ban. My particular approach was to think about it in terms of Feynman's famous sticky beads argument e.g.
https://en.wikipedia.org/wiki/Sticky_bead_argument#Description_of_the_thought_experiment
https://en.wikipedia.org/wiki/Sticky_bead_argument#Feynman.27s_argument
As soon as such is applied to the axially symmetric linear quadrupole oscillator case, it becomes evident Feynman got it very wrong. Laughably obvious when one extends it to a large, uniformly distributed circular array of sticks and beads, sticks joined end to end around a far-field r>>λ equator line! The beads will logically move azimuthally somehow?! Given the axial symmetry? He he he.

Moral - go global view - not local patch view!
****************************************************************************************************************************************************************

 

[paddoboy]

Back in 2012 I first discovered and aired this issue in a forum thread, but that was a bad move ending in a life ban.

Best of luck my friend! See you on Stockholm in November!

Worth noting again, as the good Professor himself noted, he is one of the authors of one of the papers referenced by q-reeus.....

 

[The God]

Q-reeus,

On the context, good prof response is quite balanced. He acknowledges G4v, he does not claim GR as last word, he admits that observations can be explained alternatively.

He makes a subtle statement, give maths....That's something you are not doing despite multiple asking by me. I can understand your situation, you have an argument which you are not able to express mathematically. But till then you reach nowhere.

No need to respond on this, if you do not acknowledge the need of maths to refute GR...

 

[Q-reeus]

Q-reeus,

On the context, good prof response is quite balanced. He acknowledges G4v, he does not claim GR as last word, he admits that observations can be explained alternatively.

He makes a subtle statement, give maths....That's something you are not doing despite multiple asking by me. I can understand your situation, you have an argument which you are not able to express mathematically. But till then you reach nowhere.

No need to respond on this, if you do not acknowledge the need of maths to refute GR...

We have been here before. See #265 & #266. Don't keep spoiling it.

 

[paddoboy]

Just a quick observation...........
The three Wiki links in post 272 are all .......

• "This page was last modified on 2 August 2016"
• """"""""""""""""""""""""""""""""""""""""""

Two important statements in the Professor's E-Mail in my opinion are the following........
"This is evident when you consider how both quantum mechanics and special relativity are full of paradoxes that seem to point to contradictions that go away when expressed mathematically. Paradoxes point to the inadequacies of our intuitions, not to those of the theory".
speaks for itself.
and..............
"First, Feynman's sticky bead argument played an important role in re-igniting interest in GWs at a point in history when it wasn't clear whether they were real at all; however, the argument is not a core part of the GR framework and is usually not even referred to in modern treatments of the topic—our understanding of GR has come a long way since the 50's!"
Reading that my thoughts immediately entertain the consistent and boring claims of Farsight and his "Einstein said"........
Likewise our understanding of GR has progressed heaps since the great man formulated this incredible theory that so far has stood up to all tests thrown its way.

 

[expletives deleted]

paddoboy:
and
The God:
and
Q-reeus:

@paddoboy, thankyou for getting this response from Max Isi.

@The God, it is obvious that maths without logical and physical consistency makes for all sorts of absurd results and conclusions not dealing with the real physics in our real universe (eg, Black Hole 'singularities' and Big Bang 'beginnings').

@Q-reeus, I have spotted a couple of non sequitur counter arguments in Max Isi's reply to paddoboy regarding your OP; and I will now make comment on those as part of my own overall response to what Max Isi has said.

My name is Maximiliano Isi and I am a member of the LIGO Laboratory at the California Institute of Technology. I also happen to be the author of one of the papers cited...

How do you do, Sir, and thankyou for your interest in Q-reeus's OP, and for your reply to paddoboy addressing same.

It is absolutely true that our observations do not allow us to fully rule out the existence of non-GR physics. This is just a consequence of the fact that experimental observations have the power to disprove theories, but not to prove them: scientific theories are falsifiable, but not demonstrable. The best we can do is to say that our measurements agree with GR up to some (high) confidence level. It is in that precise sense that we mean "Einstein was right" (a misleading phrase: we don't know whether GR is fully accurate, we just cannot prove it wrong with what we have seen).

Thankyou for telling paddoboy what James R, others, and I, have been pointing out to him about that situation. I also have no qualms with GR itself, but only with the seemingly unwarranted extrapolations from it based purely on unreal mathematical concepts which do not seem to take real physical effects into account when making claims of GR GWs being possible as modeled for the LIGO observational construct. I trust this is understood? The GR insights are themselves quite good for the domain to which it applies; but the unreal extrapolations from the GR maths is open to challenge on the basis that it does not represent a real phenomenon in the specific model of GWs being questioned via Q-reeus's OP.

We have several methods to make quantitative statements about the agreement between the GR prediction and the signals we measure, but I won't describe them here in detail. Note that in order to find signals in the detector noise we use templates that tell us what the waves look like, and those templates are the output of highly–advanced super-computer simulations of GR dynamics; this means that the signal cannot be too different from the GR prediction or we wouldn't have seen it at all!

That is what causes great concern. Those templates inherently bias the whole observational construct and analysis based on the very maths and assumptions which Q-reeus's OP appears to challenge with objective free space geometry arguments which have no such assumptions involved and so are totally objective towards the real space situation regardless of the arguments from GR or other theory about that space (I have further comments in support of this space aspect in my response below to your "Second" item re "potential flaws" you claim to see in Q-reeus's OP scenario and related arguments).

Now, agreement with GR is not exclusive: an alternative theory might explain our observation just as well as GR or even better. Given any two competing theories (with different predictions), we can always ask which one is favored by our data, and we have well-established statistical methods to make quantitative statements to answer. Unfortunately, however, the mathematics of GW emission and propagation has only been worked out for very few of the viable alternatives to GR and in most of those cases the theories are similar enough to GR that the signals we'd expect to see are practically indistinguishable. The reason for this is that computing GW waveforms for interesting sources is an extremely complicated mathematical problem and (as mentioned above) it takes super-computers to do it even in GR, the theory we know best (and most alternatives are intrinsically more complicated).

Thankyou again for telling paddoboy what James R, others, and I, have also tried to tell him about that situation. And again I would like to point out that those "well-established statistical methods" are themselves vulnerable to overconfidence and assumptions and interpretations which go beyond what the data and the real physics actually represents. The latest case in point is the LHC diphoton 'bump' statistical flukes which led to analytical and maths technique 'artifacts' being considered 'possibly real' despite obvious signs that they could not be so in fact, but basically likely maths and stats 'artifacts'. The LIGO observations could also fall into that category since great trail of analytical maths and assumptions preceded the 'template matching' from modeling vulnerable to invalid extrapolations of GR maths and assumptions to the GR GW type of waves which Q-reeus's OP challenges the validity of in GR terms (I am commenting on the basis that Q-reeus's OP does not challenge GR itself, but only the extrapolation of its maths and assumptions to claim that GWs can occur as claimed in the GR maths construct itself. I trust this distinction is understood by all discussing this OP, as it will save much miscommunication and misunderstanding as to where everyone is coming from in their comments and arguments either way).

So far this has all been about the relation between theory and experiment. However, most of the text in your message alluded to potential logical inconsistencies within GR itself. Since the main point relies on a thought experiment, let me begin to address this by clarifying that, although thought experiments can be a very useful tool, they are not proper logical arguments in themselves and do not formally tell us anything about the the validity of a theory. This is because natural language is too ambiguous to express formal statements: GR (as every other physical theory) is a mathematical framework and we need mathematics to discuss it properly. This is evident when you consider how both quantum mechanics and special relativity are full of paradoxes that seem to point to contradictions that go away when expressed mathematically. Paradoxes point to the inadequacies of our intuitions, not to those of the theory.

It is long known that any maths can proceed logically (from its axioms) to absurdities unless at some stage account is taken of real physical limitations and likelihoods. That occurred early on with the SR maths construct when the Twin Paradox was initially formulated to highlight such maths absurdities if the logical mathematical axiomatic trail is followed slavishly in absence of real checks as to the real physical states being mathematically treated. In such instances it is precisely because of the maths that the paradoxes arise; and only the real physical considerations can prevent that inevitable paradox persisting. For example, the acceleration of which Twin is the real physical information which the maths must be provided with in order to forestall and resolve such an absurd SR maths created paradox; else the difference in ages between the stay at home and the returned traveling twin can never be explained by the SR maths as formulated without due regard to the real situation in space and motions (accelerations) involved.

So we "need" real checks and balances to the maths. Which means your assertion, that we "need' maths because theory is maths based, misses the important logical and physical checks and balances which must always be foremost when using such maths in analysis and extrapolations such as those involved here. Utter reliance on maths without due regulation of its assumptions and extrapolations according to validity and absurdity considerations will produce such 'artifacts' and false sense of security as has recently been displayed in LHC and LIGO (and previously Bicep2) results and claims which are founded in statistical and maths techniques which may unwittingly lead to overconfident misapplication and misinterpretation. Hence the challenge from Q-reeus is quite a good test for the claimed validity and interpretations made from GR maths extrapolations which seem not to take account of the real space and motion aspects which Q-reeus's OP is apparently aimed at addressing and settling, one way or the other, by having regard to the objective geometrical arguments irrespective of theory of space and motions brought to bear in any one or other observational construct or analysis.

THIS POST TO BE CONTINUED BELOW in PART POST #278 due to text limits necessitating split into two posts.

 

[expletives deleted]

THIS POST CONTINUES from PART POST #277 ABOVE which was split due to text limits.

That said, I'd like to point out a few potential flaws in the argument presented in your email, without actually going into mathematical detail:

First, Feynman's sticky bead argument played an important role in re-igniting interest in GWs at a point in history when it wasn't clear whether they were real at all; however, the argument is not a core part of the GR framework and is usually not even referred to in modern treatments of the topic—our understanding of GR has come a long way since the 50's!

Second, our intuitions about space and time do not jive well with GR. Because spacetime can be curved, the fact that circumference of the loop in the example decreases does not say much about the radius. For example, imagine you went in a circle around a massive object (say, Sun) and measured the distance travelled (call it c, for circumference), and then travelled radially inwards towards the center and measured that distance too (call it r, for radius), then you would find that c < 2*pi*r because the massive body curve the spacetime around it. This is all to say that a shrinking circumference does not imply a shrinking radius (at least not in all frames).

Third and last, it seems to be implied in the text you quote that the existence of longitudinal gravitational waves would be in conflict with GR; however, this is only true in a narrow sense that needs to be explained. According to GR, at any point in space-time one should be able to find a particular form of the GW equations (the technical term for this freedom in the eqs. is gauge, think of it as a frame of reference though it's not the same) in which the wave can be expressed as the combination of two independent polarizations transverse to the direction of propagation. Notice some key aspects of this statement: there is a specific choice of gauge (or frame of reference, if you wish) in which the equations take this particularly nice form, and that choice can only be defined locally (i.e. a choice that works nicely in one point in space, will be bad somewhere else). This means that if you choose an arbitrary frame of reference, chances are the wave will not look transverse, though you could always switch to the specific frame and gauge which will make the waves look nice at that point (this is the so called transverse-traceless gauge). The bottom line is that you might think that you have longitudinal waves, but you can always explain that as a combination of independent, transverse waves.

Re First: Nevertheless it has relevance in Q-reeus's OP and argument based on geometry not theory based argument and analysis. So your argument for discounting or disallowing it as the premise for his OP challenge is simply biased selection and/or deselection from your own opinion and not the objective and relevant situation Q-reeus is trying to convey in his OP challenge. I therefore with respect, Max Isi, cannot accept your offhand "deselection" of the OP scenario just because it may or may not have been at the core of GR framework.

Re Second: Your example and argument for criticizing the OP scenario is baseless when considering that the OP is all about free space and motions geometry which GR GW wavs are supposed to affect far from the source of the claimed GR GW types. So your introducing irrelevant mass-distorted 'circumference' arguments is not in keeping with the spirit and facts involved in the OP free space scenario which only treats the claimed effects of the claimed traveling GR GW modeled waves on the space and the beads as geometrically arranged for the OP thought experiment as posed. Again with respect, Max Isi, I cannot therefore accept as valid or relevant the introduction of your mass-distorted space and circumference etc arguments as somehow addressing let alone countering the OP arguments and challenge.

Re Third: In many discussions here there have been dire warnings against jumping between frames. That is what your argument effectively encourages. That is not acceptable, Max Isi. The only frame relevant is the one the OP geometry in free space and the bead motions can tell us about. That is what Q-reeus seems to be concentrating on, regardless of frames and maths shifting from one convenient but irrelevant and misleading absurd frame to to whatever other misleading and absurd frame is "needed" to make the invalid maths and assumptions work. In this thought experiment, Q-reeus seems to have cut through all of that jumping and irrelevance, and concentrated on the essential geometry arguments of space and beads in order to highlight what is real and not real in the analysis to date via the maths of GR extrapolated to somehow claim GR GWs as modeled for and applied in the LIGO construct. So again, Max Isi, with great respect, I cannot logically or physically treat your frames perspectives as either real or relevant in this simple OP scenario analysis from Q-reeus.

Finally, I would like to add a few words about Carver Mead's G4v theory. Unlike most alternatives to GR, Carver's theory makes markedly different predictions than GR with respect to the polarization content of GWs. However, the relative orientation of our detectors makes LIGO not really good at distinguishing different polarizations in transient (short-lived) signals like the ones we have observed so far. Furthermore, we don't have a full prediction of what the GW trace of the merger of two compact objects would look like in G4v (Carver is working on it), so we cannot make a statement about which theory, if any, is favored by the data. So we will have to wait for more detections and more theoretical work until we are able to make a statement about G4v.

The modeled Ringdown prediction for LIGO is just as subject to question as any other prediction modeled from another theory assumptions and expectations. As you have also effectively acknowledged, it is a fact that maths and statistical treatments and methodologies using assumptions from theory and hypotheses have tailored much of the currently applied mathematical and analytical and experimental constructs. This has unwittingly but effectively become so ingrained in all the current experimental procedures and pre-procedures and design and interpretation, that it doesn't surprise an observer when the claims of high confidence and concurrence with theory etc are made. The problem is that the maths and assumptions artifacts can easily become the 'real thing' in the theorists mind, and the actual physical real things be totally missed and dismissed as 'not real' simply because they do not concur with the whole theory and maths edifice which the experiments and interpretations are based on. This in my opinion is a dangerous state of affairs, and can only lead to more false claims while we are missing the real things that tell us more about what GR does apply to, and what it does not apply to, irrespective of maths extrapolations and assumptions if concurrence with GR which has been applied beyond its real physical remit.

Thankyou for reading this (two-part) post, which expresses my opinions and objective comments on Q-reeus's OP, and also on Max Isi's reply to paddoboy re Q-reeus's OP. I hope no one takes offense at my honest responses to those involved. Best.

 

[paddoboy]

deleted

 

[paddoboy]

Thankyou for telling paddoboy what James R, others, and I, have been pointing out to him about that situation.

Thankyou again for telling paddoboy what James R, others, and I

Obviously you have some form of obsession with me that interferes with any logical objectivity that one may presume that you have.
Firstly the Professor is not reading this thread, secondly he is certainly not interested in your obsessions, and thirdly he doesn't know James from a bar of soap.
Onto the science though, and this is where your obsession shines through.
My point and the Professor's point is that GR is not invalidated, it still stands as our best theory of gravity, and it makes a mockery of the title of this thread.
The rest of your post seems to be just the usual unsupported, unqualified objections that you have and have always had with any professional scientific mainstream paper, article or in this case, E-Mail.
I suggest you read his post again, and if you still are unclear as to what he is saying, then obtain a professional opinion yourself on the subject matter.
I mean we certainly know this person's qualifications [the professor's obviously] we do not know your's although I could give an educated guess as to what it is.