Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

[timmdeeg]

No, but the recent preprint by Barker et.al. https://arxiv.org/abs/2303.11094 cited in post #10 above does purport to take non-linearities into account (and employs actual General Relativity (GR) rather than some scalar approximation to boot!).

Sure, please see #13, wherein this article is mentioned..

My remark in #34 refers to #16 and the discussion whether or not it disproves Deur.

 

[Adrian59]

You could make the same argument about perpetual motion. Every time someone claims it to work, someone complains and the thread is shut down.

I am always amazed at how they simplest remarks often engender the most comment. I didn't know there were hordes of perpetual motion supporters making a lot of noise, certainly not as much as ΛCDM supporters!

 

[Adrian59]

From a critique of Cooperstock and Tieu:

As I have said, over the past few years I have been a supporter of these alternative theories for galactic dynamics that do not need dark matter or any modification of gravity. In order to give my argument more rigour I have actively sought out several critiques of Cooperstock etc. and found them all wanting.

Your reference (Daniel Cross, 2006) appears to get hung up by an issue with the ‘z’ axis (end of section 1.) Since the ‘z’ axis is orthogonal to the motion is question, so is the argument. Furthermore, equation (30) appears to be sneaking the Keplerian approach in the back door.

In another thorough review by de Almeida et al (not mentioned in this thread so far) the Cooperstock approach is rejected on the spurious grounds that it needs extra mass to work. I say spurious since Cooperstock himself and another critique by Herrera-Aguilar et al all accept the need for some extra mass. However, de Almeida et al have no problems with the ‘z’ dependence of the metric, thus contradicting Cross.

That Cross mentions the ‘z’ dependence are undermined by a paper by Joanna Jalocha et al (referenced in #22) since they used Newtonian mechanics in their derivation, but they come to the same conclusion as Cooperstock. Jalocha and Cooperstock derive almost identical differential equations which they both solve using the Bessel function. If there was a serious issue with the metric as Cross appears to suggest, then why does Cooperstock get the same result as Jalocha?

 

[Adrian59]

It seems clear Deur ideas are wrong #16 and arxiv.org/abs/2303.11094.

are you ready to move on?

After reading your reference I agree with Ohwilleke, below.

The linked article doesn't even claim more than "probably" wrong. Also, it is only concluding that the conclusion is not pure GR not that it doesn't match the observational evidence.

Also, it appears to be questionable since towards the end of the paper they make a startling claim:

"What we will do here to compare, is to repeat our calculations above, but this time computing the lensing caused by an annulus of matter stretching from R′ to R′ + ΔR' in the R direction, and effectively infinitesimally thin in the R direction, since instead of a 3d density distribution rho(R, z) we will just ascribe to it a surface density distribution Σ(R), with R evaluated at R′ for the annulus of interest ... However, we shall show below that the actual calculation was based on finding the Newtonian potential of the annulus assuming it is concentrated along z = 0. Hence we shall follow this line in working out our results, and from these demonstrate that in fact it is allowable to take this approach for a non-infinitesimally thin annulus as well.'

My question is allowable on whose grounds - theirs because they succeed in their attempt to refute Deur!

 

[Vanadium 50]

Could you please elaborate your calculation?

I am comparing the gravitational potential energy - of which the self-energy is a part - to the amount of dark matter needed, which I approximate by the visible mass.

If this missed by a fa tor of 2, or 5, we could discuss whether a better approximation is needed. But it misses by a million.

One if free to say "Well, this isn't actually just conventional gravity - it's tweaked here and there", and that's fair, but it's equally fair then to turn around and ask "what predictions does this make for the PPN parameters and do they agree with data?" If the answer to that is "Golly, I don't know, but who cares! Dark Matter!" color mr unimpressed.

 

[Adrian59]

This thread seems to be a hodgepodge of people cheerleading for their favorite theories of modified gravity. Lets go back to the thread titie: Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

It can't, and it should be obvious.

Grabitational self-interaction will of of order the gravitational potential energy (I am ignoring factors of 2 or pi or whatever, or GM2/r this has to exceed Nc2r by around a factor of 5:
GM2r>Mc^2
GMrc^2>1
The left hand side needs to be about a million times bigger. It's not even close

Doesn't your inequality put us below the Schwarzschild radius?

 

[kodama]

I am comparing the gravitational potential energy - of which the self-energy is a part - to the amount of dark matter needed, which I approximate by the visible mass.

If this missed by a fa tor of 2, or 5, we could discuss whether a better approximation is needed. But it misses by a million.

comparable to gravitomagnetism GEMKostas Glampedakis, David Ian Jones, "Pitfalls in applying gravitomagnetism to galactic rotation curve modelling" arXiv:2303.16679

 

[strangerep]

I am comparing the gravitational potential energy - of which the self-energy is a part - to the amount of dark matter needed, which I approximate by the visible mass.

(Sigh.) Pardon my density, but I need more explanation than this. First you said that $GM^2/r$ had to exceed $N c^2 r$. I assume that $N$ should be an $M$, but what is an $r$ doing in the 2nd expression? Those 2 expressions don't have the same dimensions. I'm guessing the 2nd $r$ should be there, since in the next line you require $$\frac{GM^2}{r} ~>~ Mc^2 ~,$$which at least has correct dimensions.

But what exactly is the $M$ here? A total galactic mass? The mass of a test body??
That gravitational potential energy looks like it's between 2 bodies, each of mass $M$, separated by a distance $r$. How does this relate to gravitational self-energy? (If it's a mass interacting with itself, then shouldn't $r$ be $0$?)

Please clarify properly.

 

[Vanadium 50]

Please clarify properly

I apologize for being improper.
Maybe "goodbye" is the best clarification passible,.

 

[ohwilleke]

The rough benchmark analysis that Deur was using to estimate the potential self-interaction effect was that this is a function, roughly speaking, of system mass and system size (the quote below is a paraphrase of one of his conference presentations):

Near a proton GMp/rp=4×10^-38 with Mp the proton mass and rp its radius. ==>Self-interaction effects are negligible. . . .

For a typical galaxy: Magnitude of the gravity field is proportionate to GM/sizesystem which is approximately equal to

10^-3.

This figure for galaxies is in the ballpark as for close binary stars where gravitational field self-interactions/non-linearities are widely acknowledged.

He doesn't make the computation, but using the same analysis, for wide binary stars GM/sizesystem which is approximately equal to:

10^-7.

 

[ohwilleke]

I am comparing the gravitational potential energy - of which the self-energy is a part - to the amount of dark matter needed, which I approximate by the visible mass.

Part of the issue, I think, is that in all of the gravitational approaches with MOND-like results, the only tweaks are at the fringes of the system where gravitational fields are weakest, with a second order effect that doesn't decline as rapidly a Newtonian gravity. In contrast, DM has to act on the whole sale so the magnitude needed is much greater.

 

[kodama]

The rough benchmark analysis that Deur was using to estimate the potential self-interaction effect was that this is a function, roughly speaking, of system mass and system size (the quote below is a paraphrase of one of his conference presentations):

But it misses by a million. comparable to gravitomagnetism GEM which also misses by a million.

 

[Adrian59]

But, if it works in the complete domain of applicability of all evidence about gravity, which it appears to so far, makes novel predictions so far confirmed by new astronomy data, does it without dark matter or dark energy, and isn't mathematically pathological (there has never been a hint that it is), and can do it with a tensor theory rather than the tensor scalar of LambdaCDM and GR with a cosmological constant (which also makes generalization to quantum gravity easier), and possibly has one less free parameter (which Deur has claimed but not proven by deriving an additional parameter that is used on the assumption that it could be derived), then that's still great, Nobel prize class stuff, even if he inaccurately assumed that it was equivalent to GR and even if it actually has an additional free parameter.

I am following this thread with interest, and as such I am checking most of the references. I have had a copy of one of Deur's papers (A possible explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity) for some time. However, I note that this approach has not been without controversy, as the reference below suggests:

It seems clear Deur ideas are wrong #16 and arxiv.org/abs/2303.11094.

However, this paper by W. E. V. Barker, M. P. Hobson, A. N. Lasenby goes into some detail about a scalar extension to gravity which it then appears to show is untenable. It is not clear whether they consider that Deur's approach uses a scalar component. Of course general relativity is a tensor application, and a scalar extension is a feature of modified theories. My question is: does Deur's approach feature a scalar component?

 

[ohwilleke]

I am following this thread with interest, and as such I am checking most of the references. I have had a copy of one of Deur's papers (A possible explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity) for some time. However, I note that this approach has not been without controversy, as the reference below suggests:
However, this paper by W. E. V. Barker, M. P. Hobson, A. N. Lasenby goes into some detail about a scalar extension to gravity which it then appears to show is untenable. It is not clear whether they consider that Deur's approach uses a scalar component. Of course general relativity is a tensor application, and a scalar extension is a feature of modified theories. My question is: does Deur's approach feature a scalar component?

A full annotated bibliography for Deur's work on gravity and some related papers can be found at http://dispatchesfromturtleisland.blogspot.com/p/deurs-work-on-gravity-and-related.html

My question is: does Deur's approach feature a scalar component?

No. A scalar approximation is used by Deur solely for the purpose of simplifying the calculations. He conceives of it as a pure tensor theory.

 

[Adrian59]

No. A scalar approximation is used by Deur solely for the purpose of simplifying the calculations. He conceives of it as a pure tensor theory.

That is what I thought. I don't know if you have seen the Barker et al paper (arxiv.org/abs/2303.11094) but it appears to get bogged down in minutiae. They, as I said, spend a whole section refuting a 'scalar model' which would appear irrelevant wrt Deur's papers. They then spend time refuting a gravito-electro- magnetic approach which is also irrelevant wrt Deur's papers. They only get around to discussing Deur's paper directly in section IV where they write, 'it seems difficult to understand how factors of order 10^3 in the lensing could arise’. They seem to be suggesting that this is what Deur does, but I can not see how the ΛCDM model and Deur can be three orders of magnitude different.

 

[ohwilleke]

That is what I thought. I don't know if you have seen the Barker et al paper (arxiv.org/abs/2303.11094) but it appears to get bogged down in minutiae. They, as I said, spend a whole section refuting a 'scalar model' which would appear irrelevant wrt Deur's papers. They then spend time refuting a gravito-electro- magnetic approach which is also irrelevant wrt Deur's papers. They only get around to discussing Deur's paper directly in section IV where they write, 'it seems difficult to understand how factors of order 10^3 in the lensing could arise’. They seem to be suggesting that this is what Deur does, but I can not see how the ΛCDM model and Deur can be three orders of magnitude different.

I have quickly skimmed Barker, et al., but still haven't given it the deep dive that it deserves.

On the whole it is a sincere and fair minded effort. But I do have some issues with their approach, which is basically an attempt to reproduce Deur's claims from scratch using the same assumptions, rather than looking at Deur's analysis on a step by step basis like a geometry proof and then identifying where they think Deur made a misstep.

As readers, we are left to puzzle that out ourselves. But, it matters quite a lot.

For example, even though Deur wrote one truly classical GR paper, his original work as a quantum gravity inspiration in a weak field domain of applicability where the failure to quantum gravity efforts to remain mathematically sound in the ultraviolet doesn't matter. If he has actually picked up on a quantum gravity deviation from classical GR as conventionally applied, for example, that's a less discouraging problem than a problem with dimensional analysis or an overlooked cancellation of terms.

Another place that could be ripe for a disconnect is that in the spiral galaxy case, he picked the parameter kappa of the self-interaction term in the spiral galaxy geometry case to fit observations originally fitted for MOND rather than deriving it from first principles as a function of Newton's constant G and the geometry and mass scales involved.

Refuting a scalar model is an appropriate strategy, but by using the method of trying to reinvent it from scratch and concluding that it comes to a different result, it isn't entirely clear what the source of the problem with the scalar model is other than that they can't make one that works.

What is the tensor formulation bringing to the party that the scalar model doesn't?

Naively, the hypothesis that one can safely ignore contributions from linear momentum, angular momentum, electromagnetic flux, and pressure in the context of galaxy scale astronomy, just as the scalar Newtonian approximation of GR does, doesn't seem unsound.

Does Deur have the GR Lagrangian wrong (he does expand it into a series in a somewhat unusual way)?

Baker doesn't seem to really pick up on the strong importance conceptually of self-interaction being a second order effect that declines in magnitude more slowly with distance than the first order Newtonian term - making it irrelevant since it starts out so weak, in fields comparable in strength to those where MOND does not apply, while making it important beyond that point with a naturally realized interpolation function.

Is the main issue, in the spiral galaxy context anyway, not the GR Lagrangian itself, but the kappa parameter used for the self-interaction term which they find to be too large calculating from first principles of GR?

Also, while refuting a scalar approximation is an important step, it doesn't explain how the result could seemingly be replicated by Deur with classical GR in one paper.

In short, while Baker et al. is not confirming, it also doesn't provide much insight into why that should be the case.

I would also welcome a paper dissecting different layers of Deur's analysis to again, pin point what is problematic and what might be salvageable.

For example, most of the large scale structure and Hubble constant conclusions that Deur reaches require only a far more general model in which dark matter phenomena are actually gravitational effects, and where increased dark matter phenomena magnitudes in a galaxy or galaxy cluster translate into reduced attraction between galaxies and/or galaxy clusters. Is there any promise to this very general class of gravitational explanations of dark matter and dark energy?

As far as I can tell, there is similarly no analysis of the notion of gravitational field flux tubes, by analogy to QCD, in galaxy clusters.

 

[Adrian59]

Thanks for taking the time to provide a detailed response. A few paragraphs caught my eye.

Refuting a scalar model is an appropriate strategy, but by using the method of trying to reinvent it from scratch and concluding that it comes to a different result, it isn't entirely clear what the source of the problem with the scalar model is other than that they can't make one that works.

The issue I have with Baker et al was that I did not think, as you agreed in #49, that Deur used a scalar model, so that it is somewhat disingenuous to refute a model that was not used.

Baker doesn't seem to really pick up on the strong importance conceptually of self-interaction being a second order effect that declines in magnitude more slowly with distance than the first order Newtonian term - making it irrelevant since it starts out so weak, in fields comparable in strength to those where MOND does not apply, while making it important beyond that point with a naturally realized interpolation function.

I agree with your point here about Baker et al missing the connect with the phenomenology of MOND.

As far as I can tell, there is similarly no analysis of the notion of gravitational field flux tubes, by analogy to QCD, in galaxy clusters.

I, also, thought this was a strange addition to gravitation. Possibly, Deur was taking the analogy between QCD and gravity a bit too far though I like the similarities he delineates between gravity and QCD as field equations which steps away from the almost Keplerian approach of ΛCDM.

 

[Adrian59]

TL;DR Summary: Gravitational self-interaction cannot replace dark matter

the question is why if Deur is correct why has his results been missed by numerical general relativity and other approximations by highly qualified GR experts

The problem with Deur is that he is challenging the dominant paradigm. One needs to read 'The Structure of Scientific Revolutions' by Thomas S. Kuhn (1962) to fully understand how the establishment often reacts to such challenges.

 

[Adrian59]

TL;DR Summary: Gravitational self-interaction cannot replace dark matter

Can dark matter in galaxies be explained by relativistic corrections?​

Mikołaj Korzyński1

Abstract​

Cooperstock and Tieu proposed a model of galaxy, based on ordinary GR, in which no exotic dark matter is needed to explain the flat rotation curves in galaxies. I will present the arguments against this model. In particular, I will show that in their model the gravitational field is generated not only by the ordinary matter distribution, but by a infinitely thin, massive and rotating disc as well. This is a serious and incurable flaw and makes the Cooperstock–Tieu metric unphysical as a galaxy model

I have been following this thread with interest, and as such I have tried to read all the references. The problem I have with this paper is that it is only accessible for myself by paying for it, and I do not pay for papers.

However, I have read the Cooperstock and Tieu paper which is freely available, and I find even the Korzynski abstract questionable. There is no infinitely thin, massive disc in Cooperstock and Tieu's paper, although they discuss the discontinuity at z=0, they allow for this.

 

[kodama]

The problem with Deur is that he is challenging the dominant paradigm. One needs to read 'The Structure of Scientific Revolutions' by Thomas S. Kuhn (1962) to fully understand how the establishment often reacts to such challenges.

GR reduces to Newton in the weak field limit which is too weak to explain dark matter by a factor of a million

 

[Adrian59]

GR reduces to Newton in the weak field limit which is too weak to explain dark matter by a factor of a million

I think this should be a response my #54 entry, not my #55 entry that you quoted. However continuing the conversation I started in #55, I do not know where you get this million factor from since even uncorrected gravity, that is prior to dark matter, is not out by that order of magnitude, unless I am missing something.

Reference: Van Albada, T., Bahcall, J., Begeman, K. and Sanscisi, R. (1985). ‘Distribution of Dark Matter in the Spiral Galaxy NGC 3198’. The Astrophysical Journal; 295: pp 305-313.

 

[kodama]

I think this should be a response my #54 entry, not my #55 entry that you quoted. However continuing the conversation I started in #55, I do not know where you get this million factor from since even uncorrected gravity, that is prior to dark matter, is not out by that order of magnitude, unless I am missing something.

Reference: Van Albada, T., Bahcall, J., Begeman, K. and Sanscisi, R. (1985). ‘Distribution of Dark Matter in the Spiral Galaxy NGC 3198’. The Astrophysical Journal; 295: pp 305-313.

#16

 

[Adrian59]

#16

Actually, I did get my nos. the wrong way around. You quote Vanadium 50 from #16, but I believe that strange rep was having problems understanding how Vanadium 50 arrived at this number, see below:

Could you please elaborate your calculation? It's not obvious (to me at least) where/how you're getting these expressions and inequalities.

I thought that the quoted inequality was below the Schwarzschild radius. However, the source of this discrepancy still appears indistinct.

 

[kodama]

Actually, I did get my nos. the wrong way around. You quote Vanadium 50 from #16, but I believe that strange rep was having problems understanding how Vanadium 50 arrived at this number, see below:
I thought that the quoted inequality was below the Schwarzschild radius. However, the source of this discrepancy still appears indistinct.

Grabitational self-interaction will of of order the gravitational potential energy

agree ?

 

[Adrian59]

Gravitational self-interaction will of of order the gravitational potential energy

agree ?

No, I do not wholly agree. See #51, from which I quote:

self-interaction being a second order effect that declines in magnitude more slowly with distance than the first order Newtonian term - making it irrelevant since it starts out so weak, in fields comparable in strength to those where MOND does not apply, while making it important beyond that point with a naturally realized interpolation function.

Since I regard the gravitational potential energy as a first order phenomenon, it is clearly not of the same order as the gravitational self energy which is a second order phenomenon.

However returning to the issue you raised in #55, it is these second order effects that explain the flat rotation curves. The claim, as I understand, is that there does not have to be such a large addition from these second order effects to match the observed data.

 

[ohwilleke]

I, also, thought this was a strange addition to gravitation. Possibly, Deur was taking the analogy between QCD and gravity a bit too far though I like the similarities he delineates between gravity and QCD as field equations which steps away from the almost Keplerian approach of ΛCDM.

I actually think this is one of the brilliant aspects of Deur's work and quite likely is the insight that motivated this line of analysis in the first place.

As the QCD squared paradigm of quantum gravity demonstrates, QCD and gravity should be strongly analogous as non-Abelian gauge theories.

This is how Deur manages to elegantly address the problem of MOND underestimating inferred dark matter phenomena in galaxy clusters without changing the underlying Lagrangian.

 

[kodama]

No, I do not wholly agree. See #51, from which I quote:
Since I regard the gravitational potential energy as a first order phenomenon, it is clearly not of the same order as the gravitational self energy which is a second order phenomenon.

However returning to the issue you raised in #55, it is these second order effects that explain the flat rotation curves. The claim, as I understand, is that there does not have to be such a large addition from these second order effects to match the observed data.

in GR, gravity = curvature = energy

Gravitational self-interaction = gravitational potential energy

gravitational potential energy = Gravitational self-interactionthis can be calculated

For two pairwise interacting point particles, the gravitational potential energy U U is given by
U = − G M m R ,

where M M and m m are the masses of the two particles, R R is the distance between them, and G G is the gravitational constant.[1]

its too weak like GEM

 

[KurtLudwig]

MOND, as proposed by Prof. Mordecai Milgrom, is an empirical equation. It does correctly predict gravity at stars in the very weak gravitation regions in our Milky Way galaxy and correctly predicts the speeds of their rotation curves. According to Professor Alexander Deur gravitational fields also self-interact. Therefore, gravity at a particular star is the sum of Newtonian acceleration, due the gravitational field interacting with mass, plus Mondian acceleration due to gravitational self-interaction.
acceleration(total at local star) = GM(of distant star)/r squared + square root(GM (of distant star) a0 (Mond constant of 1.20 E-10 m/s2)/ r (not squared)
When two stars, the size of our Sun, are apart at distances travelled by light, in times stated below, gravities due to Newton and MOND are
1 minute aNewton = 4 E-1 and aMond = 7 E-6 m/s2 difference E-5
1 hour aNewton = 1 E-4 and aMond = 1 E-7 m/s2 difference E-3
1 week aNewton = 4 E-9 and aMond = 7 E-10 m/s2 difference E-1
1 month aNewton = 2 E-10 and aMond = 2 E-10 ms/2 difference E 0
1 year aNewton = 1 E-12 and aMond = 1 E-11 m/s2 difference E+1
At 1 light year distance between two suns, the acceleration due to MOND (Deur's gravitational field self-interaction) is larger that acceleration due to Newton's formula.
10 years aNewton = 1 E-14 and aMond = 1 E-12 difference E+2
100 years aNewton = 1 E-16 and aMond = 1 E-13 difference E+3
1000 years aNewton = 1 E-18 and aMond = 1 E-14 difference E-4
10,000 years aNewton = 1 E-20 and aMond = 1 E-15 difference E+5
As you can see, at the outer reaches of the Milky Way, MOND gravitational acceleration predominates.

 

[Adrian59]

Recap of this thread:

The initial question posed at the beginning of the thread was a good one:

TL;DR Summary: Gravitational self-interaction cannot replace dark matterDeur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves.

The conversation appeared to quite rightly concentrate on three-four counter papers

A. N. Lasenby, M. P. Hobson, W. E. V. Barker, "Gravitomagnetism and galaxy rotation curves: a cautionary tale" arXiv:2303.06115 (March 10, 2023).

and this from Daniel J. Cross, 'Comments on the Cooperstock-Tieu Galaxy Model' see above for link.

In response to my last query in this thread I received:

in GR, gravity = curvature = energy

Gravitational self-interaction = gravitational potential energy

gravitational potential energy = Gravitational self-interactionthis can be calculated

For two pairwise interacting point particles, the gravitational potential energy U U is given by
U = − G M m R ,

where M M and m m are the masses of the two particles, R R is the distance between them, and G G is the gravitational constant.[1]

its too weak like GEM

I am not sure what to make of this reply. I t looks like a pedagogical approach to basic Newtonian gravity which raises the question as to what level this thread is on. From the onset I would consider this thread as post grad.

I would like some further comments on the three or four papers referenced above, as I thought that was the purpose of the initial question, and not an explanation of Newton' laws of gravity.

 

[Adrian59]

When two stars, the size of our Sun, are apart at distances travelled by light, in times stated below, gravities due to Newton and MOND are
1 minute aNewton = 4 E-1 and aMond = 7 E-6 m/s2 difference E-5
1 hour aNewton = 1 E-4 and aMond = 1 E-7 m/s2 difference E-3
1 week aNewton = 4 E-9 and aMond = 7 E-10 m/s2 difference E-1
1 month aNewton = 2 E-10 and aMond = 2 E-10 ms/2 difference E 0
1 year aNewton = 1 E-12 and aMond = 1 E-11 m/s2 difference E+1
At 1 light year distance between two suns, the acceleration due to MOND (Deur's gravitational field self-interaction) is larger that acceleration due to Newton's formula.
10 years aNewton = 1 E-14 and aMond = 1 E-12 difference E+2
100 years aNewton = 1 E-16 and aMond = 1 E-13 difference E+3
1000 years aNewton = 1 E-18 and aMond = 1 E-14 difference E-4
10,000 years aNewton = 1 E-20 and aMond = 1 E-15 difference E+5
As you can see, at the outer reaches of the Milky Way, MOND gravitational acceleration predominates.

I am not sure these values are correct. Milgrom MOND only becomes significant at the outer reaches of a galaxy, so for instance in our milky wat that would be in the order of at least 25,000 light years.

 

[Structure seeker]

I've just read about resurgence theory and I understand from it that in quantum perturbation theory it is common practice to, for not simple enough systems, truncate the iterations of perturbations after a few terms. For the contributions of these perturbations are smaller at each step and it needs lots of calculations.

However, at the same time it is quite known that the series of contributions diverges after too much iterations - it is then said that the calculations become "unphysical". But in the strict mathematical model they ought to be calculated in.

Is it possible that for spin 2 self-interacting gravitons the non-linear "perturbations" display likewise behaviour? If calculated properly using resurgence theory or maybe even more is needed, these effects then might solve the gap between the first-view calculations (by for instance @Vanadium 50) and what Deur's theory numerically needs. Deur's gravitons aren't using GR equations after all, but quantum field equations.

 

[Structure seeker]

In any case Deur's methods come from QCD, and from wikipedia on perturbation theory:

In quantum chromodynamics, for instance, the interaction of quarks with the gluon field cannot be treated perturbatively at low energies because the coupling constant (the expansion parameter) becomes too large

So that's especially the field where these nonperturbative effects lie. This possibility has to be taken into account in the weighing of Deur's approach, since as QCD researcher he is probably very aware of this effect. And I'm just saying "possibility" of course.

 

[yoyoq]

i had really hoped they would explain that GMM/r > Mc^2

its so vague, it seems it could be an argument against dark matter.

the rest mass energy of the dark matter must be less than the normal Newtonian potential ?

 

[Adrian59]

I am quoting from another thread, 'CMBR Evidence for Non-baryonic Dark Matter' from the cosmology section, but my comment is more pertinent to this thread. The fact is that the rotation curve for the ultra diffuse galaxy ACG 114905 is not explained by a dark matter halo or Milgrom MOND hypothesis.

In that case of ACG 114905, the most likely cause is an angle of inclination measurement error in the initial assessment that it is Keplerian (an uncertainty that the initial paper describing ACG 114905 as a Keplerian galaxy itself identifies as a potential source of a serious problem with its assessment), citing Banik et. al. (2022) titled, “Overestimated inclinations of Milgromian disc galaxies: the case of galaxy AGC 114905“.

Contrary to the quote above by Olwilleke, the authors point out in the abstract that 'The inclination of the galaxy, which is measured independently from our modelling, remains the largest uncertainty in our analysis, but the associated errors are not large enough to reconcile the galaxy with the expectations of cold dark matter or Modified Newtonian dynamics.' I confess to being no expert in the detailed measurement of the velocity data, so I cannot say whether the authors have made sufficient provision to mitigate against this potential source of error.

If indeed the data is correct, then this is strong observational evidence for gravitational field approaches like Deur's or Cooperstock's.

I did check the other reference by Banik et al. Of note one of the et al is Pavel Kroupa who is a strong proponent of MOND. In their abstract they say, 'This plausibly reconciles AGC 114905 with MOND expectations.'

 

[Adrian59]

i had really hoped they would explain that GMM/r > Mc^2

its so vague, it seems it could be an argument against dark matter.

the rest mass energy of the dark matter must be less than the normal Newtonian potential ?

I do not know what level you are asking this question, so I apologize in advance if this is too basic.

The only time I have seen a similar inequality is when working out an escape velocity.

The easiest way that I understand this is to do it in reverse and calculate the impact velocity of an object falling to the surface of an astronomical body. Since potential energy is to be regarded as not absolute, one can assign it zero at infinity, that is sufficiently far from the astronomical body. Noting potential energy is force times distance one integrates between infinity and the surface of the body assigned r, and equates this to kinetic energy at impact:

½ mv^2 = - ∫between ∞ and R, GM m / r^2 dr

Since one has assigned zero potential energy at infinity the potential energy decreases with descent, going more negative.

So, ½ mv^2 = - [GM m / r ] between ∞ and R, = GM m / R

The mass m of the falling object cancels giving:

½ v^2 = GM / R

So the escape velocity is v = √(2GM / R).

Rearranging this equation gives: R = 2GM / v^2

One can then consider a maximum escape velocity as the speed of light (c):

Rs = 2GM / c^2

Where Rs is the Schwarzschild radius which marks the event horizon of a black hole, since if:

Rs < 2GM / c2,

even light cannot escape the astronomical body.