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

[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.

 

[timmdeeg]

Coming back to the QCD - GR analogy on which Deur's GR field self-interaction is based.

I wonder to which extent it makes sense to compare the quark - anti-quark linear confinement potential with a possible black hole - black hole counterpart.

And if in case of significant field self-interaction as Deur claims that should be detectable in the gravitational wave chirp of inspiraling black holes.

Any ideas?

https://media.springernature.com/lw...1/MediaObjects/486077_0_En_22-1_Fig2_HTML.png

 

[Structure seeker]

Any ideas?

We can't give our own ideas, forum rules. There are no written papers in the scientific community on this subject yet.

 

[ohwilleke]

It isn't clear why the arXiv posting was delayed so long. But, the response is in line with previous discussions in Deur's papers.

We comment on the methods and the conclusion of Ref. [1], "Does gravitational confinement sustain flat galactic rotation curves without dark matter?" The article employs two methods to investigate whether non-perturbative corrections from General Relativity are important for galactic rotation curves, and concludes that they are not. This contradicts a series of articles [2-4] that had determined that such corrections are large. We comment here that Ref. [1] use approximations known to exclude the specific mechanism studied in [2-4] and therefore is not testing the finding of Refs. [2-4].

A. Deur, "Comment on "Does gravitational confinement sustain flat galactic rotation curves without dark matter?'' arXiv:2306.00992 (May 13, 2023).

The introduction ends by stating:

To reach the conclusion that FSI is important for galactic rotation curves, Refs. [2, 3] performed static lattice calculations of the GR potential, and Ref. [4] computed that potential within a lensing model based on mean-field technique. The approximations of the former and the modeling of the latter break some of the tenets of GR. In contrast, the authors of [1] strive to be analytical and to preserve GR’s basic principles. Consequently, they employ different methods from Refs. [2, 3] and Ref. [4], whose results they could not reproduce. This lead the authors of [1] to refute the validity of [2–4, 7–11] and the basic connection of GEFC to GR.

In what follows, we expand (Section II) on why perturbative methods like the one used in [1] miss the non-perturbative effects of FSI of GR. Next, (Section III) we discuss the lensing-based model initially developed in [4] and signals two reasons why the calculation in Ref. [1] miss the FSI effects. Then, (Section IV) we argue that GEFC is in fact based on GR. We then summarize and conclude.

The conclusion states:

Disproving the non-perturbative, non-analytical results cannot be done by using the perturbative PPN framework as done in Ref. [1]. That GEFC is unrelated to GR is rebutted by showing that GEFC’s approximations preserve the relevant features of its starting point, viz GR. This is achieved by applying GEFC’s method to known cases, which was done for 7 distinct potentials (free-field in 1, 2 and 3 dimensions, Yukawa force, leading order PPN, φ 4 theory, and QCD). Lets consider the following five facts: (i) FSI, a feature of GR, provides naturally and without invoking DM and DE a unified explanation of the phenomena otherwise requiring DM and DE when analyzed in frameworks where FSI is absent (Newtonian gravity) or cancels (cosmological principle); (ii) FSI makes predictions of novel phenomena that have been subsequently observed; (iii) Intriguing parallels exist between GR and QCD, both for the theories and the phenomena they control;<7> (iv) FSI provides an innate framework for observations not explained naturally in ΛCDM<8>; and (v) solving the equivalent QCD problem of determining the increase of the force magnitude due to FSI has been notoriously difficult and its resolution remains a leading problem in physics.

These facts suggest that, even if a calculation yields too small FSI, it more likely points to an insufficiency of the method, as the PPN in [1], rather than a failure of GEFC.

In the worst case scenario that approximations used in lead incorrectly to conclude that GR’s FSI are significant enough, then the facts (i-v) would be pointing to GEFC missing the right mechanism rather than being wrong. In fact, even if the proposed mechanism (FSI) has been misidentified, it would only put GEFC on the same footing as ΛCDM and alternatives, e.g., MOND, that are not supported by a verified theory. It would not affect GEFC’s demonstration that alternatives to DM/DE-based models are possible even in the era of precision cosmology: contrary to oft-stated, high-precision observations, e.g., that of the CMB, do not establish the existence of DM/DE.

Another example is the claim that the Bullet Cluster observation proves DM (this article is titled “A direct empirical proof of the existence of dark matter”). This is disproved by the fact that the observation is naturally expected by GEFC, immaterial to whether or not the FSI mechanism is relevant.

That the numerous parallels between cosmology and hadronic physics are purely fortuitous coincidences is unlikely, especially because of the similar theoretical structure of GR and QCD. It is injudicious to ignore these leads only because exact calculations are impossible and approximations can be contested. This is especially true in light of the issues presently faced by ΛCDM and the ability of GEFC to explain astronomical and cosmological observations.

As GEFC’s claims are outstanding and far-reaching, they must be rigorously scrutinized. This is what Ref. [1] undertook but with a method not adapted to the problem. The way forward is to test GEFC with numerical non-perturbative methods and remember that 50 years of trying to solve the similar, but simpler QCD problem has checked many methods.

Footnote 7: Specifically, these parallels are between (a) the GR Lagrangian, (b) the observations interpreted as evidence of dark matter, (c) those for dark energy, (d) the cosmic coincidence problem, (e) the Tully-Fisher relation, (f) galactic matter density profiles on the GR side, and (A) the QCD Lagrangian, (B) the magnitude of hadron masses, (C & D) the confinement of QCD forces in hadrons, (E) hadron’s Regge trajectories, (F) hadronic density profiles on the QCD side, respectively.

Footnote 8: Inter alia, the Tully-Fisher and RAR correlations, Renzo’s rule, cosmic coincidence, Hubble tension, dwarf galaxies overcounting, absence of direct detection of dark matter particle and absence of natural candidates within particle physics.