A LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

[kodama]

. It is proven to be equivalent to first order Post Newtonian approximation of GR, which is all that is needed to be used for the most precise solar system computations. In your prior post, you mention a paper quoting a Post Newtonian correction term. This term is implicitly contained in the GEM formalism.

does

It is proven to be equivalent to first order Post Newtonian approximation of GR, which is all that is needed to be used for the most precise solar system computations. In your prior post, you mention a paper quoting a Post Newtonian correction term. This term is implicitly contained in the GEM formalism.

does Post Newtonian correction term also implicitly contained self interaction term

 

[PAllen]

does

does Post Newtonian correction term also implicitly contained self interaction term

"self interaction term" has many meanings to many people. I am discussing something much more well defined. In the 4th paragraph on p. 5 of https://www.ast.cam.ac.uk/sites/default/files/Invention_DM&DE_Rev1201_011221.pdf, a term in the Einstein-Infeld-Hoffman equations (that implement first order Post Newtonian approximation) is mentioned. This term is implicitly included in the GEM formalism. For any other question, you will need to be much more specific. IMO, GEM is sufficient to model any conceivably observable differences galaxy dynamics between Newtonian and non-Newtonian (assuming GR and nothing else as the gravity theory) and it suggests there are none of any significance.

 

[kodama]

"self interaction term" has many meanings to many people. I am discussing something much more well defined. In the 4th paragraph on p. 5 of https://www.ast.cam.ac.uk/sites/default/files/Invention_DM&DE_Rev1201_011221.pdf, a term in the Einstein-Infeld-Hoffman equations (that implement first order Post Newtonian approximation) is mentioned. This term is implicitly included in the GEM formalism. For any other question, you will need to be much more specific. IMO, GEM is sufficient to model any conceivably observable differences galaxy dynamics between Newtonian and non-Newtonian (assuming GR and nothing else as the gravity theory) and it suggests there are none of any significance.

Deur theory that proposed self interaction of GR is strong enough to explain MOND over Post Newtonian correction term

 

[PAllen]

Deur theory that proposed self interaction of GR is strong enough to explain MOND over Post Newtonian correction term

In my opinion, Deur theory is an alternate gravity theory suggested by analogies between the GR Lagrangian and QCD. This is fine, except he claims that certain results are standard GR with no convincing evidence - against much evidence to the contrary ( no method starting from GR equations reproduces his results). I just wish he would advocate for his results as a form of MOND.

 

[kodama]

In my opinion, Deur theory is an alternate gravity theory suggested by analogies between the GR Lagrangian and QCD. This is fine, except he claims that certain results are standard GR with no convincing evidence - against much evidence to the contrary ( no method starting from GR equations reproduces his results). I just wish he would advocate for his results as a form of MOND.

how could Deur theory be modified suggested by analogies between the GR Lagrangian and QCD. to get it to work as a form of MOND.?

 

[Adrian59]

Wrong.

I was asking for clarification (questions are never wrong only the answers), by suggesting alternatives, so which alternative is wrong? The trite response could be both, but I think that I have exposed the problem that the term is being used in possibly three different contexts: 1) Einstein weak field approximation; 2) a more specific combination of gravity and Maxwellian electromagnetism as in Ludwig's paper; and 3) to, erroneously, describe Deur's approach, see the Barker et al paper, referenced in this thread.

You appear to be opting for 1), but in the references, authors are using the term differently: hence my post!

 

[Adrian59]

This is fine, except he claims that certain results are standard GR with no convincing evidence - against much evidence to the contrary (no method starting from GR equations reproduces his results).

Have you seen any papers by Cooperstock. He uses GR to describe the rotation curves of galaxies without any modification, see refs below:

1) Cooperstock, F. and Tieu, S. (2005). ‘General Relativity Resolves Galactic Rotation without Exotic Dark Matter’. arXiv:astro-ph/0507619.

2) Carrick J. and Cooperstock, F. (2012). ‘General Relativistic Dynamics Applied to the Rotation Curves of Galaxies’. Astrophysics and Space Science; 337, Iss. 1: pp 321–329.

3) Cooperstock, F. and Magaheis, N. (2015). ‘Galactic mapping with general relativity and the observed rotation curves’. arXiv:1508.07491v1.

 

[PAllen]

how could Deur theory be modified suggested by analogies between the GR Lagrangian and QCD. to get it to work as a form of MOND.?

Maybe MOND is not the right word. I mean the broader class of modified gravity theories. In this case, a new theory suggested by GR and QCD analogies.

 

[PAllen]

Have you seen any papers by Cooperstock. He uses GR to describe the rotation curves of galaxies without any modification, see refs below:

1) Cooperstock, F. and Tieu, S. (2005). ‘General Relativity Resolves Galactic Rotation without Exotic Dark Matter’. arXiv:astro-ph/0507619.

2) Carrick J. and Cooperstock, F. (2012). ‘General Relativistic Dynamics Applied to the Rotation Curves of Galaxies’. Astrophysics and Space Science; 337, Iss. 1: pp 321–329.

3) Cooperstock, F. and Magaheis, N. (2015). ‘Galactic mapping with general relativity and the observed rotation curves’. arXiv:1508.07491v1.

Except that most GR experts disagree with Cooperstock, and recent papers quoted in this thread cite Cooperstock and claim to rule out his claims.

FYI: I've been aware of Cooperstock's work for many years, and was initially hopeful it would work out.

 

[PAllen]

I was asking for clarification (questions are never wrong only the answers), by suggesting alternatives, so which alternative is wrong? The trite response could be both, but I think that I have exposed the problem that the term is being used in possibly three different contexts: 1) Einstein weak field approximation; 2) a more specific combination of gravity and Maxwellian electromagnetism as in Ludwig's paper; and 3) to, erroneously, describe Deur's approach, see the Barker et al paper, referenced in this thread.

You appear to be opting for 1), but in the references, authors are using the term differently: hence my post!

Right after the word "wrong" was a paragraph of explanation. Instead of responding to this word, perhaps respond to what you don't understand in the following explanation.

 

[Adrian59]

Right after the word "wrong" was a paragraph of explanation. Instead of responding to this word, perhaps respond to what you don't understand in the following explanation.

Having re-read the thread I note a similar comment to mine in #206 was made in #55 by mitchell porter, so this is not a idiosyncratic viewpoint.

However, maybe someone can clear up an issue that I've found in the Lasenby et al paper, already referenced. The authors examine NGC 1560 saying, 'we will restrict our attention here to the model having the MN density profile (16), which can be treated almost entirely analytically and suffices to demonstrate the shortcomings of the overall approach'. Using this Miyamoto–Nagai (MN) density profile, they get equation (21) which is soluble by a numerical method. They comment that one can get a simpler expression by approximating and solving this expression (22). Both solutions are plotted in figure 2.

What they do not plot in this figure are the experimentally observed values though the authors do say 'Although the rotation curves obtained using either (21) or the analytic approximation (22) appear to fit the rotation curve data for NGC 1560 shown ... in a pleasing way'. Although, had they plotted the experimentally observed velocity values, one would see that these derived curves from the gravito-magnetic approach are compatible with these experimentally derived values. So it is difficult to square this with an alleged failure of this novel approach.

The authors, then, plot the curve without a gravito-magnetic correction and get a standard rising and decreasing curve, the one usually shown as evidence of the need for dark matter, on a separate graph (figure 3), and plot the same combined line from figure 2. They comment that this standard 'curve peaks at velocities around 420 km s−1 (readopting SI units for the moment); this is much higher than one would expect for what is meant to be a dwarf galaxy'.

But, where do you get this plot from since the experimentally observed values are no where near this, but quite accurately match the values obtained with the gravito-magnetic approach?

 

[PAllen]

Having re-read the thread I note a similar comment to mine in #206 was made in #55 by mitchell porter, so this is not a idiosyncratic viewpoint.

That post shows no confusion about GEM having anything to do with EM fields, nor with it being any different from GR except to formulate approximate field equations in a way that shows analogy with Maxwell's equations. This is the only usage of the term I have ever seen in a published paper.

 

[Adrian59]

That post shows no confusion about GEM having anything to do with EM fields, nor with it being any different from GR except to formulate approximate field equations in a way that shows analogy with Maxwell's equations. This is the only usage of the term I have ever seen in a published paper

You may like to look at the paper by Ludwig, ref:

Ludwig, G. O.(2021). 'Galactic Rotation Curve and Dark Matter According to Gravitomagnetism'. The European Physical Journal C, 81(2), suppl. 186.

In the conclusion he writes, 'The gravitomagnetic field produced by the currents plays four important roles in the self-consistent solution: (1) the Lorentz force associated to the gravitomagnetic field balances the Newtonian attractive force in the direction perpendicular to the equatorial plane in a pressureless equilibrium'.

However, I do not wish to comment further on that issue, as I believe I now fully understand the origins of the term gravito-electromagnetism (and I am dubious about Ludwig's approach), but would like an expert eye cast over the Lasenby paper referenced previously in #200, to comment on my observations made in #211.

 

[PAllen]

You may like to look at the paper by Ludwig, ref:

Ludwig, G. O.(2021). 'Galactic Rotation Curve and Dark Matter According to Gravitomagnetism'. The European Physical Journal C, 81(2), suppl. 186.

In the conclusion he writes, 'The gravitomagnetic field produced by the currents plays four important roles in the self-consistent solution: (1) the Lorentz force associated to the gravitomagnetic field balances the Newtonian attractive force in the direction perpendicular to the equatorial plane in a pressureless equilibrium'.

You misinterpret the language here. In analogy to EM, Ludwig is referring to total matter/energy currents, and the gravitic equivalent of Lorentz force. His language could be better, but his audience is assumed to understand the context. Please note the following leading sentence of the last paragraph of the introduction:

"In the present article a new model for the rotation curve of galaxies is developed including the effects associated with mass currents. " [italics mine]

The issue remains that you have less bacground than is assumed for readers of papers in the field (that's fine, often the case for me too), and are very reluctant to admit you may be misinterpreting the language (not fine at all).

 

[Adrian59]

The issue remains that you have less background than is assumed for readers of papers in the field (that's fine, often the case for me too), and are very reluctant to admit you may be misinterpreting the language (not fine at all).

This is a moot point since contrary to your suggestion that I don't understand GEM in the first order approximation, I do understand your view. Whether Ludwig is on point with that definition is also moot since I don't agree with his analysis anyway. I was trying to get you or someone with a more expert eye to re-read the Lasenby paper and comment on the issue I raised in #211. I presumed from comments already made by yourself that your are a astrophysics academic, so I was hoping for some kind of perspicacious opinion on the Lasenby paper.

 

[Adrian59]

The issue remains that you have less background than is assumed for readers of papers in the field (that's fine, often the case for me too), and are very reluctant to admit you may be misinterpreting the language (not fine at all).

The issue of whether I am misinterpreting GEM is not one I can answer myself, as that would imply full understanding! However, my understanding of GTR originally comes from reading the great man himself, see below:

This shows how the zeroth order with the vanishing of the Riemann tensor gives flat Minkowski space. The first order corrections give Newton’s law of gravity which is an inverse square relationship like that of Gauss’s law in electrodynamics. Both ΛCDM and MOND are essentially first order corrections; in the first one adds mass but keeps Newton’s law of gravity; in the second one modifies Newton’s law of gravity, but preserves its essence.

I would consider that both Cooperstock and Deur are moving beyond a first order analysis by using a more subtle gravitational field approach. The question remains whether or not this succeeds in removing the requirement for dark matter or any modification of existing laws of gravity.

It would appear to be so judging from numerous analyses comparing these methods with actual observational data: Cooperstock’s own papers (see #207), Stuckey et al (see #2), de Almeida et al (the paper suggests otherwise but the graphs contradict their premise), and Lasenby et al (see #200 - again despite their claim their Miyamoto–Nagai density profile analysis gives the right answer).

 

[PAllen]

The issue of whether I am misinterpreting GEM is not one I can answer myself, as that would imply full understanding! However, my understanding of GTR originally comes from reading the great man himself, see below:

View attachment 325588

This shows how the zeroth order with the vanishing of the Riemann tensor gives flat Minkowski space. The first order corrections give Newton’s law of gravity which is an inverse square relationship like that of Gauss’s law in electrodynamics. Both ΛCDM and MOND are essentially first order corrections; in the first one adds mass but keeps Newton’s law of gravity; in the second one modifies Newton’s law of gravity, but preserves its essence.

This is all mixed up. Lambd-CDM is a full GR cosmology model. There is no approximation whatsoever in all its defining equations; it is fully non-linear. To perform some types of calculations more easily, one sometimes approximates the full model in various ways. MOND has no relation to GR, it is (in its original form) a modifications to Newtonian mechanics that happens to explain a bunch of esp. galactic observations. It is generally treated as suggestive of the idea that more plausible modified gravity theories are worth pursuing (in itself, in the original form, it is worthless because it fails to match any of the dozens of verified GR predictions that differ from Newtonian.

I would consider that both Cooperstock and Deur are moving beyond a first order analysis by using a more subtle gravitational field approach. The question remains whether or not this succeeds in removing the requirement for dark matter or any modification of existing laws of gravity.

Cooperstock claims to use only standard GR equations. The approximation scheme and its validity are separate questions to be resolved. Deur derives equations by analogies that he never actually derives from GR equations. Thus, I claim Deur is actually a modification of GR. The approximations used have nothing to do with it.

 

[timmdeeg]

Deur derives equations by analogies that he never actually derives from GR equations. Thus, I claim Deur is actually a modification of GR. The approximations used have nothing to do with it.

It's an interesting point. Deur claims his anisotropic model is within GR.

https://link.springer.com/content/pdf/10.1140/epjc/s10052-019-7393-0.pdf

If the assumptions of isotropy and homogeneity are lifted, new terms, including off-diagonal ones, appear in Rμν and Si j . Eqs. (5–8) then change to:

 

[PeterDonis]

Deur claims his anisotropic model is within GR

Deur has more than one model. The "anisotropic model" in that particular paper is indeed "within GR", in that the Einstein Field Equation is not modified. But it also is different from other models Deur proposes, which cannot be expressed in terms of an unmodified Einstein Field Equation.

 

[strangerep]

MOND has no relation to GR, it is (in its original form) a modifications to Newtonian mechanics that happens to explain a bunch of esp. galactic observations.

MONDians slip a little extra assumption into the mix when discussing weak lensing. Since a factor of 2 is involved (in ordinary GR) when comparing lensing trajectories of massive particles compared to lensing along null paths, MOND introduces a fudge factor of 2 (as an "educated guess") because MOND cannot directly deal with null paths. Imho, this should be an explicit tenet of MOND.

Cooperstock claims to use only standard GR equations.

IIUC, he uses a "reverse" approach. I.e., he sets up a coordinate system and metric that roughly corresponds to disk-like rotation, then crunches the GR field equations and see what $T{\mu\nu}$ results. Then he tries to fit that $T{\mu\nu}$ to observations of mass distributions in actual galaxies. His critics claim that the $T{\mu\nu}$ is unphysical in various ways, such as a singular plane on $z=0$, and possibly a need for some exotic matter (negative mass). Cooperstock (in his book) rejects these criticisms, but since he has now passed away, I get the feeling his work will slowly fade into the mists of time.

 

[strangerep]

It would appear to be so judging from numerous analyses comparing these methods with actual observational data: Cooperstock’s own papers (see #207), [...]

Since you assert "it appears to be so", I get the feeling you haven't studied the various rebuttal papers against Cooperstock? Imho, the situation is still not crystal clear, but I won't be putting any bets on Cooperstock, alas.

 

[ohwilleke]

This is all mixed up. Lambd-CDM is a full GR cosmology model. There is no approximation whatsoever in all its defining equations; it is fully non-linear. To perform some types of calculations more easily, one sometimes approximates the full model in various ways.

In practice, at the scale of galaxies and galaxy clusters, Lambda-CDM is approximated with Newtonian gravity.

MOND has no relation to GR, it is (in its original form) a modifications to Newtonian mechanics that happens to explain a bunch of esp. galactic observations. It is generally treated as suggestive of the idea that more plausible modified gravity theories are worth pursuing (in itself, in the original form, it is worthless because it fails to match any of the dozens of verified GR predictions that differ from Newtonian.

MOND proponents are not GR deniers in strong gravitational fields. These are PhD astronomers who fully endorse and accept the experimental validations of GR to date as true and correct.

MOND proponents are merely advocates for a second order gravitational effect (whose deeper mechanism and exactly functional form are unknown) in addition to GR as conventionally applied in very weak gravitational fields in circumstances where no significant external fields are present encompassing the whole system.

MOND proponents do assert that external field effect in MOND (in which two bodies that would have an enhanced MOND gravitational attraction since the Newtonian acceleration between them would be very weak do not do so when a gravitational field external to the two free falling bodies from something like a nearby galaxy is present at a strength greater than the MOND acceleration constant) contradicts the strong equivalence principle of GR, as supported by statistical evidence from many galaxy observations. See arXiv:2009.11525 (published in ApL in 2020). This is not contrary to any precision tests of GR.

People who are using MOND are implicitly only using it in a domain of applicability where a Newtonian approximation of GR would be used instead. They readily assume that significantly above the a₀ threshold that GR is actually what applies.

Likewise, other assumptions of GR (e.g. that light is bent by gravitational fields in proportion to the strength of the gravitational field in both the MOND and non-MOND regimes to the same extent as it would be in GR) are also assumed.

MOND is agnostic on the existence of the cosmological constant or dark energy whose existence depends upon observations outside of its domain of applicability. Nothing about MOND is inherently inconsistent with the cosmological constant of GR, but MOND, since it is agnostic about the mechanism by which this effect arises, also does not require a cosmological constant or dark energy to explain the predictions it makes in its domain of applicability.

Criticizing MOND for failure to match GR predictions is a straw man fallacy that misunderstands what the theory really is. There are several relativistic generalizations of MOND that explicitly incorporate GR effects in the appropriate domains of applicability.

There are legitimate grounds to criticize simple toy-model MOND and its relativistic generalizations. The most widely known and acknowledged flaw of MOND is that it underestimates the magnitude of dark matter phenomena in galaxy clusters and doesn't scale the magnitude of dark matter phenomena in galaxy clusters with the right exponent, even though it partially captures these effects. But these flaws don't cure the many known flaws of other theories that also get lots of things wrong like LambdaCDM.

From a phenomenology perspective, Deur brings three main things to the table that MOND lacks: (1) a plausible way to generalize it to galaxy cluster phenomena (including the Bullet cluster), (2) an explanation of all or more dark energy phenomena that conserves mass-energy both locally and globally, (3) a plausible means to reconcile the Hubble constant tension, (4) a theoretical framework from which to derive the exact form of the MOND interpolation function and its other conclusions, and (5) one fewer degree of freedom than GR with a cosmological constant, two fewer degrees of freedom than MOND without dark energy or the bare LambdaCDM theory with a single type of sterile dark matter, and three fewer degrees of freedom than MOND with dark energy or LambdaCDM theory with self-interacting dark matter or a fifth DM-baryonic matter force.

If the observationally fitted parameter of Deur's scalar simplification of the GR Lagrangian can't be derived from Newton's constant and geometry and scale, then Deur's theory isn't just a reformulation of Einstein's GR. This would also mean that Deur's approach has the same number of degrees of freedom as GR with a cosmological constant, but it still superior to Lambda-CDM with a single kind of sterile dark matter, in terms of Occam's Razor.

But, if, in fact, Deur's approach is a GR modification rather than true GR (something that can perhaps be described as a quantum gravity effect), for reasons that he failed to appreciate and which critics discerned, this doesn't detract from the fact that:

(1) Deur's approach correctly models systems that LambdaCDM gets wrong observationally,
(2) this approach correctly models systems that MOND gets wrong. observationally,
(3) this approach makes a couple of novel predictions not found in any other prior theory which are confirmed by observations,
(4) this approach has no circumstances where it fails to conform to observational tests and reproduces all of the successes of MOND and of dark matter particle theories, and
(5) integrates all of its conclusions into a theoretical framework with overwhelmingly vanilla theoretical assumptions and just one experimentally measured parameter other than Newton's constant, which has already been determined at the percent level of precision (which is comparable to or better than a number of experimentally measured parameters of the Standard Model and to the cosmological constant of GR and much better than the wildly unconstrained parameter space for dark matter particle theories).

Deur's approach would still be the only theory of dark matter and dark energy phenomena with an unlimited domain of applicability, which makes it an extremely notable theory, even if it turns out that it is actually, contrary to Deur's claims, a modification of GR.

There are also at least a couple of observational tests imminently teed up to compare Deur's predictions to MOND in galaxy scale systems as opposed to the galaxy clusters where Deur already outperfoms MOND: one is the behavior of bodies outside the galactic plane of spiral galaxies (preliminary data favors Deur on this point), and another is the behavior of wide binary systems that are not subject to an external field effect (preliminary data is mixed for this test).

Deur derives equations by analogies that he never actually derives from GR equations. Thus, I claim Deur is actually a modification of GR. The approximations used have nothing to do with it.

Deur takes two distinct approaches to reach the same result, at least in the limited case of spiral galaxies.

One is to use the GR Lagrangian which is equivalent to Einstein's equations but states those equations in a different form.

Starting from the settled GR Lagrangian, in practice, he then uses a scalar approximation of the GR Lagrangian, which is equivalent to saying that he disregards the elements of the GR stress-energy tensor on the RHS of Einstein's equations other than rest mass (e.g. electromagnetic flux, angular momentum, linear momentum, pressure) which is the same simplifying approximation made when using a Newtonian approximation of GR, and Deur is using this scalar approximation of the GR Lagrangian only in the same circumstances that the Newtonian approximation of GR is used.

For purposes of galaxy and galaxy cluster scale systems, this seems to be a reasonable approximation because there is little interstellar electromagnetic flux (so you can look at the bending of photons by gravity without accounting for the curvature of space flowing from the photons themselves without meaningful loss of accuracy), and because the momentums typical for a galaxy system are much smaller than the speed of light and a zero pressure approximation is common in astronomy systems like these. But, in general, this approximation is not valid in circumstances such as neutron stars, close binary systems, particles moving at relativistic speeds, and magnetars, where full GR and not a scalar approximation of it is needed.

What Deur is not neglecting, however, which conventional GR applications for astronomy in these kinds of systems would, is the non-linearities on the LHS of Einstein's equations that reflect gravitational field self-interaction, which he sometimes calculates with non-perturbative lattice methods.

The new paper reviewing his work argues, although not with complete conviction, that their effort to do the same thing resulted in deviations from Newtonian gravity that are qualitatively similar to those of Deur, but quantitatively much smaller.

The most obvious candidate for the discrepancy is that the self-interaction term of the GR Lagrangian includes a physical constant that should in principle be determinable from first principles in GR using only Newton's constant G and the geometry of the mass distribution. Deur doesn't actually calculate this constant from first principles in GR, however. Instead, he uses the same observations used to establish the MOND critical acceleration a₀ to calibrate this constant in the case of mass distributions with a geometry in line with an idealized spiral galaxy. He basically has faith that the physical constant in question could be calculated and would reproduce the observed value, without actually doing that involved calculation and no later paper from Deur has attempted to do that calculation.

As best I can discern, however, the paper reviewing Deur's work, basically does appear to use first principles to establish the value of this physical constant and in doing so finds that the effect is to small.

My analysis above of what I surmise is going on involves some guesswork and reading between the lines because the paper critical of Deur's approach basically reconstructs its own scalar approximation from scratch and compares its end results with Deur's, rather than going step by step through the analysis that Deur did in order to pinpoint where they believe he veered off course. It could be that this is not actually the issue, but it seems like the point of Deur's analysis most prone to a magnitude of conventional GR self-interaction effect outcome.

If I am right about what is going on, then the basic issue is that Deur is implicitly modifying GR by assuming a stronger coupling between gravitons of a given mass-energy than the coupling between gravitons and other fundamental particles from the Standard Model. (I'd be particularly curious if the strength of the attraction between gravitons was implicitly the square of the naive expectation, but I don't know how the observationally estimated parameter and the first principles parameter compare to each other.)

Another possible source of the discrepancy is that paper reviewing Deur's work is not adequately modeling the system's geometry and overall mass scale correctly, because it fails to appreciate the central importance of these factors.

One problem with simply claiming that Deur's scalar version of the GR Lagrangian approach is wrong, however, is that Deur has replicated the result for spiral galaxies by another independent method that more directly flows from Einstein's equations, rather than from a scalar approximation of the GR Lagrangian.

The other approach used by Deur, although only in a single published paper, is to use a mean field approximation of more conventional classical GR rather than the QCD inspired GR Lagrangian approach. It doesn't appear that the paper critiquing his body of gravitation work considered the approach of that paper.

So, for Deur's analysis to be wrong, both approaches need to have basically the same flaw for different reasons in the specific analysis done in each case.

 

[ohwilleke]

MONDians slip a little extra assumption into the mix when discussing weak lensing. Since a factor of 2 is involved (in ordinary GR) when comparing lensing trajectories of massive particles compared to lensing along null paths, MOND introduces a fudge factor of 2 (as an "educated guess") because MOND cannot directly deal with null paths. Imho, this should be an explicit tenet of MOND.

Agreed.

Essentially, GR is followed when applying the effects of gravitational fields to photons, but the electromagnetic flux components of the stress-energy tensor are ignored when estimating the character of the gravitational field.

The curvature of space-time from sources of gravity other than photons on photons which gives rise to gravitational lensing is considerable and can't be ignored.

But, it isn't unreasonable to ignore photons when calculating gravitational fields in galaxy and galaxy cluster scale systems that give rise to gravitational curvature of space-time.

In the current era of the universe, even in a universe that has baryonic matter and neutrinos but not dark matter or dark energy, the proportion of the mass-energy of the universe that is in interstellar photons at any given moment is ten to a hundred and seventy times smaller than the ability of our observations to distinguish a case where this radiation has a gravitational effect (as it does in GR calculated with full rigor) and a case where it does not (as we do when we do our gravitational calculations ignoring the contribution to space-time curvature from interstellar photons).

In the Planck CMB observations,

Ω_𝑅,0=9.23640×10⁻⁵

in other words 0.000092364 which is roughly 0.0001.

In contrast, the baryonic matter percentage is about Ω_b=0.0486 ± 0.0010 (which is about 526 times larger than the radiation percentage and has an uncertainty alone of about ten times the best fit value of the radiation percentage) and the matter density (including both baryonic and dark matter) in a Lambda CDM model from the same observations is Ω_m=0.315 ± 0.017.

The neutrino mass fraction (which I derived with a couple of unit conversions from the data in the link, and using up to date cosmological and neutrino oscillation experiment bounds on values of the sum of the three Standard Model neutrino masses) is on the order of 0.001 to 0.002, which is twenty five to fifty times smaller than the baryonic mass fraction, and ten to twenty times as large as the mass-energy fraction of interstellar photons. The neutrino mass fraction is comparable in magnitude to the uncertainty in the proportion of baryonic matter in the universe, and is about 8-17 times smaller than the uncertainty in the amount of baryonic and dark matter combined in the LambdaCDM model.

 

[timmdeeg]

But it also is different from other models Deur proposes, which cannot be expressed in terms of an unmodified Einstein Field Equation.

Ah I see, so Deur's field self-interaction isn't somehow contained in the "non-linearities" of the GR Lagrangian, right?

 

[PeterDonis]

Deur's field self-interaction isn't somehow contained in the "non-linearities" of the GR Lagrangian, right?

I think it depends on which Deur paper you're talking about.

 

[timmdeeg]

I think it depends on which Deur paper you're talking about.

It's this one, where equation (6) shows the angular bending.

https://arxiv.org/pdf/2004.05905.pdf

FIG. 3 Comparison field lines ... with and without field self-interaction.

 

[PeterDonis]

It's this one, where equation (6) shows the angular bending.

https://arxiv.org/pdf/2004.05905.pdf

FIG. 3 Comparison field lines ... with and without field self-interaction.

Ok, in that paper he's not using GR, he's using a post-Newtonian approximation. If such an approximation is done correctly, the nonlinearities in the higher order terms should match those in the full GR equations, but Deur doesn't give enough detail that I can see in the paper for me to tell exactly how the approximation is being done.

 

[timmdeeg]

Ok, in that paper he's not using GR, he's using a post-Newtonian approximation. If such an approximation is done correctly, the nonlinearities in the higher order terms should match those in the full GR equations, but Deur doesn't give enough detail that I can see in the paper for me to tell exactly how the approximation is being done.

Ok, thanks!

 

[ohwilleke]

Ah I see, so Deur's field self-interaction isn't somehow contained in the "non-linearities" of the GR Lagrangian, right?

The non-linearities of the GR Lagrangian and the non-linearities of the LHS of Einstein's field equations, should be the same ones.

 

[Adrian59]

This is all mixed up. Lambd-CDM is a full GR cosmology model. There is no approximation whatsoever in all its defining equations; it is fully non-linear. To perform some types of calculations more easily, one sometimes approximates the full model in various ways.

There certainly seems some issues here since I do not consider ΛCDM in any way full GR. Its original concept was to add mass to correct the original Keplerian, decreasing curve for galaxy dynamics. The NFW profile (Navarro, J.F., Frenk, C.S. and White, S.D.M. (1997). Atrophysical Journal; 490: pp430-508) was a density profile of the proposed dark matter halo, and as far as I can see did not alter the dynamical equations. As an aside it would appear that my post #216 has been liked by one other contributor to this thread so I can't see it being as wide of the mark as you suggest.

I would like to make one correction to my post #216, I said Gauss's law but I actually should have said Coulomb's law.

MOND has no relation to GR, it is (in its original form)

We agree on this.

Cooperstock claims to use only standard GR equations.

He does use an axially symmetric metric:

Deur derives equations by analogies that he never actually derives from GR equations.

This issue has been covered before in this thread, c.f. #43, #56, and #58. Also, I agree with the subsequent comments (#218 and #219) made in response to this suggestion of yours.

IIUC, he uses a "reverse" approach. I.e., he sets up a coordinate system and metric that roughly corresponds to disk-like rotation, then crunches the GR field equations and see what $T{\mu\nu}$ results. Then he tries to fit that $T{\mu\nu}$ to observations of mass distributions in actual galaxies. His critics claim that the $T{\mu\nu}$ is unphysical in various ways, such as a singular plane on $z=0$, and possibly a need for some exotic matter (negative mass). Cooperstock (in his book) rejects these criticisms, but since he has now passed away, I get the feeling his work will slowly fade into the mists of time.

As I think you have commented before as well, Cooperstock died recently (2018 I think), so he is no longer around to publicise his approach. But as you suggest he does use GR and even if he does things in reverse, he does match observational data. This z=0 issue is slightly disingenuous: doesn't Newton's law of gravity have a singularity at r=0?

Since you assert "it appears to be so", I get the feeling you haven't studied the various rebuttal papers against Cooperstock? Imho, the situation is still not crystal clear, but I won't be putting any bets on Cooperstock, alas.

I was guilty of understating my position. I have read many rebuttals and found then all wanting. Many claim to be such when in fact they are almost supportive: c.f. de Almeida, A., Piattella, O. and Rodrigues, D. (2016). ‘A method for evaluating models that use galaxy rotation curves to derive the density profiles’. MNRAS; 462: 2706. The authors suggest they refute Cooperstock but their plot using Cooperstock's own method is not all that different from Cooperstock's own work.

If any of your other rebuttals contain the authors Cross, Garfunkle of Korzynski; then I need something better to tergiversate.

 

[Adrian59]

#222 is an excellent post.

In practice, at the scale of galaxies and galaxy clusters, Lambda-CDM is approximated with Newtonian gravity.

Completely agree with this.

MOND proponents are merely advocates for a second order gravitational effect (whose deeper mechanism and exactly functional form are unknown) in addition to GR as conventionally applied in very weak gravitational fields in circumstances where no significant external fields are present encompassing the whole system.

I was previously assigning MOND as a first order effect, although I can agree with your point here, and with your proviso that the situation is far from resolved.

The new paper reviewing his work argues, although not with complete conviction, that their effort to do the same thing resulted in deviations from Newtonian gravity that are qualitatively similar to those of Deur, but quantitatively much smaller.

Am I right to assume that this new paper is the one by Barker, Hobson and Lasenby that we discussed previously?

One problem with simply claiming that Deur's scalar version of the GR Lagrangian approach is wrong, however, is that Deur has replicated the result for spiral galaxies by another independent method that more directly flows from Einstein's equations, rather than from a scalar approximation of the GR Lagrangian.

This is the crux of the issue, surely. Many of these alternatives like Cooperstock and Deur are getting results that match observation data. I thought that was what physics was all about, but it seems these new ideas need something extra to convince many, and as yet I am not sure what this extra component needs to be.

 

[Structure seeker]

My reason for hoping that Deur is right is simple although pretty basic. Due to the rather general rejection of MOND, there are "MOND people" and "dark matter people". If I guess right, the dark matter people originally chose their preferred theory mainly for keeping Einstein's GR as is, for having the big bang theory explanation of cosmology and for the beauty of supersymmetry or other cleverly devised symmetric theories, with the assuring sentiment that "Einstein was right" (but didn't yet know about the extra gravitational attraction needed below $a_0$ which could be explained by dark matter).

Again if I guess right, MOND proponents chose mostly based on the idea of renewal of what is a realistic perspective, when new data comes in. If new data systematically deviated in the same direction, they chose to take the effort to try to formulate competing MOND theories, initially leaving the beauty of the symmetries of GR, of quantum gauge theories describing all forces and leaving the authority of Einstein's written theory (but not the spirit of Einstein's thinking! MOND is a more deterministic theory ATM because we can't directly see or measure where dark matter would be). MOND is a bold move.

Now my reason for hoping Deur is right is because it explains the MOND phenomenology while preserving the main reasons for dark matter people to choose for dark matter: gravity is just as was expected in the Standard model but self-interacts, preserving all the possible symmetry possibilities but not assuming new particles. Einstein's heritage of quantum gauge theories is preserved! And Deur even gave a version of the big bang theory in his framework, with a great fit to the CMB.

So the only thing dark matter people would have to give up, is explaining the extra gravity with a dark matter particle. Deur's approach says nothing about whether there are particles beyond the standard model, there are enough opportunities for that. If Deur is right the only thing they need to change is to look for new particles elsewhere.

 

[PAllen]

There certainly seems some issues here since I do not consider ΛCDM in any way full GR. Its original concept was to add mass to correct the original Keplerian, decreasing curve for galaxy dynamics. The NFW profile (Navarro, J.F., Frenk, C.S. and White, S.D.M. (1997). Atrophysical Journal; 490: pp430-508) was a density profile of the proposed dark matter halo, and as far as I can see did not alter the dynamical equations. As an aside it would appear that my post #216 has been liked by one other contributor to this thread so I can't see it being as wide of the mark as you suggest.

This is just absurd. Lambda-DCM is described by a GR metric and nothing else - the FLRW metric family. All its physical content is contained in this full GR model. This is a theory of cosmology. There is no Lambd-CDM model of galaxy. That is a separate problem, in which dark matter is typically used, but it is not using the Lambda-CDM cosmological model.

 

[PeterDonis]

I do not consider ΛCDM in any way full GR.

This is wrong. The $\Lambda CDM$ model is based on the Friedmann equations, which in turn are solutions to the Einstein Field Equation of GR.

Its original concept was to add mass to correct the original Keplerian, decreasing curve for galaxy dynamics. The NFW profile (Navarro, J.F., Frenk, C.S. and White, S.D.M. (1997). Atrophysical Journal; 490: pp430-508) was a density profile of the proposed dark matter halo, and as far as I can see did not alter the dynamical equations.

None of this has anything to do with the $\Lambda CDM$ model. You are talking about models of individual galaxies that are developed to try and explain their observed rotation curves. $\Lambda CDM$ is a model of the universe as a whole.

 

[PeterDonis]

Both ΛCDM and MOND are essentially first order corrections

This is false for both. As has already been pointed out, $\Lambda CDM$ is a model of the universe as a whole, and is based on "full GR", the full Einstein Field Equation, not any kind of approximation. MOND is not based on GR at all, it is an ad hoc proposal for a different dynamics in a particular regime and is not an approximation to GR.

 

[PeterDonis]

it would appear that my post #216 has been liked by one other contributor to this thread so I can't see it being as wide of the mark as you suggest.

Your confidence is misplaced. To me, your posts show a mixture of reasonably accurate statements and falsehoods based on misunderstandings of the subject matter. A "like" might be given to a post because it contains a reasonably accurate statement that the "liker" considers to be important, while at the same time containing falsehoods. That is how I would account for your post #216 receiving "likes".

 

[Structure seeker]

None of this has anything to do with the $\Lambda CDM$ model. You are talking about models of individual galaxies that are developed to try and explain their observed rotation curves. $\Lambda CDM$ is a model of the universe as a whole.

In the sense of $\Lambda CDM$ as in "what dark matter people propose as models for galaxies", the point @Adrian59 makes is entirely correct. If you don't like the point he is making, why not tell it straight? If that's not the case, this misunderstanding of $\Lambda CDM$ by him is just a tiny distraction. Surely nobody would prefer that $\Lambda CDM$ has no model at all for galaxies?

As to his confidence being misplaced, I truly see no other proposals from dark matter people so either they agree to ignore the proven predictions of MOND or they have Deur's model in my view as the current best alternative. Oh my, perhaps I should stop telling the inevitable reality that lies in MOND analysis? Leave it to the experts? If we just all agree that MOND can be discarded and alll evidence is overwhelmingly in favour of dark matter, oops nature doesn't care what we think. Look, more MOND enthusiasts posting this lopsided view of the cosmology literature. It's amazing people still react!

Let's reproduce a MOND equivalent of your insistence that $\Lambda CDM$ is not about galaxy dynamics. So if you say, in MOND structure is formed too early at redshifts too high, I reply that MOND has nothing to do with cosmologic history, it is a theory of galaxy dynamics and gravitation. Except that JWST did find that structure formed that early sometimes and MOND can be proud of yet another succesful prediction.

 

[PeterDonis]

In the sense of $\Lambda CDM$ as in "what dark matter people propose as models for galaxies"

There is no such "sense" of $\Lambda C D M$; that is a model of the universe, not of galaxies. If people want to say "what dark matter people propose for galaxies", then that is what they should say. They should not misdescribe the $\Lambda C D M$ model as something it is not.

the point @Adrian59 makes is entirely correct.

I disagree. Nor was the criticism I made limited to his wrong use of the term $\Lambda C D M$.

 

[PeterDonis]

I truly see no other proposals from dark matter people

Maybe you should spend more time reading actual papers by "dark matter people". There is a lot of research going on in this area, and we have had many PF threads on it.

 

[PeterDonis]

Surely nobody would prefer that $\Lambda CDM$ has no model at all for galaxies?

Whether anybody would "prefer" it or not, that is in fact the case: $\Lambda C D M$ is a model of the universe, not of individual galaxies. Of course we would like our models of individual galaxies to be consistent with the $\Lambda C D M$ model for the universe as a whole, but that is very different from $\Lambda C D M$ itself having a model of individual galaxies.

 

[timmdeeg]

@Structure seeker: It is perhaps helpful to recognize that the FLRW-metric on which L-CDM is based assumes perfect fluid. Hence it doesn't know about galaxies.

 

[Structure seeker]

Maybe you should spend more time reading actual papers by "dark matter people". There is a lot of research going on in this area, and we have had many PF threads on it.

I'm curious to know how they explain galaxy rotation curves without adding mass? Or did you mean research on GEM? If it is, do go in detail please. I'd like to know what criticism you have specifically.

 

[weirdoguy]

I'm curious to know how they explain galaxy rotation curves without adding mass?

Then why don't you do some research and find out?

 

[Structure seeker]

Because cosmology is not my area of expertise, but mathematics with an inclination towards physics. I can only judge the quality of one argument as answer to a line of reasoning, and in order to understand an approach I'm dependent on how it is presented here. But if I see that @Adrian59 makes a point and it is waved away with "your posts show a mixture of reasonably accurate statements and falsehoods based on misunderstandings of the subject matter", I am smart enough to recognize that no specific argument is given on the content at stake. I could say the same of anyone's posts, and if I'm a moderator and know the cosmology community generally thinks the direction of the attacked posts undesirable, I have good odds that it will be generally approved of without having to give too specific arguments. If no explicit arguments are given this would be social engineering, which of course I don't want to accuse anyone of, in the context of reviewing science. So I ask, I myself need a lower-level explanation of an example paper. To dismiss many posts at once without giving specific papers or arguments isn't convincing. Do we have to look up our own counterarguments? That's just a monologue, I doubt anyone volunteers. Do you really have arguments?

 

[astronomer]

Rotation curves of disk galaxies are just one of the reasons astronomers invoke DM. DM is also needed (in newtonian gravity) also in elliptical galaxies (and in clusters of galaxies) many of them non rotating appreciably: this very simple empirical fact should be enough to close complicated discussions about the role of GEM (for example). Notice that DM is also required by gravitational lensing.

 

[PeterDonis]

I'm curious to know how they explain galaxy rotation curves without adding mass?

Adding dark matter to the model is adding mass. Dark matter has mass. It's just not visible mass. In other words, the dark matter hypothesis is that the actual mass of galaxies is larger than the mass we infer from what we can see.

 

[PeterDonis]

cosmology is not my area of expertise, but mathematics with an inclination towards physics

So what? This is an "A" level thread in the cosmology forum. That means you are expected to have background knowledge in the subject matter equivalent to a graduate student. If you don't have that background knowledge, you need to go get it if you want to be able to make useful posts in this thread. We are not going to clutter up an "A" level thread with explanations of things that anyone with the requisite background knowledge should already know. That includes the basic tenets of the $\Lambda C D M$ model and the dark matter hypothesis and the reasons for it. Anyone posting in this thread needs to already know all those things.

 

[astronomer]

As an astronomer, I have a few general comments on the current (interesting) discussion. From the astronomical point of view, it is a little bit surprising that a few, well established empirical facts, appear to be ignored. First: the flat rotation curve of disk galaxies is just one (and certainly not the most relevant) evidence that (in newtonian gravity) we "need" DM. Non/weakly rotating systems (such as elliptical galaxies and clusters of galaxies) also require DM (in newtonian gravity) to explain their internal dynamics (with converging results obtained from hydrostatic equilibrium of hot gas, gravitational lensing, stellar dynamics). No convincing answer is provided by GEM framework on this point: what GEM effect mimics DM in non rotating systems? Data just requires that the claimed GR effects should be independent of rotation. Second: some low-mass stellar systems (with lower stellar velocities than in disk galaxies) requires (in newtonian gravity) larger DM-to-baryon ratios: why GR effects increase at decreasing mass? Third: some low-mass stellar systems (with mass in the same range of systems in previous point) do not require DM at all: why in some system GR effects are big and in other system of similar mass are not required?

Astronomically, it would be very useful (and interesting) to have a reasonable and convincing global picture of the proposed scenario, before focusing on very specific aspects.

 

[Structure seeker]

@astronomer, I think you are overlooking some literature. Although this thread is more about Deur's theory which also possibly explains galaxy clusters much better, the other phenomena you present are well explained in the most actual MOND models.

Elliptical galaxies: http://www.scholarpedia.org/article/The_MOND_paradigm_of_modified_dynamics#Elliptical_galaxies including citations.

Gravitational lensing:
https://arxiv.org/abs/2007.00082
From the paper: "It (the proposed theory) must (i) return to GR (hence, Newtonian gravity) when r~ Φ ≫ a0 in quasistatic situations while (ii) reproducing the MOND law (1) when r~ Φ ≪ a0. It should also (iii) be in harmony with cosmological observations including the CMB and MPS, (iv) reproduce the observed gravitational lensing of isolated objects without DM halos, and (v) propagate tensor mode gravitational waves at the speed of light". And also versions of BIMOND cover this.

Ultra-diffuse galaxies (those that are usually explained as that they have no or little DM):
https://arxiv.org/abs/1901.02679
They are probably due to the MOND EFE (External Field Effect), although AFAIK there are some outliers with large error bars in the distance to the nearby massive galaxy causing the EFE.

Although cosmology is not my area of expertise, I follow the discussion on MOND or dark matter as a hobby.

 

[astronomer]

I agree with you about MOND. In fact (I did some work on MOND, some also in collaboration with some of the Authors in the papers you mention) one of the phenomenological advantages of MOND over the (current) GR proposals, is that MOND has an unifying concept that (in principle) is able to deal with the points I mentioned in #248, i.e., the existence of an universal acceleration scale a_0. However, I do not think MOND is the solution of DM problem, for other reasons, but here we are discussing GR.

In the astronomical community, what it seems missing from the GR attempts (at least, those of what I am aware of) is the they deal with specific cases, often presenting quite "ad hoc" solutions (I searched in the literature the ideas behind GR solutions, and the span of the proposed solutions is quite amazing, ranging from GEM - and what about nn rotating galaxies? to GR retarded potential effects due to unsteady gas accretion - and DM evidence in gas free systems? to binary black holes placed along the symmetry axis of disk galaxies - do we really believe that all galaxies do have a binary black hole on the rotation axis??? to effects of vacuum solution of GR - but also in newtonian gravity you can add an harmonic function to the potential produced by the sources, without affecting the Poisson equation, and yet producing enormous fields if you like, but no one is advocating this possibility). Nothing wrong with it, but of course we all know very well that in astronomy, many problems are of "general" nature, i.e., the global picture is as important as the solution of a single, specific problem. Therefore, it would be already a step forward if general consensus is reached (for example) about the viability of GEM to really substitute DM. As a side note, it is worth to recall that the burden of the proof rests on the proponent. For example, a very well known fact of disk dynamics is the instability of self-gravitating stellar disk made by almost circular orbits (as orbits are in disk galaxies), and it has been established beyond discussion that a DM halo can stabilize the disk (it should be recalled that the stability of disk galaxies was the first hint of the existence of DM halos in disk galaxies, before the observation of flat rotation curves). What about GR?