A LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

[ohwilleke]

What parts of MTW have caused a problem for this research?

The citations that follow are from MTW, "Gravitation" (1973).

Section 18.3 "the energy momentum conservation formulated here contains no contributions or effects of gravity! From this one sees that linearized theory assumes that gravitational forces do no significant work." But the text is shallow in really quantifying the limits of linearized theory in weak fields rigorously.

Section 19.2 "If the particle is sufficiently far from the source, its motion is affected hardly at all by the source's angular momentum or by the gravitational waves; only the spherical, Newtonian part of the gravitational field has a significant influence. Hence, the particle moves in an elliptical Keplerian orbit."

Section 20.4 stating "Anybody who looks for a magic formula for 'local gravitational energy-momentum' is looking for the right answer to the wrong question. Unhappily, enormous time and effort were devoted in the past to trying to 'answer this question' before investigators realized the futility of the enterprise. Toward the end, above all mathematical arguments, one came to appreciate the quiet but rock-like strength of Einstein's equivalence principle. One can always find in any given locality a frame of reference in which all local 'gravitational fields' (all Christoffel symbols . . . . disappear. No [Christoffel symbols] means no 'gravitational fields' and no local gravitational field means no 'local gravitational energy-momentum.' Nobody can deny or wants to deny that gravitational forces make a contribution to the mass-energy of a gravitationally interacting system. The mass-energy of the Earth-moon system is less than the mass-energy that the system would have if the two objects were at infinite separation. The mass-energy of a neutron star is less than the mass-energy of the same number of baryons at infinite separation. Surrounding a region of empty space where there is a concentration of gravitational waves, there is a net attraction, betokening a positive net mass-energu ion that region of space. . . .At issue is not the existence of gravitational energy, but the localizability of gravitational energy. It is not localizable. The equivalence principle forbids. . . . The over-all effect one is looking at is a global effect, not a local effect. That is what the mathematics cries out."

Section 20.5 stating the interbody non-Newtonian gravitational potential can be ignored in "The solar system . . . the Galaxy . . . [and] clusters of galaxies, but [not] the universe as a whole."

See also Section 16.5 disavowing the notion that a gravitational field can be defined precisely. Section 18.1 and Box 18.1 (comparing the Einstein derivation and Spin-2 derivation of Einstein's field equations, but largely discounting the Spin-2 derivation from which the analysis of self-interaction effects is more intuitively obvious, in the rest of the material).

It isn't that MTW deny the effects that people using GR effects to explain dark matter rely upon are using in later treatments (and maybe editions of textbooks in the subject post-1973 have improved), but the discomfort express about "going there" at all, supported by the ad hominem argument that everybody looked and didn't find anything as if every other scientist examining the issue was an idiot, and the specific ruling out of an effect, without much analysis based upon a back of napkin heuristic in Section 20.5 that there could be an effect in galaxies and galaxy clusters.

There is also sloppiness in the Section 20.4 discussion, on one hand acknowledging that a system as localized as the Earth-Moon system, or a neutron star can have gravitational contributions to the mass of the system from the perspective of a distant observer, in particular to systems much smaller than a light year relative to a vast universe, and then denying that any kind of localization whatsoever is possible when verbally, the authors have just localized the gravitational energy effect on mass to a fairly localized system.

Basically, the attitude seems to be that since we didn't find a way to address the question of gravitational field self-interaction that many researchers grappled with, that it is futile and impossible to do so, even through they don't really have a rigorous no go theory that means what they imply or a rigorous quantification of the magnitude of the effects in galaxy and galaxy cluster scale systems.

Another big name whose work may have been generalized beyond its technical holdings is S. Deser who often co-authored with Misner. He makes an analysis of the gravitational self-interaction (1970); clarified and expanded upon in 2009. And, he makes some related non-obvious observations about the properties of stress energy tensors.

Criticism

Criticism of S. Deser's conclusions about gravitational self-interactions and a similar one by Feynman in 1995 that shows an out of the box thinking alternative analysis can be found here.

A.I. Nikishov of the P.N. Lebedev Physical Institute in Moscow states in an updated July 23, 2013 version of an October 13, 2003 preprint (arXiv:gr-qc/0310072), these arguments "do not seem convincing enough." For example, Feynman's lectures on gravitation assumed that gravity was mediated by a graviton that could be localized with a self-interaction coupling strength equal to the graviton's energy, just as the graviton would with any other particle. String theory and supergravity theories, generically make the same assumptions.

Nikishov also made the same analysis of Deur in his paper "Problems in field theoretical approach to gravitation" dated February 4, 2008 in its latest preprint version arXiv:gr-qc/04100999 originally submitted October 20, 2004, when he states in the first sentence of his abstract that:

We consider gravitational self interaction in the lowest approximation and assume that graviton interacts with gravitational energy-momentum tensor in the same way as it interacts with particles.

Deur and Nikishov are not the only investigators to note the potential problems with the anomalous ways that conventional General Relativity treats gravitational self-interactions, and they are not alone in this respect. Carl Brannen has also pursued some similar ideas.

As another example, consider this statement by A.L. Koshkarov from the University of Petrozavodsk, Russia in his November 4, 2004 preprint (arXiv:gr-qc/0411073) in the introduction to his paper entitled "On General Relativity extension."

But in what way, the fact that gravitation is nonabelian does get on with widely spread and prevailing view the gravity source is energy-momentum and only energy-moment? And how about nonabelian self-interaction? Of course, here we touch very tender spots about exclusiveness of gravity as physical field, the energy problem, etc. . . .All the facts point out the General Relaivity is not quite conventional nonabelian theory.

Koshkarov then goes on to look at what one would need to do in order to formulate gravity as a conventional nonabelian theory like conventional Yang-Mills theory.

Alexander Balakin, Diego Pavon, Dominik J. Schwarz, and Winfried Zimdahl, in their paper "Curvature force and dark energy" published at New.J.Phys.5:85 (2003), preprint at arXiv:astro-ph0302150 similarly noted that "curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy." Balakin, et al., reach their conclusions using the classical geometric expression of general relativity, rather than a quantum gravity analysis, suggesting that the overlooked self-interaction effects do not depend upon whether one's formulation of gravity is a classical or a quantum one, but the implication once again, is that a failure to adequately account for the self-interaction of gravitational energy with itself may account for all or most dark sector phenomena.

A suggestion that the order of magnitude of the non-Newtonian implications of General Relativity (possibly generalized slightly) may be sufficient to explain the entire dark sector comes from Hong Sheng Zho in a preprint last modified on June 9, 2008 and originally submitted on May 27, 2008 arXiv:0805.4046 [gr-qc] that "the negative pressure of the cosmological dark energy coincides with the positive pressure of random motion of dark matter in bright galaxies."

Another indication that these effects may be of the right order of magnitude to explain dark energy as well as dark matter comes from Greek scientists K. Kleidis and N.K. Spyrou in their paper "A conventional approach to the dark-energy concept" (arXiv: 1104.0442 [gr-qc] (April 4, 2011). They too note that energy from the internal motions of the matter in the universe (both baryonic and dark) in a collisional dark matter model are of the right scale to account for existing observational data without dark energy or the cosmological constant.

It is also worth noting that the cosmological constant is small enough that other kinds of careful analysis of sources for dark energy effects in the Standard Model and non-Newtonian effects in general relativity other than the cosmological constant may explain some or all of it.

For example, Ralf Schutzhold in an April 4, 2002 preprint at arXiv:gr-qc/0204018 in a paper entitled "A cosmological constant from the QCD trace anomaly" noted that "non-perturbative effects of self-interacting quantum fields in curved space times may yield a significant contribution" to the observed cosmological constant. The calculations in his four page page conclude that: "Focusing on the trace anomaly of quantum chromo-dynamics (QCD), a preliminary estimate of the expected order of magnitude yields a remarkable coincidence with the empirical data, indicating the potential relevance of this effect."

See also Sourav Kesharee Sahoo, Ashutosh Dash, Radhika Vathsan, Tabish Qureshi, "Testing Gravitational Self-interaction via Matter-Wave Interferometry" arXiv:2203.01787 (March 3, 2022) (applying gravitational self-interaction to decoherence issues).

Also related

The gravitational stability of a two-dimensional self-gravitating and differentially rotating gaseous disk in the context of post-Newtonian (hereafter PN) theory is studied. Using the perturbative method and applying the second iterated equations of PN approximation, the relativistic version of the dispersion relation for the propagation of small perturbations is found. We obtain the PN version of Toomre's local stability criterion by utilizing this PN dispersion relation. In other words, we find relativistic corrections to Toomre's criterion in the first PN approximation.

Two stability parameters η and μ related to gravity and pressure are introduced. We illustrate how these parameters determine the stability of the Newtonian and PN systems. Moreover, we show that, in general, the differentially rotating fluid disk is more stable in the context of PN theory relative to the Newtonian one. Also, we explicitly show that although the relativistic PN corrections destabilize non-rotating systems, they have the stabilizing role in the rotating thin disks. Finally, we apply the results to the relativistic disks around hypermassive neutron stars (HMNSs), and find that although Newtonian description predicts the occurrence of local fragmentations, PN theory remains in agreement with the relevant simulations, and rules out the existence of local fragmentations.

Ali Kazemi, Mahmood Roshan, Elham Nazari "Post-Newtonian corrections to Toomre's criterion" (August 17, 2018) (accepted in ApJ).

And another paper noting the usefulness of a scalar theory of gravitation as a way to approximate self-interaction of gravitational field effects in full GR or the Post-Newtonian approximation.

We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework, we analyze several specific scalar theories of gravitation and check their predictions for the solar system post-Newtonian effects.

Diogo P. L. Bragança, José P. S. Lemos "Stratified scalar field theories of gravitation with self-energy term and effective particle Lagrangian" (June 29, 2018).

The conclusion to this paper notes that:

In this paper, we presented a general stratified scalar field theory of gravitation in a Minkowski background. Then, we calculated two post-Newtonian parameters from three general parameters of the theory B, C and k, concluding that it is perfectly possible for such a scalar theory to explain the four solar system tests. Finally, we used this general theory to rapidly compute the PPN parameters β and γ for a set of scalar theories of gravitation to verify if they agree with the experimental tests of gravitation in the solar system. Therefore, with this formalism, one can directly find those two PPN parameters only from the field equation and the particle Lagrangian of a given scalar theory of gravitation. Although this is a very efficient method to calculate β and γ for a given theory, it does not allow one to compute the other PPN parameters. It would be interesting to generalize this approach to efficiently calculate the remaining PPN parameters for scalar theories and verify if it is possible for such a theory to explain every phenomenon predicted by general relativity.

The stratified theories that were analyzed (Page and Tupper’s, and Ni’s) yielded the correct PPN parameters relevant for solar system tests. One could wonder whether this indicates that they are valid theories, and the answer to that relies in analyzing the remaining PPN parameters. This analysis was done by Nordtvedt and Will [60] and Ni [50] and the conclusion was that stratified theories cannot account for Earth-tide measurements due to the motion of the solar system relative to the preferred frame (defined by the distant stars).

The conformal theories that were analyzed did not yield the correct γ parameter even in very general cases. This motivates future work on the analysis of a relativistic scalar theory including a derivative coupling in the Lagrangian, of the type T ab(∂aΦ)(∂bΦ). Such a theory would not have preferred frame effects (it would respect Lorentz symmetries), so if it predicted the correct parameters β and γ it would not have the problem of Earth-tide measurements.

If such a scalar theory correctly predicts the outcome of every weak field gravity experiment, then we can only rule it out using strong gravity experiment results (e.g. LIGO, neutron star binaries, cosmology). Note also that a scalar theory of gravity is much simpler than general relativity, since it describes gravity with one function instead of ten. In such theories, unlike general relativity, it is generally possible to define a local gravitational energy-momentum tensor, which is always an attractive feature, and is still a problem in general relativity.

Note that some of the preprints cited (maybe most) have been subsequently published, but I haven't clicked through to update the status of these papers since a last took note of them.

 

[PeterDonis]

@ohwilleke thanks for all the references! You've added a bunch of items to my reading list.

Regarding MTW, their basic position on the "energy stored in the gravitational field" not being "localizable" is simple: there is no tensor that describes any such thing, indeed there can't be if the equivalence principle is correct, and anything that is "localizable" in the sense they are using the term must be described by a tensor. I realize there is a significant portion of the literature that does not agree with that position, but I don't think MTW itself is sloppy or ambiguous in describing the position they are taking.

Of course their position assumes that standard GR is correct within its domain of validity and that theories containing extra fields associated with "gravity", such as scalar-tensor theories, are not necessary to explain the data. Whether the voluminous amount of data collected since 1973 when MTW was published includes effects that standard GR cannot easily explain is, of course, the point of very open area of research we are discussing, at least with regard to the data on galaxy rotation curves. If it turns out that standard GR can, when calculated properly, explain the galaxy rotation curve properties that are currently believed by many to require dark matter, that might invalidate some of the more specific statements MTW makes, but not their general position on "energy stored in the gravitational field" not being "localizable" in their particular precise sense of that term.

 

[ohwilleke]

@ohwilleke thanks for all the references! You've added a bunch of items to my reading list.

Regarding MTW, their basic position on the "energy stored in the gravitational field" not being "localizable" is simple: there is no tensor that describes any such thing, indeed there can't be if the equivalence principle is correct, and anything that is "localizable" in the sense they are using the term must be described by a tensor. I realize there is a significant portion of the literature that does not agree with that position, but I don't think MTW itself is sloppy or ambiguous in describing the position they are taking.

Of course their position assumes that standard GR is correct within its domain of validity and that theories containing extra fields associated with "gravity", such as scalar-tensor theories, are not necessary to explain the data. Whether the voluminous amount of data collected since 1973 when MTW was published includes effects that standard GR cannot easily explain is, of course, the point of very open area of research we are discussing, at least with regard to the data on galaxy rotation curves. If it turns out that standard GR can, when calculated properly, explain the galaxy rotation curve properties that are currently believed by many to require dark matter, that might invalidate some of the more specific statements MTW makes, but not their general position on "energy stored in the gravitational field" not being "localizable" in their particular precise sense of that term.

What I am calling "sloppiness" in their discussion is using the term "localizable" only to refer to an exact point value, basically a well defined point gradient function (without clearly calling out that they are using such a restrictive definition) when they are recognizing that the effects can be isolated to essentially any closed system of any size as a whole (even one of just a few km in longest dimension), which is far from what one is usually talking about when one says that an effect can only be "global" (particularly after following on with a discussion about effects being negligible below the scale of the entire universe in a following section).

Another area of sloppiness is their logic that because there is some frame of reference in which you can take localized gravitational energy to zero for any given free falling system, that this means that you can't use mutually consistent well chosen frames of reference to provide useful information about the gravitational energy of a system. By analogy, you can always set "potential energy" to zero in classical Newtonian gravity, but that doesn't limit the usefulness of giving it positive value from other frames of reference.

 

[PeterDonis]

Ali Kazemi, Mahmood Roshan, Elham Nazari "Post-Newtonian corrections to Toomre's criterion" (August 17, 2018) (accepted in ApJ).

Btw, is the "Toomre" of "Toomre's criterion" Alar Toomre? It looks like it could be from the references in the paper. Alar Toomre was a professor of math at MIT when I was there; his class in complex analysis was the one that convinced me that I should be taking the math classes I needed for my degree (which was not in math) from the physics department instead of the math department. Brilliant, but way over my head.

 

[ohwilleke]

Btw, is the "Toomre" of "Toomre's criterion" Alar Toomre? It looks like it could be from the references in the paper. Alar Toomre was a professor of math at MIT when I was there; his class in complex analysis was the one that convinced me that I should be taking the math classes I needed for my degree (which was not in math) from the physics department instead of the math department. Brilliant, but way over my head.

I hear you. Complex analysis was probably among the classes I took that convinced me that I should not pursue a math PhD (although I considered other heavily math dependent fields like actuarial science, operations research, and quantitative economics seriously before going to the dark side to become a lawyer).

 

[strangerep]

[MTW...]

Section 20.4 stating "[...] One can always find in any given locality a frame of reference in which all local 'gravitational fields' (all Christoffel symbols . . . . disappear. No [Christoffel symbols] means no 'gravitational fields' and no local gravitational field means no 'local gravitational energy-momentum.'

Every time I read textbook statements like this I think: "But what about geodesic deviation?". That relative motion of neighboring geodesics depends on the curvature tensor and cannot be transformed away.

In Newtonian gravity, do gravitational tidal forces do work?
(Hmm, I need to review that...)

 

[PeterDonis]

That relative motion of neighboring geodesics

...is not described by Christoffel symbols, but by the curvature tensor. MTW's statement about the Christoffel symbols is basically a version of the equivalence principle: at any event in spacetime, you can always find a local freely falling frame in which there is no "gravitational field". In such a frame, the metric coefficients, to first order, will be those of the Minkowski metric; but at second order, curvature effects will appear. (If you make your local frame small enough, those curvature effects will be negligible within the confines of the frame.)

In Newtonian gravity, do gravitational tidal forces do work?

In Newtonian gravity, the Newtonian gravitational force itself does work. A fortiori so would gravitational tidal forces.

 

[strangerep]

[geodesic deviation] is not described by Christoffel symbols, but by the curvature tensor. MTW's statement about the Christoffel symbols is basically a version of the equivalence principle: at any event in spacetime, you can always find a local freely falling frame in which there is no "gravitational field". In such a frame, the metric coefficients, to first order, will be those of the Minkowski metric; but at second order, curvature effects will appear. (If you make your local frame small enough, those curvature effects will be negligible within the confines of the frame.)

Er, yes, that's of course what I meant.

In Newtonian gravity, the Newtonian gravitational force itself does work. A fortiori so would gravitational tidal forces.

Thanks -- that's what I figured.

 

[ohwilleke]

Another paper in this theme:

[Submitted on 17 Jul 2022]

Gravitational orbits in the expanding universe revisited​

Vaclav Vavrycuk

Modified Newtonian equations for gravitational orbits in the expanding universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived under the assumption of the space expansion described by the standard FLRW metric. In this paper, an alternative metric is applied and the modified Newtonian equations are derived for the space expansion described by the conformal FLRW metric. As shown by Vavryčuk (Frontiers in Physics, 2022), this metric is advantageous, because it properly predicts the cosmic time dilation and fits the SNe Ia luminosity observations with no need to introduce dark energy. Surprisingly, the Newtonian equations based on the conformal FLRW metric behave quite differently than those based on the standard FLRW metric. In contrast to the common opinion that local systems resist the space expansion, the results for the conformal metric indicate that all local systems expand according to the Hubble flow. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Pioneer anomaly, the Faint young Sun paradox, the Moon's and Titan's orbit anomalies or the presence of rivers on ancient Mars.

Comments:	17 pages, 9 figures
Subjects:	General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO)
Cite as:	arXiv:2207.08196 [gr-qc]

 

[PeterDonis]

Another paper in this theme

So basically he's proposing that conformal time is actually the same as "experienced time" for comoving objects? He should talk to Penrose.

 

[mitchell porter]

His initial papers were quantum gravity, but he has reproduced the result in two or three recent papers classically. The insights are certainly quantum gravity inspired, but the results flow from purely classical GR. See, e.g., Alexandre Deur, "Relativistic corrections to the rotation curves of disk galaxies" (April 10, 2020) (lated updated February 8, 2021 in version accepted for publication in Eur. Phys. Jour. C).

I'm a little baffled because I don't see any relationship between this paper and his quantum gravity papers. I thought the point of the quantum gravity papers was to claim that there is a specific large quantum correction to classical GR on galactic scales, whereas this paper seems to be about a new ansatz for approximately solving "the self-gravitating disk problem in GR" - in classical GR, one would assume.

As for the other papers in this thread, I note that a lot of them (including Immirzi et al) treat the galaxy as a zero-pressure system. But Robin Hanson argues plausibly that this is conceptually wrong. In the context of Earth's atmosphere, we're used to pressure meaning the force applied by the impact of innumerable molecules. But Hanson says that in the galactic context, it refers to momentum flux. The stars orbiting the galaxy aren't colliding with anything, but their passage still creates a flow of momentum through a given region of space.

 

[PeterDonis]

Hanson says that in the galactic context, it refers to momentum flux.

He's wrong. Momentum flux is the "time-space" components of the stress-energy tensor. Pressure is the diagonal "space-space" components. They're not the same.

 

[ohwilleke]

I'm a little baffled because I don't see any relationship between this paper and his quantum gravity papers. I thought the point of the quantum gravity papers was to claim that there is a specific large quantum correction to classical GR on galactic scales, whereas this paper seems to be about a new ansatz for approximately solving "the self-gravitating disk problem in GR" - in classical GR, one would assume.

He was really arguing even in the quantum gravity papers that it was the self-interaction of the field that produces the effect.

He comes at it by analogy to QCD which is, of course, formulated as a quantum theory. And, the logic of why it should have that effect is a lot more obvious when formulated in quantum form and in a way that can exploit known analogies in QCD.

But, fundamentally, the self-interaction that matters is already present in classical GR. It is just a lot harder to see when you try to work directly with Einstein's field equations, in which, of course, the gravitational field isn't on the right hand side in the stress-energy tensor, but instead appears on the left hand side as the non-linearity in the gravitational field part.

Indeed, one of the things, in general that makes GR difficult for students, is that the definitions of the inputs into the stress-energy tensor are formulated in a way that is not very comparable to the way that for example, Newtonian gravity and Maxwell's equations are, and wrapping your head around what is going on in that very compact form can be challenging.

Ultimately, it is just a stylistic issue. But, even for him, he had to reach the conclusion that applies in both quantum and classical formulations in the quantum formulation first, and then back out the fact that it can also follow classically second, so that it isn't actually a quantum specific effect.

In addition to the papers cited above, another work in progress paper that works out the classical GR treatment to reach the same result, which benefits from co-authors, is A. Deur, Corey Sargent, Balša Terzić, "Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" (August 31, 2019, last revised January 11, 2020) (pre-print). Latest update May 18, 2020. https://arxiv.org/abs/1909.00095v3 The abstract of this paper states:

The discrepancy between the visible mass in galaxies or galaxy clusters, and that inferred from their dynamics is well known. The prevailing solution to this problem is dark matter. Here we show that a different approach, one that conforms to both the current Standard Model of Particle Physics and General Relativity, explains the recently observed tight correlation between the galactic baryonic mass and its observed acceleration. Using direct calculations based on General Relativity's Lagrangian, and parameter-free galactic models, we show that the nonlinear effects of General Relativity make baryonic matter alone sufficient to explain this observation.

 

[ohwilleke]

Arguing that GEM doesn't work.

[Submitted on 20 Jul 2022]

On the rotation curve of disk galaxies in General Relativity​

Luca Ciotti (Dept. of Physics and Astronomy, University of Bologna (Italy))

Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter halos. In this paper, by using the well known weak field, low velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of Newtonian gravity for the same disks in absence of Dark Matter. As expected, the resulting rotation curves are indistinguishable, with GR corrections at all radii of the order of v2/c2≈10−6. Next, the gravitomagnetic Jeans equations for two-integral stellar systems are derived, and then solved for the Miyamoto-Nagai disk model, showing that finite-thickness effects do not change the previous conclusions. Therefore, the observed phenomenology of galactic rotation curves at large radii requires Dark Matter in GR exactly as in Newtonian gravity, unless the cases here explored are reconsidered in the full GR framework with substantially different results (with the surprising consequence that the weak field approximation of GR cannot be applied to the study of rotating systems in the weak field regime). In the paper, the mathematical framework is described in detail, so that the present study can be extended to other disk models, or to elliptical galaxies (where Dark Matter is also required in Newtonian gravity, but their rotational support can be much less than in disk galaxies).

Comments:	16 pages, 4 figures, ApJ, accepted
Subjects:	Astrophysics of Galaxies (astro-ph.GA); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:2207.09736 [astro-ph.GA]

 

[kodama]

Arguing that GEM doesn't work.

[Submitted on 20 Jul 2022]

On the rotation curve of disk galaxies in General Relativity​

Luca Ciotti (Dept. of Physics and Astronomy, University of Bologna (Italy))

Comments:	16 pages, 4 figures, ApJ, accepted
Subjects:	Astrophysics of Galaxies (astro-ph.GA); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:2207.09736 [astro-ph.GA]

might also apply to Deur

 

[ohwilleke]

might also apply to Deur

It might. But it isn't engaging with the same argument.

 

[kodama]

It might. But it isn't engaging with the same argument.

GEM equations are well understood in analogy to EM, and are 10-6 too weak to explain dark matter.

Are there equations of GR self-interaction directly derived from GR that would result in enough deviation from Newtonian approximation in the weak field that would explain dark matter without dark matter?

 

[ohwilleke]

GEM equations are well understood in analogy to EM, and are 10-6 too weak to explain dark matter.

Are there equations of GR self-interaction directly derived from GR that would result in enough deviation from Newtonian approximation in the weak field that would explain dark matter without dark matter?

I don't have the math and GR chops to independently confirm that, but I've read that papers that say so, they passed peer review and got published, and they make sense. I also wouldn't agree that the GEM issue is definitively resolved. Different gravity theory specialist researchers are making different assumptions and I'm not in a position to say which one's are correct.

 

[kodama]

I don't have the math and GR chops to independently confirm that, but I've read that papers that say so, they passed peer review and got published, and they make sense. I also wouldn't agree that the GEM issue is definitively resolved. Different gravity theory specialist researchers are making different assumptions and I'm not in a position to say which one's are correct.

Gravity probe B was designed to test planet Earth's GEM. it confirms it to within 0.5% but with the entire mass of planet Earth spinning on its axis is an extremely weak effect requiring extremely sensitive measurements,

 

[PeterDonis]

Gravity probe B was designed to test planet Earth's GEM.

Earth is a very different geometry from a galaxy. Earth is spherical to a very good approximation. A galaxy is not; it's a flat disk with some bulge in the center but still very different from spherical. The basic claim of the theorists who are saying that GR nonlinear effects can explain galaxy rotation curves without dark matter is that the relative order of magnitude of those effects, as compared with the usual Newtonian ones, are much larger for a flat disk than for a spherical configuration of matter. I'm not enough of an expert to independently do the calculations, but that's the basis of the claim as I understand it.

 

[kodama]

Earth is a very different geometry from a galaxy. Earth is spherical to a very good approximation. A galaxy is not; it's a flat disk with some bulge in the center but still very different from spherical. The basic claim of the theorists who are saying that GR nonlinear effects can explain galaxy rotation curves without dark matter is that the relative order of magnitude of those effects, as compared with the usual Newtonian ones, are much larger for a flat disk than for a spherical configuration of matter. I'm not enough of an expert to independently do the calculations, but that's the basis of the claim as I understand it.

MOND requires 1/r in the deep MOND regimen. could s a flat disk explains that

 

[PeterDonis]

MOND requires 1/r in the deep MOND regimen. could s a flat disk explains that

Go read the papers and see. That's basically what they are saying, but they include calculations.

 

[kodama]

Go read the papers and see. That's basically what they are saying, but they include calculations.

does MOND differ depending on location, i.e. 1/r only apply for coplanar stars and not perpendicular to galaxy

 

[PeterDonis]

does MOND differ depending on location, i.e. 1/r only apply for coplanar stars and not perpendicular to galaxy

Go read the papers on MOND and see.

 

[mitchell porter]

A lot of theories and models are being discussed at once in this thread, but (in my opinion) without any clarity or precision. It would help if we could pick out a few, and actually understand them, and how they differ. I would nominate (1) the textbook weak-field models described by Ciotti in #44 (2) Ludwig's model, as an exemplar of gravitomagnetic models (3) whatever it is that Deur is doing.

Regarding (1) and (2), Ciotti apparently carries out gravitomagnetic calculations in the context of ordinary textbook models, and obtains that the force is minuscule. But cautiously, he does not say that this refutes Ludwig, since he knows that Ludwig has a different starting point. He says only that it would be very surprising if a different kind of approximation led to such a different result from the textbook results, for weak fields.

So this raises the question that Robin Hanson tried to answer (#41, #42): exactly what is different about Ludwig's assumptions, that makes them capable of producing such a different result? Hanson proposed that it is the assumption of zero pressure, an assumption shared by several other papers cited in this thread. I am wondering if it's initial conditions: maybe if you start with large gravitomagnetic forces, they will continue to be generated, but if you don't, they won't become so strong? Surely, careful study of Ludwig's work, and careful comparison with the textbook models in Ciotti, can yield a definite answer to the question above.

As for (3), Deur's work, it is being described in this thread (#43) as a model which takes into account the "self-interaction" of gravity in general relativity; and it was even suggested (#31) that the conventional wisdom, that gravitational energy in general relativity cannot be localized, has inhibited the study of gravitational self-interaction... I am skeptical about this second claim. There has been plenty of research on nonlinearity in general relativity; there has been plenty of research on stress-energy pseudotensors and partially localized definitions of energy; are there really dramatic new empirical consequences waiting to be revealed, once these two lines of research are considered together?... I also want to understand the relationship between the classical and quantum parts of Deur's research. Hopefully all this can be disentangled with sufficient patience and care.

 

[ohwilleke]

A lot of theories and models are being discussed at once in this thread, but (in my opinion) without any clarity or precision.

Fair enough, although one of my purposes in posting the thread was to illustrate the overall state of the GR effects as DM literature which is quite a bit bigger than a lot of people realize, but apart from Deur and Ludwig, not very sustained and developed, in an effort to identify common themes and contradictions, if any, and also to demonstrate that this is not just one or two isolated individuals pursuing a research program that no one else is exploring (as well as to illustrate the concentration of the work on this research agenda in the time period since 2018 more or less).

I agree that the field itself is scattered and the people involved aren't listening to each other very much.

Deur's work is definitely the most developed line of scholarship in the GR effects cause DM phenomena research agenda, and unlike Ludwig, who is purportedly contradicted by Hanson and Ciotti, there isn't really any work out there engaging with his line of analysis for good or ill, despite the growing number of publications that Deur has made in the field.

Maybe this is because nobody inclined to do so has noticed him, but it also might be because those who have noticed intuitively believe that he must be wrong but haven't taken the time to work through the math because Deur is working with math inspired by QCD and familiar to people in that field but unfamiliar to most people in the heartland of GR theory and phenomenology. So, its a lot more work for them to dig into Deur's analysis than it is for them to work over GEM analysis that is far more familiar to them in Ludwig's papers.

Regarding (1) and (2), Ciotti apparently carries out gravitomagnetic calculations in the context of ordinary textbook models, and obtains that the force is minuscule. But cautiously, he does not say that this refutes Ludwig, since he knows that Ludwig has a different starting point. He says only that it would be very surprising if a different kind of approximation led to such a different result from the textbook results, for weak fields.

So this raises the question that Robin Hanson tried to answer (#41, #42): exactly what is different about Ludwig's assumptions, that makes them capable of producing such a different result? Hanson proposed that it is the assumption of zero pressure, an assumption shared by several other papers cited in this thread. I am wondering if it's initial conditions: maybe if you start with large gravitomagnetic forces, they will continue to be generated, but if you don't, they won't become so strong? Surely, careful study of Ludwig's work, and careful comparison with the textbook models in Ciotti, can yield a definite answer to the question above.

Along that line, one of Ludwig's assumptions, also found in the paper in #1 that started this thread, is that the system is "rotationally supported" which goes to your initial conditions speculation. GEM may not provide a good source for revving up the spin from a dead halt, but could provide the field needed to sustain it once it is going.

Intuitively, it makes more sense that the rotationally supported assumption matters, than it does that it assumes zero pressure (even though zero pressure seems like a reasonable enough assumption at face value in a spiral galaxy system).

An earlier post also noted, and I don't think it should be dropped, the importance of assumptions about the geometry of the system (disk-like in Ludwig and the paper in #1 v. spherical in many other treatments) which is almost surely a material assumption.

As for (3), Deur's work, it is being described in this thread (#43) as a model which takes into account the "self-interaction" of gravity in general relativity . . . I also want to understand the relationship between the classical and quantum parts of Deur's research. Hopefully all this can be disentangled with sufficient patience and care.

One important aspect of Deur's earlier quantum oriented work is that it is modeled in a static equilibrium model that explicitly disregards GEM effects that arise from the motion of the particles in the system. Systems not near equilibrium are expressly noted by Deur in those papers to be beyond the scope of applicability of his quantum oriented work.

(Incidentally, there is some MOND scholarship by Stacey McGaugh and others that also observes that MOND does not hold in systems not close to equilibrium and even uses a poor MOND fit as a flag that a system might be out of equilibrium. I won't cite it here as MOND itself is really off topic to this thread. This is notable, however, because, in the geometry of a spiral galaxy Deur's approach with pure GR closely approximates MOND, and Deur's approach could provide a solid GR theoretical basis for the MOND conclusions while expanding its domain of applicability in systems like galaxy clusters where MOND underperforms by resorting to the different geometry of the mass in these systems.)

In Deur's classical work, different simplifications, in addition to or in lieu of the static equilibrium assumption of the quantum work, are used in ways that less transparently differentiate gravitational field self-interaction from GEM effects. Crosta and Balasin in #2, for example, also make a static equilibrium analysis that cannot be due to GEM effects (and like Deur, have not triggered refutation papers.)

(I'm also not entirely convinced that the GEM effects aren't, through some back door in the equations, basically harnessing gravitational field self-interactions, particularly if the initial conditions in the GEM works turns out to be the key different assumption. Deur's quantum work makes it seem unlikely to me that the reverse, that his self-interaction effect is really a backdoor implicating GEM effects, is true).

Deur's recently published classical paper at #1, Alexandre Deur, "Relativistic corrections to the rotation curves of disk galaxies" (April 10, 2020) (lated updated February 8, 2021 in version accepted for publication in Eur. Phys. Jour. C)., uses a mean field approximation to do the GR analysis.

Some different methodological tools were used in the working paper, A. Deur, Corey Sargent, Balša Terzić, "Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" (August 31, 2019, last revised January 11, 2020) (pre-print). Latest update May 18, 2020. https://arxiv.org/abs/1909.00095v3

Some key points from the body text:

The rotation curves of several disk galaxies were computed in (Deur 2009) based on Eq. (1) and using numerical lattice calculations in the static limit (Deur 2017). . . . Although based directly on the GR’s Lagrangian, the lattice approach is limited since it is computationally costly and applies only to simple geometry, limiting the study to only a few late Hubble type galaxies at one time. To study the correlation from MLS2016 over the wide range of disk galaxy morphologies, we developed two models based on: 1) the 1/r gravitational force resulting from solving Eq. (1) for a disk of axisymmetrically distributed matter; and 2) the expectation that GR field self-interaction effects cancel for spherically symmetric distributions, such as that of a bulge, restoring the familiar 1/r 2 force.

and from the appendix:

The direct calculation of the effects of field self-interaction based on Eq. (1) employs the Feynman path integral formalism solved numerically on a lattice. While the method hails from quantum field theory, it is applied in the classical limit, see (Deur 2017). The first and main step is the calculation of the potential between two essentially static (v c) sources in the non-perturbative regime. Following the foremost non-perturbative method used in QCD, we employ a lattice technique using the Metropolis algorithm, a standard Monte-Carlo method (Deur 2009, 2017). The static calculations are performed on a 3-dimensional space lattice (in contrast to the usual 4-dimensional Euclidian spacetime lattice of QCD) using the 00 component of the gravitational field ϕµν. This implies that the results are taken to their classic limit, as it will be explained below. Furthermore, the dominance of ϕ00 over the other components of the gravitational field simplifies Eq (1) in which [ϕ n∂ϕ∂ϕ] → anϕ n 00∂ϕ00∂ϕ00, with an a set of proportionality constants. One has a0 ≡ 1 and one can show that a1 = 1 (Deur 2017).

 

[kodama]

A lot of theories and models are being discussed at once in this thread, but (in my opinion) without any clarity or precision. It would help if we could pick out a few, and actually understand them, and how they differ. I would nominate (1) the textbook weak-field models described by Ciotti in #44 (2) Ludwig's model, as an exemplar of gravitomagnetic models (3) whatever it is that Deur is doing.

Regarding (1) and (2), Ciotti apparently carries out gravitomagnetic calculations in the context of ordinary textbook models, and obtains that the force is minuscule. But cautiously, he does not say that this refutes Ludwig, since he knows that Ludwig has a different starting point. He says only that it would be very surprising if a different kind of approximation led to such a different result from the textbook results, for weak fields.

So this raises the question that Robin Hanson tried to answer (#41, #42): exactly what is different about Ludwig's assumptions, that makes them capable of producing such a different result? Hanson proposed that it is the assumption of zero pressure, an assumption shared by several other papers cited in this thread. I am wondering if it's initial conditions: maybe if you start with large gravitomagnetic forces, they will continue to be generated, but if you don't, they won't become so strong? Surely, careful study of Ludwig's work, and careful comparison with the textbook models in Ciotti, can yield a definite answer to the question above.

As for (3), Deur's work, it is being described in this thread (#43) as a model which takes into account the "self-interaction" of gravity in general relativity; and it was even suggested (#31) that the conventional wisdom, that gravitational energy in general relativity cannot be localized, has inhibited the study of gravitational self-interaction... I am skeptical about this second claim. There has been plenty of research on nonlinearity in general relativity; there has been plenty of research on stress-energy pseudotensors and partially localized definitions of energy; are there really dramatic new empirical consequences waiting to be revealed, once these two lines of research are considered together?... I also want to understand the relationship between the classical and quantum parts of Deur's research. Hopefully all this can be disentangled with sufficient patience and care.

does the energy in empty space, the cosmological constant, gravitate, and contribute to "self-interaction" of gravity in general relativity

for that matter, does the cosmological constant interact with GEM at cosmological distances

if the space of an entire galaxy that contains the cosmological constant also rotates with the galaxy, doesn't this also produce a GEM effect and also a self-interaction of gravity effect

 

[ohwilleke]

does the energy in empty space, the cosmological constant, gravitate, and contribute to "self-interaction" of gravity in general relativity

for that matter, does the cosmological constant interact with GEM at cosmological distances

if the space of an entire galaxy that contains the cosmological constant also rotates with the galaxy, doesn't this also produce a GEM effect and also a self-interaction of gravity effect

Deur is modeling GR without a cosmological constant.

 

[kodama]

Deur is modeling GR without a cosmological constant.

Emergent Gravity and the Dark Universe arXiv:1611.02269​

we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

301 citations

Verlinde's entropic gravity proposal makes the cosmological constant central to his MOND like proposal and has 301 citations.

the energy in empty space should curve space time in GR and may even have a GEM component to it. MOND ao is related to the cc.

 

[Nik_2213]

{ My head hurts, my head hurts, my head hurts... }

Does any of these support or falsify the few String Theory versions using Teleparallel Gravity ??