General Relativity And Missing Mass II

I was preparing a Physics Forum post following up on the papers discussed in my recent General Relativity and Missing Mass post. This blog posts adapts that Physics Forum post.

Introduction and Motivation

The pair of related papers whose abstracts and citations and links are provided below (both pre-prints were ultimately published after peer review) by professional non-specialists in the subfields in low profile departments, are not particularly new (2015 and 2016 preprints, published in 2016 and 2018) haven't gotten much attention in the field, and were just recently brought to my attention by a Physics Forums Insights article by one of the co-authors of these papers. A comment thread on this wide ranging article, overall, which makes the point below as one of many, is found here. The pertinent part of the discussion in the article itself explains that:

Given this result, one immediately wonders if general relativity (GR) can be brought into the mix via NPRF [“no preferred reference frame"] and the gravitational constant G. Of course it can and the associated counterintuitve aspect (“mystery”) in GR is the contextuality of mass. We already showed how this might resolve the missing mass problem without having to invoke non-baryonic dark matter [23][24].

Specifically, I am pointing out the well-known result per GR that matter can simultaneously possess different values of mass when it is responsible for different combined spatiotemporal geometries. Here “reference frame” refers to each of the different spatiotemporal geometries associated with one and the same matter source. Tacitly assumed in this result is of course that G has the same value in each reference frame, which is consistent with NPRF as applied to c and h above. This spatiotemporal contextuality of mass is not present in Newtonian gravity where mass is an intrinsic property of matter.

For example, when a Schwarzschild vacuum surrounds a spherical matter distribution the “proper mass” Mp of the matter, as measured locally in the matter, can be different than the “dynamic mass” M in the Schwarzschild metric responsible for orbital kinematics about the matter [25, p. 126]. This difference is attributed to binding energy and goes as dMp=(1−2GM(r)c2r)−1/2dM.

In another example, suppose a Schwarzschild vacuum surrounds a sphere of Friedmann-Lemaitre-Robertson-Walker (FLRW) dust, as used originally to model stellar collapse [15, pp. 851-853]. The dynamic mass M of the surrounding Schwarzschild metric is related to the proper mass Mp of the FLRW dust, as joined at FLRW radial coordinate χo, by

(1)MpM=3(2χo−sin⁡(2χo))4sin3⁡(χo)

where

(2)ds2=−c2dτ2+a2(τ)(dχ2+sin2⁡χdΩ2)

is the closed FLRW metric [26].

I should quickly point out that this may prima facie seem to constitute a violation of the equivalence principle, as understood to mean inertial mass equals gravitational mass, since inertial mass can’t be equal to two different values of gravitational mass. But, the equivalence principle says simply that spacetime is locally flat [27, pp. 68-69] and that is certainly not being violated here nor with any solution to Einstein’s equations.

(Source) The papers below are references 23 and 24 in this excerpt.

At a crude level, the authors argue that dark matter and dark energy are methodological artifacts of using a Newtonian approximation of GR to explain the phenomena that the give rise to the dark matter and dark energy hypotheses, when the GR effects, while subtle, can't be ignored entirely in the circumstances where these phenomena are observed.

In particular they make some bold claims based upon two tweaks to conventional applications of general relativity. Also, unlike many other proposed solutions to dark energy and dark matter phenomena without dark matter particles or dark energy substances (e.g. here), their dark energy fix is more or less independent or their dark matter fix.

The Dark Energy Fix

One tweak suggests a tweak to the formula used to convert redshift to time depth that if adopted would conclude that dark energy is just a "chimera" of an overly simplistic conversion formula which when adjusted gives rise to a universe whose expansion is occurring at a constant Hubble rate. A heuristic motivation for the tweak, rooted in the observation that relativistic effects in the frequencies of photons emitted billions of years ago were mostly due mostly not to gravity from EM fields (which is negligible) but to gravity from matter fields between the place of emission and the place of observation, and that the formula used to convert redshift z scores to time depth doesn't, in the author's view, properly account for this fact.

The adjustment is negligible a low z, but significant at high z and with the adjustment, they allege and show with charts comparing the observational data to the expectation given their conversion factor, you get a no cosmological constant solution that closely matches the smallish data set they use to test the theory.

This is cool, important, quite possibly wrong as it is motivated by some less than mainstream hypotheses about fundamental issues in GR and quantum gravity. Critically, this tweak also means that GR would conserve matter-energy globally and not locally which is a very desirable feature of any quantum gravity theory ("Realizing dark energy and the observed de Sitter spacetime in quantum gravity has proven to be obstructed in almost every usual approach.") that is usually solved by proposing some sort of BSM particle that creates a scalar (or more complex) dark energy field that pervades the universe.

The simplicity of the fix isn't terribly striking because the cosmological constant in the mainstream lambdaCDM model is also very simple. But, finding a different analytical perspective in a common status quo formula that on its face looks too simple to be more than a first order approximation of the correct way to make the conversion, naively, seems rather attractive. It is particularly attractive if it can serve as a way to eliminate a lack of global mass-energy conservation in General Relativity (a very ugly feature of GR), and if it can render unnecessary the shocking notion that 75%ish of all of the stuff in mass-energy in the universe is seemingly unobservable dark energy. Maybe energy non-conservation and a universe made up mostly of dark energy truly is unavoidable and that is just a hard fact that we have to accept. But these realities are ugly enough that they deserve a second look at alternatives to resolve the issues with the data that they explain without these ugly features.

This isn't the first proposed non-BSM fix in recent years, which suggests a methodological issue may be giving rise to a false perception that dark energy exists. See also, e.g., here, here, here, and here.

The Dark Matter Fix

The second tweak suggests that (1) the apparent mass-energy of something is observer dependent, and (2) starts from an assumption, in the tradition of loop quantum gravity and kindred quantum gravity theories, that spacetime is fundamentally discrete at some fine grained level and that locality is an emergent property of spacetime that at a more fundamental level has points that are directly connected to each other that are not local, i.e. spacetime is "disordered" at a fundamental level (e.g. some small number of points have direct links to points in other galaxies). Based upon this, they used what they called Modified Regge Calculus (MORC) and "geometrically modify proper mass interior to the Schwarzschild solution" to tweak GR in an effort to explain dark matter phenomena.

The theoretical foundation and motivation for this tweak, again, isn't terribly widely accepted and not terribly rigorously spelled out either. It is an ansatz, rather than a full fledged theory derived from first principles. Ultimately, the show stopper with the second tweak, much like in the case of MOND and other modified gravity theories (some of which the papers consider) is not the theoretical motivation but the phenomenological success of their quite simple to apply adjustment.

The authors claim that they can fit not just galactic rotation curves, which many modified gravity theories do and some dark matter particle theories do to some extent (often with weaknesses regarding how dark matter halos acquire their shapes). They also claim to be able to fit all three peaks of the Cosmic Microwave Background (CMB) that is the crowning achievement of the lambdaCDM standard model of cosmology and one of the strongest arguments for dark matter, as shown in the illustration immediately below.

A fit to the CMB was also achieved by a relativistic generalization of MOND earlier this year, and Moffat has also claimed to have managed it, so the lambdaCDM claim to being the only model that can predict and explain the CMB is no longer true.

They also claim to have good success rivaling the best modified gravity theories in this domain at explaining dark matter phenomena in galactic clusters, where MOND fails to predict sufficient dark matter effects, but other gravitational approaches to explaining dark matter phenomena have also claimed success.

Other Gravitational Dark Matter Fixes Compared

This broad phenomenological domain of applicability with a theory whose formulas aren't particularly complex relative to MOND or other leading modified gravity theories, in a way that modifies GR in a way that is simple but more subtle way than a lot of other modified gravity theories, is notable indeed.

For example, the reduction of this approach to GR in strong fields at short distances, and the lack of a need for scalar, and vector, and tensor fields (like TeVeS that generalizes MOND to be relativistic), Moffat's STVG theory, and MSTG (which is another iteration of Moffat's gravity modification theory work) is impressive and overcomes constraints on Yukawa type modified gravity laws with massive gravitons that are tightly constrained by multi-messenger observations of black hole-star mergers emitting both photons and gravitational waves whose times of travel can be compared in an only slightly model dependent manner. (These authors don't consider another promising comparison theory that only slightly modifies GR while purporting to explain dark matter phenomena, called conformal gravity).

Admittedly, the analysis is a bit wooly, and the credentials of the team of researchers behind the papers is not all that impressive. But their empirical successes at fitting the data in a way that has at least some theoretical motivation, with fairly simple tweaks to GR, surely deserves further attention and examination as a possible explanation of dark matter and dark energy phenomena, unless it contains some obvious flaw.

Also, it is worth observing that their formula and approach is very different from that of Alexandre Deur, who motivates his gravitation work, that also seeks to change how GR is applied in a minimalist fashion rather than truly modifying GR, that purport to explain dark energy phenomena, galactic rotation curves, dark matter phenomena in clusters, and select other dark matter phenomena (although not the CMB spectrum so far, simply for want of trying), as basically quantum gravity effects that flow naturally from a vanilla graviton based quantum gravity Lagrangian with an emphasis on the graviton self-interaction component, that is simplified enough to make it tractable to apply by using a scalar graviton approximation (equivalent to a static equilibrium approximation of the tensor case which is computationally intractable), even though his approach isn't inherently quantum and can be formulated classically in a less transparently well motivated manner.

The fact that this team of authors and Deur can purport to get almost identical phenomenological fits to dark matter and dark energy phenomena over a very wide domain of applicability, with very subtle tweaks to GR that are very different in heuristic motivation and in the mathematical structure of the modifications, is also in and of itself pretty remarkable too.

Relevance To CDM, WDM, SIDM, ALP DM and Other Dark Matter Particle Approaches

Perhaps this paper is completely off base in its motivation for its equations or there is some other specific observationally established fact that proves that this particular set of equations must be wrong. But to the extent that its fit to the observational data is good, as it naively seems to be, over a very broad domain of applicability, with some very straight forward simple adjustments to conventionally applied GR, it is proof of concept that dark matter and dark energy phenomena can be explained purely with gravity modification that isn't particularly Byzantine.

Cold Dark Matter (CDM), Warm Dark Matter (WDM) and even Self-Interacting Dark Matter (SIDM) theories have all received a great deal of very careful vetting that have revealed serious and intractable conflicts with observations in domains where modified gravity theories have fit the data pretty well without contortions or special pleading (see also, e.g. here and here and here and here). Axion-like particle dark matter theories also have few new breakthroughs to show for themselves or a priori predictions that have been tested and proved true.

Multiple authors have now concluded (see e.g., here and here and here), although this certainly not universally disseminated or accepted in the particle dark matter field, is that it is very hard to explain dark matter phenomena at the galaxy level with dark matter particles that interact exclusively via gravity, or even with dark matter particles that have self-interactions with each other through some new boson mediated Yukawa force, despite the fact that there are strong experimental constraints on such interactions. The correlations between baryonic matter distributions and inferred dark matter halo shapes over a wide range of baryon configurations seems to be just too strong for there not to be some fifth force between the dark matter sector and the baryonic matter sector.

But a fifth force like that looks a lot like a gravity modification. And if you need to modify gravity anyway, Occam's Razor would seem to favor a gravity modification that can do the job without a new particle zoo in the dark sector over one that can modify gravity or posit a fifth force that acts directly on baryonic matter and dispenses with the dark sector entirely.

Yellow Flags

Since both sets of investigators (the authors of these papers, and Deur and his co-authors, respectively) are outsiders in the relative astrophysics sub-disciplines with a body of work that hasn't attracted much attention in the field, these proposals haven't been very thoroughly vetted by enough experts in the discipline who may be tempted to simply assume these each of these approaches doesn't deserve attention because they are so unconventional and unpolished, and the conventional folk wisdom in the discipline is that these kind of approaches shouldn't work and therefore must be flaws in some manner or another.

The peer view publication in legitimate journals of both groups' work demonstrates that these aren't simply crackpot proposals.

But there is a vast amount of territory between not crackpot and credible enough to win widespread acceptance as a worthwhile line of investigation in a discipline that is likely to be fruitful and is likely to bear out as correct upon a closer serious "kicking the tires" by specialists in the discipline.

Some of skepticism of outsiders comes from sociological bias factors, and some of that comes from the cold hard reality that extraordinary claims made by non-specialists are often flawed, and that the flaws of non-specialists who are still professional physicists tend to be particularly subtle.

Also, these authors, unlike MOND and the work of Deur, does not make (so far) any new a priori predictions that can be searched for in new experimental data, rather than merely retrodicting existing data with a new formula. Ultimately, this is partially a function of bad timing - the authors only came up with their idea after a lot of data was already available, and partially a function of limited resources (i.e. the authors haven't had enough time and energy to consider situations when their proposals would make novel predictions and describe them with precision yet - unless I missed something in these papers). But this too is a bit of a yellow flag.

 The papers 

The two papers are, first:

[Submitted on 21 Sep 2015 (v1), last revised 24 Oct 2017 (this version, v5)]

The Missing Mass Problem as a Manifestation of GR Contextuality
W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein

In Newtonian gravity, mass is an intrinsic property of matter while in general relativity (GR), mass is a contextual property of matter, i.e., matter can simultaneously possess two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility that the astrophysical missing mass attributed to non-baryonic dark matter (DM) actually obtains because we have been assuming the Newtonian view of mass rather than the GR view. Since an exact GR solution for realistic astrophysical situations is not feasible, we explore GR-motivated ansatzes relating proper mass and dynamic mass for one and the same baryonic matter, as justified by GR contextuality. We consider four GR alternatives and find that the GR ansatz motivated by metric perturbation theory works well in fitting galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (CMB, Planck 2015 data) without DM. We compare our galactic rotation curve fits to modified Newtonian dynamics (MOND), Burkett halo DM and Navarro-Frenk-White (NFW) halo DM. We compare our X-ray cluster mass profile fits to metric skew-tensor gravity (MSTG) and core-modified NFW DM. We compare our CMB angular power spectrum fit to scalar-tensor-vector gravity (STVG) and ΛCDM. Overall, we find our fits to be comparable to those of MOND, MSTG, STVG, ΛCDM, Burkett, and NFW. We present and discuss correlations and trends for the best fit values of our fitting parameters. For the most part, the correlations are consistent with well-established results at all scales, which is perhaps surprising given the simple functional form of the GR ansatz.

Comments:	18 pages text. Twice revised per referee/reviewer comments. Fit of CMB angular power spectrum and dark matter halo fits added
Subjects:	General Physics (physics.gen-ph)
Journal reference:	International Journal of Modern Physics D 27, No. 14, 1847018 (2018)
DOI:	10.1142/S0218271818470181
Cite as:	arXiv:1509.09288 [physics.gen-ph]
	(or arXiv:1509.09288v5 [physics.gen-ph] for this version)

Then there is another overlapping version:

[Submitted on 26 May 2016 (v1), last revised 27 Jul 2016 (this version, v3)]
End of a Dark Age?
W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein

We argue that dark matter and dark energy phenomena associated with galactic rotation curves, X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit THINGS rotation curve data rivaling modified Newtonian dynamics, ROSAT/ASCA X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling ΛCDM without non-baryonic dark matter or a cosmological constant. In the case of dark matter, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein-deSitter cosmology. Therefore, the phenomena of dark matter and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.

Comments:	This version was accepted for publication in the International Journal of Modern Physics D; revised version of an essay that won Honorable Mention in the Gravity Research Foundation 2016 Awards for Essays on Gravitation. 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1509.09288
Subjects:	General Physics (physics.gen-ph)
Journal reference:	International Journal of Modern Physics D 25(12), 1644004 (2016)
DOI:	10.1142/S0218271816440041
Cite as:	arXiv:1605.09229 [physics.gen-ph]
	(or arXiv:1605.09229v3 [physics.gen-ph] for this version)