What now about Dark Matter?

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  • #76
Buzz Bloom
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I thought the 1st modern usage of the term was by Zwicky in the 1930s.
Hi Alain:

I stand corrected.
https://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis#History_of_theory
The history of Big Bang nucleosynthesis began with the calculations of Ralph Alpher in the 1940s. Alpher published the Alpher–Bethe–Gamow paper that outlined the theory of light-element production in the early universe.

During the 1970s, there was a major puzzle in that the density of baryons as calculated by Big Bang nucleosynthesis was much less than the observed mass of the universe based on measurements of galaxy rotation curves and galaxy cluster dynamics. This puzzle was resolved in large part by postulating the existence of dark matter.​

Regards,
Buzz
 
  • #77
ohwilleke
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It doesn’t predict gravitational time dilation or the correct light deflection or the precession of Mercury or the Shapiro effect or frame dragging.
MOND isn't meant to do any of those things. It is unabashedly and has been from the start, a toy model. The reason that it is described as modifying Newtonian dynamics, rather than modifying general relativity itself, is that in weak fields at galactic scales, Newtonian gravity is an excellent approximation of general relativity. Mordehai a.k.a. Moti, Milgrom, who invented MOND was perfectly familiar with GR (and indeed basically a GR physicist) and knew that a non-toy model version of MOND that perfectly described reality would have to be a general relativistic generalization of MOND (a mathematically consistent generalization called TeVeS was devised by Bekenstein, but as it turns out, that particular generalization doesn't describe what is observed in certain respects, so it is the wrong generalization) and might deserve a new name (e.g. MORD for Modified Relativistic Dynamics).

The domain of applicability of pure, toy model MOND, is limited to weak fields in circumstances where GR is well approximated by Newtonian gravity, to the point where post-Newtonian GR effects are too small to measure, and where Newtonian gravity is used in practice by astronomers as a result because the math is much, much easier with no consequences that aren't much smaller than their observational measurement error (it turns out that lots of astronomy measurements at the galactic scale actually have pretty big error margins relative to experimental measurements in other parts of fundamental physics; the MOND acceleration constant, for example, is known only to about 1% accuracy).

But, the concept of modified gravity is that you really start with GR or quantum gravity theory that approximates GR in the classical limit, and then tweak the extremely weak field behavior of that gravitational theory in such a way that it gives rise to a transition from the effectively almost perfectly Newtonian gravitational regime to the MOND behavior gravitational regime when the gravitational field gets weaker than the critical field strength that is the single fixed parameter in MOND.

While in its domain of applicability we describe that transition point as a transition from the Newtonian regime to the MOND regime, what everyone who uses it understands is that what is called the "Newtonian regime" is really just plain vanilla GR, and that the MOND regime is simply used to determine the magnitude of the gravitational field strength at a particular location, understanding that it will deflect light at that point in the same way that a field of that strength in conventional GR would.

So, while it is called modified "Newtonian' dynamics, at local scales MOND is actually, definitionally, conventional, unmodified general relativity, which we know holds true with exceptional precision, even thought we don't know precisely how to put MOND effects into the GR equations in fields that are weaker than the cutoff acceleration value.

By analogy, at velocities much smaller than the speed of light, we neglect the effects of special relativity because they are so tiny that they aren't measurable, just as in the situations where MOND is applied, the effects of general relativity relative to Newtonian gravity are so tiny that they aren't measurable for gravitational field strengths of slightly more than the acceleration constant of MOND at which MOND effects kick in. But, just as engineers who neglect special relativistic effects when modeling aerodynamics for an airplane design don't in any way presume to be saying that special relativistic effects aren't part of the laws of Nature, astronomers who apply MOND without considering the GR effects that you mention (other than the deflection of light) don't in any way presume to be saying that gravity outside the MOND regime is actually Newtonian rather than general relativistic.

What is probably going on is that MOND arises from some sort of second order quantum gravity effect in which the strength of the second order effect gets smaller with distance at an exponentially slower rate than the first order gravitational effect described by GR and approximated by Newtonian gravity, but with the second order effect multiplied by some very small constant, such that the second order effect isn't close in magnitude to the first order effect, until you reach the MOND cutoff acceleration. So, in gravitational fields stronger than the MOND cutoff, the first order effect is much stronger than the second order effect, and in gravitational fields weaker than the MOND cutoff acceleration, the second order MOND effect is very swiftly much stronger than the first order gravitational effect described exactly by GR and approximately by Newtonian gravity, as the first order effect gets weaker with distance much more rapidly than the MOND effect does.

The one way that MOND toy models differ from each other (discussed in Milgrom's papers on the topic back in the 1980s) is in the interpolation function used to transition from the "Newtonian" (actually conventional GR) regime to the MOND regimes. Many of these interpolation functions, by design, reflect this kind of understanding of what is going on.

The bottom line of all of this is that above the MOND acceleration cutoff, MOND is understood by everyone who uses it to actually be conventional GR, despite the name. So, there is no failure of MOND at local scales.

In particular, since the gravitational field of the Sun is stronger everywhere in the solar system than the MOND acceleration constant, there are no solar system effects of MOND, which is simply exactly equal to GR in the solar system.

Dark matter particle theories likewise predict that it is indistinguishable from GR without dark matter at solar system scales with existing levels of observational precision, because the amount of dark matter in that volume of space is so small and because that dark matter is so evenly spread out within the solar system.
 
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  • #78
ohwilleke
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Perhaps. I admittedly have not followed any recent developments of MOND, having examined them and lost interest in them quite some time ago. It could be that something new has overcome previous problems.

What I have seen from MOND theories at best is capable of explaining galaxies, but fails at both cosmological scales and local scales. I have yet to see a MOND theory which is not contradicted by already existing evidence at cosmological scales and at local scales.

If you know of a MOND theory which is consistent with all currently available evidence at all scales then I would be glad for a reference.
There are modified gravity theories such as Moffat's MOG theory that works at galaxy cluster and cosmological scales. Deur's gravitational approach to understanding dark matter and dark energy phenomena also applies at galaxy cluster scales and has been applied to some cosmological phenomena. And, both of those approaches reduce to conventional GR in the strong field limit (as does TeVeS). FWIW, I call Deur's work a "gravitational approach" rather than a "modified gravity theory" because he conceives of his analysis as merely a quantum gravity generalization of GR, rather than a modification of GR, even though it makes, as any quantum gravity theory must, some predictions that differ from classical GR (e.g. in classical GR, gravitational energy is not localized, but any graviton based quantum gravity theory necessarily localizes gravitational energy), including its weak field behavior.

But, because the amount of research effect that has been available to work on gravitational approaches to dark matter phenomena has been so much smaller than for dark matter theories (there are probably only half a dozen core scientists working on it, and another dozen who have dabbled in it), and because the math involved in these theories is non-linear and much more difficult than in the lambdaCDM scenario, there are lots of matters at the cosmological scale in these approaches for which a gravitational approach description has simply not been worked out at all. So, these theories aren't proven to fail at cosmological scales, they just haven't been elaborated to the point that there are not precise predictions to compare to observation at those scales. Generally speaking, however, modified gravity theories that replicate dark matter phenomena appear to cause similar local structure (e.g. the earliest galaxy formation) and cosmological developments more generally, to develop as in lambdaCDM, but they occur sooner after the Big Bang than they do in lambdaCDM. Thus, for example, these theories, generically, tend to resolve the Impossible Early Galaxy Problem, found in lambdaCDM.

There are also lots of modified gravity theories in the general relativity subfield that are specifically designed to (and succeed in) describing dark energy phenomena without a cosmological constant (such as f(R) gravity theories) whose implications at a cosmological scale are better understood, but most of those theories aren't designed to explain dark matter phenomena or replace the CDM component of the lambdaCDM concordance model of cosmology (a.k.a. the Standard Model of Cosmology, which is terminology that I prefer to avoid to prevent confusion with the Standard Model of Particle Physics).

In the same way, lambdaCDM is model for which its own predictions have not been worked out rigorously at the galactic cluster and smaller scales. These dark matter particle models allow you to estimate what kind of dark matter halo ought to exist to explain a particular system's dynamics, but each system needs to be explained by three parameters or so, some of which are degenerate with each other, and there is no theory of mass assembly in the universe that accurately explains the values of those parameters on something other than a case by case, ad hoc, basis. In lambdaCDM that is on the "to do" list and has not been worked out yet. To the extent that lambdaCDM does make predictions, moreover, at these scales, those predictions are contradicted by the observational evidence.

The most recent contribution to the literature establishing that the nearly collisionless dark matter assumed in the lambdaCDM model is an inaccurate description of reality, from the perspective of a dark matter particle oriented theorist (as opposed to someone taking the gravitational approach), is Paolo Salucci, "The distribution of dark matter in galaxies" (November 21, 2018) (60 pages, 28 Figures ~220 refs. Invited review for The Astronomy and Astrophysics Review).

In contrast, in gravitational theories, such as toy model MOND, a particular distribution of baryonic matter in a galaxy fully and uniquely describes the dark matter phenomena which are predicted to exist in that galaxy with a single parameter that applies to every galaxy of every size. This is a truly stunning accomplishment for such a rigid theory with so little wiggle room, as illustrated in several recent papers discussed by the leading MOND investigator.
 
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  • #79
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There are modified gravity theories such as Moffat's MOG theory that works at galaxy cluster and cosmological scales. Deur's gravitational approach to understanding dark matter
Thanks, that is interesting and quite helpful!

MOND isn't meant to do any of those things.
Neither was GR, but it did it anyway. That is a large part of what makes GR so compelling and MOND not, in my mind. They both do what they were designed to do, but GR also explains many things that it was not designed to explain, completely new gravitational phenomena that were not even conceived before the theory. MOND does not.

perfectly described reality would have to be a general relativistic generalization of MOND ... So, there is no failure of MOND at local scales
I disagree completely with the final statement. Until the generalization is actually developed MOND indeed fails locally. As you noted yourself, such a generalization is necessary but not trivial and attempts so far have failed.
 
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  • #80
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Imagine Einstein would have added an additional force term to gravity to explain Mercury's perihelion precession. It is easy to find one that fixes Mercury's orbit while keeping the other orbits as they are. What would we have learned from it? Not much.
 
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  • #81
Mapping of Dark Matter in the universe shows it concentrated around massive structures and, at the quantum level, it is both a wave and a particle. Is it possible that Dark Matter is gravity, itself?
 
  • #82
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at the quantum level, it is both a wave and a particle.
No it is not - wave-particle duality is an outdated concept and is not part of modern quantum physics.

Is it possible that Dark Matter is gravity, itself?
Gravity is a curvature of spacetime, so based on the meaning of 'curvature of manifold' and 'dark matter' the answer is 'no'.
 
  • #83
No it is not - wave-particle duality is an outdated concept and is not part of modern quantum physics.



Gravity is a curvature of spacetime, so based on the meaning of 'curvature of manifold' and 'dark matter' the answer is 'no'.
Got it. Thanks.
 
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