How are dark matter, general relativity, and standard model related?

[nortonian]

In other words, can dark matter be reconciled with GR without drastically changing the idea that force is due to space-time curvature? and in the case of the standard model is there any thoughts of how the force of dark matter is transmitted via the exchange of a particle? It seems that this question would have to be considered in a unifying theory such as string theory, but I have never seen anybody's ideas about it.

 

[marcus]

In other words, can dark matter be reconciled with GR without drastically changing the idea that force is due to space-time curvature? and in the case of the standard model is there any thoughts of how the force of dark matter is transmitted via the exchange of a particle? It seems that this question would have to be considered in a unifying theory such as string theory, but I have never seen anybody's ideas about it.

Dark matter is already fully compatible with GR without any modification of GR. The basic GR equation says how matter (of whatever sort) bends spacetime geometry. That is how any type of matter asserts its gravitational effect.

The big question is: what IS dark matter? Can it be described in quantum field theory terms?
QFT is the basic language of the Standard Model. It says the world is composed of FIELDS (an electron field, a muon field, this that and the other type of quark field…) and in the humongous mother of all Lagrangians these fields are COUPLED to each other by coefficients called "coupling constants". This is how forces arise in the context of QFT.

It is probably a bit misleading to think of QFT in terms of particles, and to imagine forces operating by the exchange of particles. "Virtual particle" is something of a metaphor and Feynman diagrams serve to identify stages in a calculation. The "exchange of virtual particles" should be taken with a grain of salt.

I would say that the big question from a QFT perspective is how to add some new field or fields to the Standard Model and some new coupling constants so as to represent DM and its (presumably negligible or weak) interaction with other matter? What should be the spin and symmetries of this new field or fields? How do we extend the Standard Model, in the conventional QFT framework, so as to include a predictive representation of DM?

I doubt string research will play a role. It hasn't "gelled" into a unique predictive theory and no evidence for supersymmetry (vital to string-thinking) has been found. Physics departments in US and Canada have essentially stopped hiring string theorists to junior faculty positions presumably because those in charge think other lines of theory research (e.g. phenomenology, astroparticle, cosmology…) have better prospects. Of course they (the department heads and hiring committees) could be wrong. I could be wrong, in my skepticism. We'll just have to see.

Either way, the quantum field theory Standard Model is likely going to be EXTENDED over the next 5 or 10 years so as to include a DM field. And this will be described by the usual metaphor, as a DM "particle".

 

[nortonian]

Dark matter is already fully compatible with GR without any modification of GR. The basic GR equation says how matter (of whatever sort) bends spacetime geometry. That is how any type of matter asserts its gravitational effect.

The big question is: what IS dark matter?

It seems you are saying that dark matter has an effect on spacetime curvature but it is different than that of baryonic matter. Since astronomers are looking for dark matter in the galaxy disk they are assuming it has a local effect unlike baryonic matter most of which is located at galaxy center. So even if the Einstein tensor is the same the stress-energy tensor would have to change drastically. That would be a considerable modification. In fact that's what Einstein was trying to do for the last 30 years of his life: modify the equations so that they also govern local forces and principally electromagnetism.

It is probably a bit misleading to think of QFT in terms of particles, and to imagine forces operating by the exchange of particles. "Virtual particle" is something of a metaphor and Feynman diagrams serve to identify stages in a calculation. The "exchange of virtual particles" should be taken with a grain of salt.

Thanks for the insight on QFT. It is hard to know whose "explanations" are closest to the actual theory.

I would say that the big question from a QFT perspective is how to add some new field or fields to the Standard Model and some new coupling constants so as to represent DM and its (presumably negligible or weak) interaction with other matter? What should be the spin and symmetries of this new field or fields? How do we extend the Standard Model, in the conventional QFT framework, so as to include a predictive representation of DM?

As far as extending QFT I can't imagine how would you even begin to do that when dark matter doesn't reveal itself as a time evolution except in the millions of years for galaxies, but all other fields are observed in microseconds. Also I assume that such an extension would have to be based on particle accelerator research that is applied to the scale of the universe. A pretty tall order.

 

[Naty1]

Also took me quite a while to stumble through similar questions.

wikipedia

The Standard Model [SM}falls short of being a complete theory of fundamental interactions because it does not incorporate the physics of dark energy nor of the full theory of gravitation as described by general relativity. The theory does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology.

So the SM utilizes relativistic [high speed] quantum field theory...quantum theory in flat, Minkowski, spacetime. Nobody has figured out yet how to incorporate the curved spacetime of GR, but many times gravity is so weak that particle interactions are very accurately modeled without gravity.

It is also helpful to realize that the SM consists of a bunch of theories patched together utilizing observations as well; it does not miraculously pop of of a group of first principles...so it has empirical, measured inputs, like the mass and charge of the electron. Big progress was made in the 1960's when the weak force of radioactive decay and the electromagnetic force were found to have common mathematical origins,now call electroweak theory, the Higgs field was theorized to impart mass to particles, and the quark model was proposed by different teams of scientists.

Maybe quantum gravity will evolve to incorporate gravity in the SM.

 

[nortonian]

Also took me quite a while to stumble through similar questions.

It is also helpful to realize that the SM consists of a bunch of theories patched together utilizing observations as well; it does not miraculously pop of of a group of first principles...so it has empirical, measured inputs, like the mass and charge of the electron. Big progress was made in the 1960's when the weak force of radioactive decay and the electromagnetic force were found to have common mathematical origins,now call electroweak theory, the Higgs field was theorized to impart mass to particles, and the quark model was proposed by different teams of scientists.

Maybe quantum gravity will evolve to incorporate gravity in the SM.

As far as I can tell dark matter doesn't fit in with any theory at all, not even Newtonian theory which is based on a central force field. It seems to be an exotic, stand-alone material that is hypothesized to have exactly the properties (and location) needed to account for the observed motions of stars. Although it supposedly has mass the concept of mass was developed from different types of observations such as impenetrability and inertia.

 

[marcus]

As far as I can tell dark matter doesn't fit in with any theory at all,...

I think that is wrong. It already fits in with GR, as I explained--and there are various ways DM could fit in with some modest extension of Standard Model. We simply do not know which will turn out to be right.

If you are really interested in learning something about what DM could turn out to be, then you should read this paper by Marco Drewes:
http://arxiv.org/abs/arXiv:1303.6912
The Phenomenology of Right Handed Neutrinos
Marco Drewes
(Submitted on 27 Mar 2013)
Neutrinos are the only particles in the Standard Model of particle physics that have only been observed with left handed chirality to date. If right handed neutrinos exist, they could be responsible for several phenomena that have no explanation within the Standard Model, including neutrino oscillations, the baryon asymmetry of the universe, dark matter and dark radiation. After a pedagogical introduction, we review recent progress in the phenomenology of right handed neutrinos. We in particular discuss the mass ranges suggested by hints for neutrino oscillation anomalies and dark radiation (eV), sterile neutrino dark matter scenarios (keV) and experimentally testable theories of baryogenesis (GeV to TeV). We summarize constraints from theoretical considerations, laboratory experiments, astrophysics and cosmology for each of these.
Comments: Invited review for the International Journal of Modern Physics E.

You see, Norton, this is ONE thing DM could turn out to be. It has a good chance of being the right one, I think. There is a GAP in the Standard Model catalog of particles. All the other particles except neutrinos exist in two versions (called right and left handed). If you look at the layout of basic particles you see a row missing where the righthand-type neutrinos should be, you could almost PREDICT that they should turn up. But they have not been seen yet.

Neutrinos are very hard to detect because they do not have charge and they do not interact with light and they pass through most matter with hardly any interacting or colliding.

the article by Marco Drewes explains how if this kind of neutrino were found it would solve several puzzles including about Dark Matter. But not just that. Several other puzzles as well.

It is a fairly simple article to read, written as a review (current status report) for wider audience. Not just for specialists.

Drewes is a worldclass expert on this, and he has also coauthored with Shaposhnikov who I consider one of the great living physicists. I would urge anyone who is really interested in DM and the Standard Model to have a look at least at the Introduction (at the beginning) and the Conclusions (at the end) and anything else you can understand---and take it seriously.

We don't know for certain that the righthand neutrino is the correct explanation, but it would fit in just fine with both GR and the Standard Model, and it has a reasonable chance of turning out to be the correct solution.

 

[Ibix]

Apologies if I'm mis-judging this, OP, but you seem to me to have mis-conceptions about gravity. Your posts read as if you think that the Newtonian model of the galaxy is of all the stars orbitting in a single force field of the form F=GMm/r², where r is the distance of a star (of mass m) from the centre of the galaxy (of total mass M).

If not, I am mis-reading you. If so, your understanding is not correct. If it were, the Earth would orbit the galactic centre, not the Sun. In fact, the orbits of stars around the galactic centre depend on the detail of the distribution of mass in the galaxy. The problem is that the orbits do not match our estimate of the visible mass distribution.

That leaves us with three possibilities:
1. Our estimate of the masses of stars is off.
2. Our model of gravity is off.
3. There's stuff out there we can't see.

Every test we can think of for 1 and 2 say we are right (Einstein vs Newton doesn't make much difference in this context). That leaves 3, and we've seen hints that it is right above and beyond process of elimination. In the context you are talking about, all dark matter does is adjust the mass distribution in the galaxy. Its gravitational effect is indistinguishable from normal matter; it's just that we can't see it.

 

[Naty1]

As far as I can tell dark matter doesn't fit in with any theory at all,...

As Marcus noted it does seem to [sort of] fit in at least one place, but considering we knew almost nothing about 95% of the mass and energy in the universe until rather recently, it must have been a shock to people in related fields when those were discovered. I would hope if we knew as much as we think we do, theoretical considerations would have led us to DM and DE...That's how we were pointed to the Higgs, for example. It is often hard to see something when you don't know what you are looking for.


Yet discoveries such as dark matter often start out 'not fitting' because when stuff is new, discoveries incomplete and tentative, especially something hard to detect and perhaps even difficult to envision, then it usually takes time to find if and where it fits.

That's one of the things I was getting at when I posted:

Big progress was made in the 1960's when the weak force of radioactive decay and the electromagnetic force were found to have common mathematical origins, now call electroweak theory, the Higgs field was theorized to impart mass to particles, and the quark model was proposed by different teams of scientists.

I very much doubt those discoveries were part of a carefully planned, organized and coordinated overall scientific effort; much more likely three groups of really smart people working in separate isolated teams on something in which they shared a deep interest.

And Higgs was just confirmed...when, last year, at CERN ? So with luck you will be around as news emerges of discoveries regarding more detailed characteristics of dark matter.

Meantime, there are good insights posted here...linked from another discussion in these forums...

http://blogs.discovermagazine.com/co...matter-exists/

 

[nortonian]

Apologies if I'm mis-judging this, OP, but you seem to me to have mis-conceptions about gravity. Your posts read as if you think that the Newtonian model of the galaxy is of all the stars orbitting in a single force field of the form F=GMm/r², where r is the distance of a star (of mass m) from the centre of the galaxy (of total mass M).

If not, I am mis-reading you.

Not a single force field, but whatever force field has the strongest local influence. All particles have a 1/r^2 gravitational field whether atom, star, or black hole so if dark matter is a type of particle with mass why doesn't it gradually coalesce into non-uniform clumping?

Every test we can think of for 1 and 2 say we are right (Einstein vs Newton doesn't make much difference in this context). That leaves 3, and we've seen hints that it is right above and beyond process of elimination. In the context you are talking about, all dark matter does is adjust the mass distribution in the galaxy. Its gravitational effect is indistinguishable from normal matter; it's just that we can't see it.

My purpose in starting this thread was to look at inconsistencies in the hypothetical properties of DM with respect to the classical model of ordinary matter. You may call this an outdated approach, but it has the advantage that it can be visualized. In that sense it is not true to say that the only difference from normal matter is that we can't see it. Because there are other differences why do we call it matter when its primary purpose is to "adjust the mass distribution in the galaxy" and does not have the other more familiar properties of matter? Why can't we call it a force or a space-time geometry instead?

 

[nortonian]

As Marcus noted it does seem to [sort of] fit in at least one place, but considering we knew almost nothing about 95% of the mass and energy in the universe until rather recently, it must have been a shock to people in related fields when those were discovered. I would hope if we knew as much as we think we do, theoretical considerations would have led us to DM and DE...That's how we were pointed to the Higgs, for example. It is often hard to see something when you don't know what you are looking for.

I am trying to grasp the concept of dark matter in a classical sense. Although the SM began by association with classical models I am aware that at present in nearly all research classical concepts have been replaced by mathematical concepts developed over many years. The paper cited by Marcus is a case in point. I respect that viewpoint and am not passing judgment on it, but I wanted to see how DM holds up under classical analysis, whether relativistic or Newtonian. Is there any objection to using a classical approach? After all I believe we are using classical methods to try to detect it in space.

Meantime, there are good insights posted here...linked from another discussion in these forums...

http://blogs.discovermagazine.com/co...matter-exists/

This link no longer works.

 

[Chalnoth]

I am trying to grasp the concept of dark matter in a classical sense. Although the SM began by association with classical models I am aware that at present in nearly all research classical concepts have been replaced by mathematical concepts developed over many years. The paper cited by Marcus is a case in point. I respect that viewpoint and am not passing judgment on it, but I wanted to see how DM holds up under classical analysis, whether relativistic or Newtonian. Is there any objection to using a classical approach? After all I believe we are using classical methods to try to detect it in space.

What are you talking about? Since Newton, physics has been mathematical at its core.

As for dark matter, while there have been some people who have attempted to explain the observations by using a modification of gravity instead of dark matter, those attempts have, for the most part, failed. Currently the leading candidate is a weakly-interacting massive particle. This is basically believed to be like a neutrino but with a larger mass (neutrinos are too light and produced with too high of energies in too small of an abundance). For the most part, no modification of General Relativity to account for dark matter is considered.

 

[Naty1]

nortonian..in your second post:

As far as extending QFT I can't imagine how would you even begin to do that when dark matter doesn't reveal itself as a time evolution except in the millions of years for galaxies, but all other fields are observed in microseconds.

What do you mean?? Are you aware dark matter presumably has been around as long as normal matter? Dark matter has almost certainly played a significant role in galaxy formation.


From a prior discussion in these forums:
Chalnoth:

In the early universe, normal matter and dark matter tended to attract one another, so that an overabundance of dark matter generally also coincides with an overabundance of normal matter.

The normal matter, however, experiences friction, and so collapses much more than the dark matter, which experiences no friction. So it's not so much that dark matter collects around the edges of galaxies, but that galaxies form in the centers of large blobs of dark matter.

Now, it isn't quite as simple as this, because when stars start to form, things tend to get violent, and a low-mass overdensity will blow out most of the matter shortly after the first stars form, leaving a galaxy with almost nothing but dark matter.